# The Constructal Law of Flow Systems

Guest Post by Willis Eschenbach

One of the most fundamental and far-reaching discoveries in modern thermodynamics is the Constructal Law (see the wiki entry as well). It was first formulated by Adrian Bejan in 1996. In one of his descriptions, the Constructal Law is:

For a finite-size (flow) system to persist in time (to live), its configuration must evolve such that it provides easier access to the imposed currents that flow through it.

Figure 1. An example of the Constructal Law processes at work in a river system. Formation of meanders, followed by cutting through a meander to form an oxbow lake. Image Source.

The Constructal Law has been described as being as important as the first two Laws of Thermodynamics, but most people have never heard of it. What does the Constructal Law mean in plain English, and what does it have to do with the climate?

Here is a different statement (pdf) of the Constructal Law, again from Bejan:

In 1996, the constructal law was formulated and proposed to expand thermodynamics in a fundamental way.

First was the proposal to recognize that there is a universal phenomenon not covered by the first law and the second law. That phenomenon is the generation of configuration, or the generation of ‘design’ in nature.

All thermodynamic systems in nature are flow systems (i.e. live, non-equilibrium systems), and they all have configuration. If they do not have it, then they acquire it, in time. The generation of configuration is ubiquitous, like other phenomena covered by other ‘laws’ in physics. Biological systems are configured. Geophysical systems are configured. Engineering and societal systems are configured. The configuration phenomenon unites the animate with the inanimate. All the other phenomena of physics (i.e. of ‘everything’) have this unifying power. Falling rocks, like falling animals, have weight, conserve energy, generate entropy, etc.

Second was the statement that this universal phenomenon should be covered by the constructal law. This law accounts for a natural tendency in time (from existing flow configurations, to easier flowing configurations). This tendency is distinct from the natural tendency summarized as the second law.

Again not necessarily the clearest statement, but the general idea of the Constructal Law is that flow systems continually evolve, within the physical constraints of the particular system, in order to maximize some variable(s).

A meandering river in bottomland is a good physical example to understand what this means. In the case of a river, what is being maximized by the flow system is the length of the river. However, this ideal condition is never achieved. Instead, the river length oscillates above and below a certain value.

As shown in Fig. 1, in an “S” shaped river, the moving water erodes the outside of the bends and deposits silt on the inside of the bends. Of course, this inevitably makes the river longer and longer. But when the river does this for a while, it gets too stretched out for the land to bear. At some point, the river cuts through and leaves an island and what will become an oxbow lake.

That leaves the river shorter. Again the lengthening process continues, until the river cuts through some other bend and shortens again. And as a result, the length of the river oscillates around some fixed value. It is constantly evolving to maximize the length, an ideal which it never attains.

Now, here’s the point of this whole example. Suppose I didn’t know about this active, evolutionary, homeostatic characteristic of rivers. If someone asked me if a river could be shortened, I’d say “Sure. Just cut through a meander.”. And if I cut through the bend I could physically measure the river length and prove that indeed, the river was shorter.

But would that really make the river shorter?

Of course not. Soon the relentless forces of flow would once again increase the length of the river until the next cutoff forms another oxbow lake, and the cycle repeats.

Net effect of my cut on the length of the river? None. The length of the river continues to oscillate around the same fixed value.

The key to understanding flow systems is that they are always “running as fast as they can”. They are not just idling along. They are not at some random speed. They are constantly evolving to maximize something. The Constructal Law ensures that they are up against the stops, so to speak, always going flat out.

What does all of this have to do with climate? The Earth’s climate is a huge flow system. It circulates air and water from the tropics to the poles and back. As a result the climate, like the river, is subject to the Constructal Law. This means that climate is constantly evolving to maximize something. Climate, like the river, is also “running as fast as it can”.

What does the climate flow system maximize? Because it is a heat engine (converting sunlight into the physical work of the planetary circulation), Bejan says (pdf) that it is doing a dual maximization. It maximizes the sum of the work done driving the planetary circulation, and the heat rejected back to space at the cold end of the heat engine. Again in Bejan’s words:

The earth surface model with natural convection loops allows us to estimate several quantities that characterize the global performance of atmospheric and oceanic circulation. We pursue this from the constructal point of view, which is that the circulation itself represents a flow geometry that is the result of the maximization of global performance subject to global constraints.

The first quantity is the mechanical power that could be generated by a power plant operating between Th and Tl, and driven by the heat input q. The power output (w) is dissipated by friction in fluid flow (a fluid brake system), and added fully to the heat current (qL) that the power plant rejects to Tl.

where Th and Tl are the temperatures of the hot and cold ends of the system. The system is maximizing the sum of work done and heat rejected.

There is a most fascinating interplay between those two. When the speed of the planetary circulation is low, so are the turbulent losses. So as speed increases, up to a certain point the sum of work done (circulation speed) and heat rejected is also increasing.

But as the speed increases further, the turbulence rapidly starts to interfere with the circulation. Soon, a condition exists where further speed increases actually decrease the total of work done and heat rejected. That is the point at which the system will naturally run. This is why nature has been described in the past as running at “the edge of turbulence”.

What does that mean for understanding the climate? This is a new area of scientific investigation. So I don’t know what all of that means, there’s lots of ramifications, some of which I may discuss in a future post. However, one thing I am sure of.

If we want to understand the climate, or to model the climate, we have to explicitly take the Constructal Law into account.

We are not modeling a simple system with some linear function relating forcing and response. That kind of simplistic understanding and modeling is not valid in the type of system where, for example, cutting a river shorter doesn’t make it any shorter. We are modeling a dynamic, evolving system which may not be affected by a given forcing. The modelers claim (falsely, but we’ll let that be) that their models are based on “physical principles”.

However, they have left one central, vital, physical principle out of the mix, the Construcal Law. And at the end of the day that means that all of their modelling is for naught. Sure, they can tweak the model so that the output resembles the actual climate. But the actual system does not change over time in a random way. It is not driven here and there by forcing fluctuations. It changes in accordance with the Constructal Law. The future evolution of the climate, what Bejan calls the “generation of configuration”, is ruled by the Constructal Law. It cannot be understood without it.

PS – For those that think that the Constructal Law is some crackpot theory, it is not. Bejan is one of the 100 most cited engineering authors of our time, and the results of the Constructal Law have been verified in a host of disciplines. It is indeed a new fundamental law of thermodynamics, one which we cannot ignore.

## 214 thoughts on “The Constructal Law of Flow Systems”

1. jack mosevich says:

Mark Twain proposed a version of the Costructal law:
The Mississippi between Cairo and New Orleans was twelve hundred and fifteen miles long one hundred and seventy-six years ago. It was eleven hundred and eighty after the cut-off of 1722. It was one thousand and forty after the American Bend cut-off. It has lost sixty-seven miles since. Consequently its length is only nine hundred and seventy-three miles at present.
Now, if I wanted to be one of those ponderous scientific people, and `let on’ to prove what had occurred in the remote past by what had occurred in a given time in the recent past, or what will occur in the far future by what has occurred in late years, what an opportunity is here! Geology never had such a chance, nor such exact data to argue from! Nor `development of species’, either! Glacial epochs are great things, but they are vague–vague. Please observe. In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. This is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upward of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.

2. George E. Smith says:

Very interesting post willis.
I can see an immediate area of application. Ocean currents are well known to meander just as if they were actual rivers cutting through land; so I suppose the Constructal law would apply to them too.
This is important when it comes to makign temperature measurements from surface waters; as was the historic case for the 70% of the earth surface that is ocean.
Because of meanders, a survey ship could go back to the exact same geographical co-ordinates; and end up in a totally different water structure from what was there six month ago.
So all of that hokey surface water proxies for lower tropospeheric Temperature, that is the bulk of the 150 years of global temperature data, must have a variance due to the constructal law, and ocean current meanders.
In Jan 2001 Dr John Christy et al also reported that the water surface Temperatures, and the lower troposphere temperatures were not the same; and were not correlated; but the standard assumption was that the water bucket reading was as good as meauring the air temperature.
Why would anyone expect them to be the same or correlated, when the air over Hawaii, could end up over California next week; so air and water don’t remain in thermal contact long enough to equilibrate.
So willis; what do YOU know about ocean current meanders and the Constructal law.

3. Dave Dardinger says:

How does the Constructal Law differ from maximizing entropy?

4. James Macdonald says:

As a meteorologist I can readily see this happening to the Jet stream. It oscillates between almost straight line flow and one of deep troughs and ridges, winding up as a cutoff low. Then the straighter line flow resumes. Almost identical to a river.
I am one of 15 scientists—climate realists- in the Hartford, CT area. Prof. Larry Gould is one of us as well as Art Horn.

5. J.Hansford says:

Constructal Law would be describing equilibrium in a dynamic system then…..?

6. etudiant says:

Wonderful. A major law that makes eminent sense hiding in plain sight.
Does make one worry what else we might be missing.
Meanwhile, it would seem that law should be applicable to the overall atmospheric flow system.
Unfortunately, the law gives zero guidance as to the configuration that is adopted and is even silent as to the claim that the system seeks to maximize the work done and the heat rejected by the atmosphere, even though Bejan makes that claim. Still, it gives another way to drive/evaluate the models, which is a real step forward. We may look for interesting new insights in the near future.

7. Curious George says:

Could you please formulate this “law” a little more mathematically? Unless you do, I propose an equivalent formulation of (a possilbly diferent) Constructal law:
The good should be rewarded, the bad should be punished.

8. Rhoda R says:

“It is indeed a new fundamental law of thermodynamics, one which we cannot ignore. ” I love it – that we are still finding fundamental laws of anything is great.

9. Gary Palmgren says:

I have an alternate description that comes directly from the 2nd law. The increase in entropy in any closed system can always be seen as the conversion of potential energy to low level uniform heat. Even temperature differences can be rigorously proven to be potential energy. The second law never allows any local uniform temperature to be turned back into local potential energy.
A dynamical system will evolve to maximize the generation of entropy at every location. In the river model we have two forms of potential energy that can be used to do work. One is the pressure head or total elevation from source to basin. The other is the kinetic energy of the moving water. (Yes kinetic energy can be looked at as a form of potential energy as the energy of motion can be used to do work.) At every location the system will try to minimize both. A short river will have the least amount of friction so the kinetic energy of the flowing water will be maximized. Erosion will occur rapidly and the meanders will increase. Friction increases increasing the generation of entropy.
When the meanders get to big, the friction is too high, the water backs up, and the pressure head increases. An increased pressure head results in the water crossing the meander to make a shorter path. Thus the river length oscillates around some constant as described by Willis Eschenbach.
I may be combining the structural law with the maximization of entropy, but I suspect they are both saying the same thing.

10. Willis:
“That leaves the river shorter. Again the lengthening process continues, until the river cuts through some other bend and shortens again. And as a result, the length of the river oscillates around some fixed value. It is constantly evolving to maximize the length, an ideal which it never attains.”
That’s not really what I’m seeing. I’m seeing a constant attempt to MINIMIZE the length of the river, which fits in with thermodynamics quite nicely. The original elongation was an aberation. Once in the lowest energy state possible between two points (straight line) there’s absolutely nothing to cause it to create additional corners.
The “generation of configuration” in this case is the lowest-energy path between two points. Once it has the optimal configuration there’s no reason for it to change.
I think your use of this example with climate isn’t really very useful. As conditions change, the optimal configuration may change, and the climate systems may drift in that direction, but that relies on variables changing, not an intrinsic part of the system to always seek change.

11. Willis Eschenbach says:

Curious George says:
November 15, 2010 at 6:19 pm

Could you please formulate this “law” a little more mathematically? …

Sure … if you can first give me a mathematical formulation of the Second Law of Thermodynamics.
The problem is that both these Laws only give the direction of the change. The Second Law says only says that net heat only flows from warm to cold. It doesn’t give numbers.
Similarly, the Constructal Law says that systems evolve to give easier access to the currents. And like the Second Law, it doesn’t give numbers.
However, there are a whole host of mathematical results made possible by the Constructal Law. See the references given in the head post for examples.

12. Alex Heyworth says:

As an interesting aside, the ratio of a river’s length to the length of a straight line between its source and mouth is approximately Pi.

13. Pamela Gray says:

Every single Wallowa County river fishing enthusiast understands this. I saw this law in action this past summer. That it can be applied to weather makes perfect sense. We are about to be inundated with an over the top windy pressure gradient in and around the NE portion of the Washington/Oregon state line. So I get to watch this law in action. You can see it in pressure gradients. Way cool.
The jet stream is another place to see this law in action.

14. Willis Eschenbach says:

Dave Dardinger says:
November 15, 2010 at 5:57 pm

How does the Constructal Law differ from maximizing entropy?

Thanks for the question, Dave. Bejan goes over this in great detail here (pdf).

15. Alex Heyworth says:

PS, a reference for Pi being the ratio length/source to mouth distance:
Stølum, H.-H. “River Meandering as a Self-Organization Process.” Science 271, 1710-1713, 1996.

16. John Day says:

@CuriousGeorge:
> Could you please formulate this “law” a little more mathematically?
Ditto. I also can’t seem to get my head around this, sounds more like philosophy or hand-waving. It needs some theorems that can be tested or implemented constructively.
All bun, no meat.

17. Carl Chapman says:

Wouldn’t that imply that the earth’s climate would exhibit strong negative feedback?
My guess is that the feedback reduces temperature changes by forcings such as CO2 to 1/3. The IPCCs guess is that feedback increases changes to 3 times.
No warming since 1998, while CO2 goes up and up, makes the 3 times theory extremely hard to believe.

18. AusieDan says:

Hi Willis
Is this anything different from chaos theory?
Hurst wrote a paper on his 847 year study of the River Nile in 1951.
He was interested in river heights as he was planning the River Dam Project.
The language used was quite different but there seems to be some similarity.
I hope to contact you soon with a climate paper using this concept.
Regards Dan

19. Bruce says:

Meanwhile in CRU headquarters: “Ah these pesky models would work so much better if the Earth just would stop rotating. Hmm. Hey, I have an idea….”

20. Robert of Ottawa says:

A river “running as fast as it can” can be restated as losing energy as rapidly as possible; in the case of a river flow, this energy loss is restrained by the river sides and bottom. The maximum rate of energy loss is at a waterfall, such as the Rideau Falls here in Ottawa. http://www.google.ca/imgres?imgurl=http://farm4.static.flickr.com/3108/2918568397_8b972f3a76.jpg&imgrefurl=http://www.flickr.com/photos/41455313%40N08/galleries/72157622637220789&h=405&w=500&sz=104&tbnid=B7mGNPpDV5ItXM:&tbnh=105&tbnw=130&prev=/images%3Fq%3Drideau%2Bfalls%2Bottawa&zoom=1&q=rideau+falls+ottawa&hl=en&usg=__6fIaQPpQRHkyRjK6dT_mCVCm-bo=&sa=X&ei=OurhTIGmFYnLnAerq93-Dw&ved=0CCoQ9QEwAg
A flow cannot lose energy at a greater rate than this. So, interestingly this is a case where the increase in entropy actually has a maximum rate.

21. Jim says:

I’m wondering if the curves are carved during periods of high flow. The river breaches a bank and the turbulent waters carve a new curve, following generally the land. Then during periods of low flow, the river straightens itself out again. So it would be an interaction of water volume, the shape of the bank, and the lie of the land.

22. jimmi says:

This looks like one of those observations that are qualitative rather than quantitative, a bit like Le Chatelier’s Principle (A system when perturbed reacts to minimise the perturbation). It may even be a variant of Le Chatelier.
I think you can express the 2nd law mathematically if you start from statistical thermodynamics.

23. guidoLaMoto says:

This is really just another way of stating the Law of Survival of the Fittest: things survive when they don’t do anything that would make themselves go extinct. The Constructionist Law would only seem to hold for chaotic systems while they are exhibiting cyclicity or pseudocyclicity. The problem is, chaotic systems can reach bifurcation points where they take off in unexpected directions. We Warming Skeptics cannot necessarily take heart in this Law. Remember that the Amazon once flowed east to west.

24. Dave Springer says:

The path of least resistance is a very basic concept but not fundamental thermodynamic law as it’s derived from the first three.
Constructal law, at least as described by wiki, gets a little weird when it starts talking about nature as a designer. Basically it’s saying nature keeps improving on means of raising entropy. Not just following paths of least resistance but rather designing paths of least resistance. In that view we can make an argument that humans are an improved way of getting the low entropy in fossil fuels into a higher entropy configuration.
Let’s just hope nature didn’t design atom bombs for that purpose too.

25. David L. Hagen says:

Bejan published a very useful book:
Shape and Structure, from Engineering to Nature. Cambridge University Press, 2000, ISBN 0-521079388 2
Recently: Design with Constructal Theory
Ferenc Miskolczi has applied entropy maximization in his climate formulations.
Greenhouse effect in semi-transparent planetary atmospheres

We believe that the β parameter is governed by the maximum entropy principle, the system tries to convert as much SW radiation to LW radiation as possible, while obeying the 2OLR/(3 f ) = F0 + P0 condition. The cloud altitude, where the clear-sky A
OLR = OLR = ED depends only on the SW characteristics of the system (surface and cloud albedo, SW solar input) and alone, is a very important climate parameter.

26. Willis Eschenbach says:

AusieDan says:
November 15, 2010 at 7:11 pm

Hi Willis
Is this anything different from chaos theory?
Hurst wrote a paper on his 847 year study of the River Nile in 1951.
He was interested in river heights as he was planning the River Dam Project.
The language used was quite different but there seems to be some similarity.
I hope to contact you soon with a climate paper using this concept.
Regards Dan

The Constructal Law is different and distinct from both chaos theory and Hurst’s work on long-term persistance. Let me know how your paper goes.

27. Grey Lensman says:

Simple statement of the law
Symmetry is, Non symmetry works.
Thats why it is bad JU Ju to canalise and straighten rivers. That causes the flood disasters.

28. Charles Higley says:

Wow! That is so cool!!!
Do not forget that the floods that occur carve out the various flood plains for the 10, 50, 100, 500, and 1000-year floods, helping the system dig out the next big bend.

29. Willis Eschenbach says:

John Day says:
November 15, 2010 at 7:06 pm

@CuriousGeorge:
> Could you please formulate this “law” a little more mathematically?
Ditto. I also can’t seem to get my head around this, sounds more like philosophy or hand-waving. It needs some theorems that can be tested or implemented constructively.
All bun, no meat.

In that case the Second Law of Thermodynamics is also “all bun, no meat”. It contains no more math than the Constructal Law.
In any case, here’s enough math and practical applications to give you a headache …

30. Willis,
The Second Law is quite quantitative (and falsifiable). It says, in one form, that entropy can’t decrease. Now entropy is a well-defined quantity, derived from other measureable quantities.
It’s true that it is somewhat unusual in being one-sided – it says entropy can’t decrease but makes no prediction about how much increase. But the statement of no decrease is precise.
The Constructal Law seems to lack that precision. How would you falsify it?

31. Willis Eschenbach says:

guidoLaMoto says:
November 15, 2010 at 7:28 pm

This is really just another way of stating the Law of Survival of the Fittest: things survive when they don’t do anything that would make themselves go extinct. The Constructionist Law would only seem to hold for chaotic systems while they are exhibiting cyclicity or pseudocyclicity.

No, no, and no. Please, folks. I have given you good references to a host of both very general and very detailed discussions of the Constructal Law. Read them first before you decide what the Constructal Law is and isn’t.
Bejan didn’t get to be one of the top cited scientific authors on the planet by writing foolishness, by being “all bun, no meat”, or by “handwaving”. C’mon, do your homework before uncapping your electronic pens …

32. James Sexton says:

Huh? I thought this particular line of thought fairly well understood. Maybe its because I’m old enough to have witnessed the making of an elbow lake, and “islands” that are no longer surrounded by water. If I live long enough, I’ll see this occur again. I hope not, the “Big Island” holds a special place in my heart. A place where the Neosho splits and then rejoins. Isolating ~ 10 sq. miles. One part of the river is lively, the other, dying. I digress.
Equilibrium is always sought by nature, yet never attained. There is always a symmetrical ebb and flow.(It isn’t always obvious.) Movement of water expresses energy.
Willis, I thank you. I hadn’t realized this thought needed to be brought to light.
There is one point, though, I’m unsure of.
“The Constructal Law ensures that they are up against the stops, so to speak, always going flat out.” (I believe this properly paraphrases the law.)
It seems to me, (and I believe this is what many warmists hang their hat on) is that when unnaturally altered, nature seems to have an urgency to correct, or seek a balance. Mind you, it is simply a judgment based on observations that may be tinted, yet, it seems that way to me. Of course, the door swings both ways.
Again, Willis,
thanks.
James

33. Grey Lensman says:

Has Willis enabled me to define energy?
I think he has!
Energy is the evolution of time and space.
Can any maths wizzes get their heads around that and write a formula.
It ties in with all of the above

34. If you look at the surges in the atmospheric circulation caused by the interactions of the 18.6 year period of lunar tidal variations, as being similar to the erosion caused by periods of increased flow rate in spring or monsoonal periods. Why would this effect not be understandable as the driver of the positions of the jet streams?
Above is a compilation of threads where lunar declinational tides in the atmosphere are discussed as to applicable uses in increasing the validity of long range forecasting methods. On the site are daily forecast maps with a lead time now of 35 months, still seem to be working ok.

35. Greg Cavanagh says:

I get the impression that any fluid flow through any other medius acts pretty much the same way every time. Water through earth, jet streams, ocean currents, hot air rising through cool air.
It appears to be a fundamental of fluid mechanics, as applied to any fluid.

36. Thanks Willis. This goes a long long way in explaining what a lot of geology is all about. I can remember being a GSA and AAPG meetings in the 80’s trying to convince these modelers they were on the wrong track. I was not alone either. Thanks too to all the fine comments and suggestions from the other commentators.

37. Steve Koch says:

Willis,
Great post about a fundamental concept that is intuitively obvious once it is stated. It applies to so many different things, not just energy. You can see it in roads or electricity or neighborhoods or politics or human relationships or football or investing or on and on.

38. Barbee says:

If a society could contain lava flows in this manner it may actually save lives.

39. Grey Lensman says:

Willis is getting frustrated with the hand waving. Dont blame him. Come on guys, put thinking caps on, this makes real sense. I have even quantified it for you. Now you can ascertain values and appoint symbols and get calculating. My logic even defines entropy.
This will only be resolved by discussion not hand waving.
In space, the earth can be considered a closed system in balance but what are the total inputs and total outputs to achieve that balance and more importantly, how.

40. Michael D Smith says:

Rivers oscillate to balance the flow rate with the sediment load. Rivers can be direct and straight when the load to move is more than the capability of the flow rate to do work. This is seen in straight, deep ravines where high flows have a high erosion impact. In high flow situations, more sediment is carried, thereby carving away new material, which falls into the river whenever sediment is left higher than the angle of repose. In low flow, sediment is carried at a much lower rate, with light materials being moved downstream. Meandering rivers have a load that is lower, usually very lightweight silt and organic matter. The river balances this by producing a lower slope, reducing the work done per unit length. The only way to reduce slope is to meander producing a longer distance between inlet and outlet. This can be seen readily in the difference between the Missouri river, which has a high slope (and a rocky bottom), and the Lower Mississippi river, which has a very low slope, lightweight load, and huge meanders. Both effects can be seen in braided rivers, where the sediment load is fairly high, with a gravel bottom. You’ll get straight areas that can carry a heavy load, but if the velocity increases too much, stones are carried downstream and deposit in deltas a few meters away. This lowers the speed by widening the flow, smaller particles and sand will deposit, and this backs up until the slope is too small. Another channel will be carved through this delta and the rocks will be moved further downstream as a result, forming a new delta that is soon also carried away. Here’s an example: http://www.teara.govt.nz/files/p18195gns.jpg
So in a river, the equilibrium that is never reached is getting the slope and sediment load to match the power delivered by the water flow.

41. Jim says:
November 15, 2010 at 7:24 pm

I’m wondering if the curves are carved during periods of high flow. The river breaches a bank and the turbulent waters carve a new curve, following generally the land. Then during periods of low flow, the river straightens itself out again. So it would be an interaction of water volume, the shape of the bank, and the lie of the land.

During periods of low flow, the water isn’t moving fast enough to rearrange the banks.
A river with a steep vertical gradient tends to erode downward and the river stays stright or follows some guide, like a fault line. (Their rocks are often easy to erode, hence they’ll capture a river.) When a river has a very shallow gradient, then the forces to erode downward no longer exist and erosion acts on the river banks.
One interesting effect is if a meandering river is uplifted and the vertical gradient increases. Then an “incised meander” is formed, sometimes with a deep canyon.
http://en.wikipedia.org/wiki/Meander seems pretty decent.
Apparently meanders can have a climatic signature,
http://www.sciencemag.org/cgi/content/abstract/327/5972/1497 says:

Climate controls landscape evolution, but quantitative signatures of climatic drivers have yet to be found in topography on a broad scale. Here we describe how a topographic signature of typhoon rainfall is recorded in the meandering of incising mountain rivers in the western North Pacific. Spatially averaged river sinuosity generated from digital elevation data peaks in the typhoon-dominated subtropics, where extreme rainfall and flood events are common, and decreases toward the equatorial tropics and mid-latitudes, where such extremes are rare. Once climatic trends are removed, the primary control on sinuosity is rock weakness. Our results indicate that the weakness of bedrock channel walls and their weakening by heavy rainfall together modulate rates of meander propagation and sinuosity development in incising rivers.

42. Grey Lensman says:

That should read ” total inputs and total outputs to achieve” , thats what happens when you get excited and think on the hoof

43. Jim D says:

Let’s follow this through.
So if the energy from the sun to the earth and radiated back out is the flow, and adding CO2 is adding a resistance to the flow, which it is, then the river level goes up, that being the temperature. Do I have that right? Sounds like the theory works.

44. David A. Evans says:

I have vague memories of this from years gone by.
As I always understood it, the law is about optimising entropy, not maximising.
If entropy is optimised, there is a sustainable loss. If, (in the case of a river>, entropy were maximised, all rivers would be straight, they’re not and whenever straightening occurs, it’s corrected at a later date.
I think the same sort of thing happens with climate and that’s where constructal law comes in. difficult if not impossible to quantify however.
DaveE.

45. Smokey says:

I may be out of my depth here, but Prof Lindzen has written that the earth’s temperature at the equator has not varied by more than 1°C over the past billion years. So the large variations at the higher latitudes might correspond to oscillations above and below that temperature?
Also, just for fun, reversing entropy.

46. Rational Debate says:

I think the modeler’s have an even more fundamental flaw – they’ve left a central, vital, principle out of the mix. In their application of the scientific method to the entire question, they’ve utterly failed to control for confounding factors. That, and the flip side as well – they’ve similarly failed to include all of the major influential factors of the system in question.

47. Willis Eschenbach says:

Greg Cavanagh says:
November 15, 2010 at 8:10 pm

I get the impression that any fluid flow through any other medius acts pretty much the same way every time. Water through earth, jet streams, ocean currents, hot air rising through cool air.
It appears to be a fundamental of fluid mechanics, as applied to any fluid.

This is exactly why the Constructal Law is a fundamental law with applications in so many fields of science. It applies to all flow systems, not just one or two, and it makes no difference what is flowing.

48. John F. Hultquist says:

Pamela Gray says: at 6:58 pm …over the top windy
For those not familiar with Pamela’s part of the world here is a rough translation of her technical jargon – complements of the Pendleton NWS:
WINDS: WEST TO NORTHWEST WINDS BETWEEN 35 TO 45 MPH WITH
GUSTS TO AROUND 60 MPH ARE EXPECTED. LOCAL GUSTS TO 70 MPH
ARE POSSIBLE.

49. Dave Springer says:

willis writes:
“Bejan didn’t get to be one of the top cited scientific authors on the planet by writing foolishness, by being “all bun, no meat”, or by “handwaving”. C’mon, do your homework before uncapping your electronic pens …”
I bet Michael Mann has been cited far more times than Bejan.
Food for thought.

50. John Whitman says:

Willis,
Thanks for the post.
I do not see how this expands on general/basic thermodynamics concepts.
In what fundamental way does it add to the basic / general applied science of thermodynamics?
Is it a useful engineering application tool instead of a basic new law? Tool is my impression based on your post.
John

51. Barry L. says:

This reminds me of the big red spot predicted by climate models.
http://sciencespeak.com/MissingSignature.pdf
If the air temp is increased by co2 at the equator, then a reaction must take place to accommodate this. Could this reaction be based on the Construction law?
Could the increase in lower level temperature actually increase the convection rate to space?
http://en.wikipedia.org/wiki/File:Convection-snapshot.gif
And eventually cause a slight increase in radiation to space? With an overall balancing effect?

52. Doug in Seattle says:

Willis:
This (or something akin to it) may indeed be what is missing from climate and other finite difference models. I’ve never been comfortable with the idea that climate, with all its apparent symmetry, could be chaotic. I’ve thought that this was a cop out for poor modeling.
Such models resolve linearly when we know from empirical evidence that the processes they model (mimic) are cyclical. The push-pull between order and disorder that can be observed in natural systems is nicely accounted for with the Constructal Law.
Now all that is needed is for some math wizards to wrap it all up in a series of formulas that can used to model climate, fluvial flow, crustal motion, planetary and galactic motion, etc. All well beyond my age and talents, but there is bound to be some 20 year old (i.e. fresh) brains out there somewhere ready to work this for the next 20 years.

53. crosspatch says:

Well, there is a portion of this that is left out. One of the reasons the Mississippi has lost length is because of levees. What normally happens is that a river drops silt along its travel. At some point the river and its surrounding flood plain is a little higher in altitude than some surrounding ground from all the deposited silt. Then one day there is a flood and the river finds a lower level outside of its regular bank and begins to cut a new channel and a meander is born. If the Mississippi were left on its own, its total length wouldn’t change much. As old meanders are cut off in oxbow lakes, new meanders are formed someplace else.
Levees prevent the river from spreading out. As are result, the channel silts up and you must either continue making the levees taller or you must dredge the channel. In many portions of the Southern Mississippi, you have to look UP to see ships passing on the channel if you are standing away from the levee. The channel is tens of feet higher now than when those levees were first formed.
At some point those levees will fail and the river will cut a new channel. We have been fighting the river trying to cut a new channel for decades down the Atchafalaya. (See Old River Control Structure: http://www.johnweeks.com/river_mississippi/pages/lmiss23.html )
Some day the river will win.

54. Jeff L says:

Interesting. The first thought I had “Is this truly a fundamental law or just a result of the interaction of more fundamental laws such as gravity, 1st & 2nd law etc?”
Care to comment?
Has this been proven?
If it is a result of interaction of other laws & those laws are incorporated in the climate models, might they then actually have the constructal law built into them, even if unintentionally?

55. jimmi says:

“I’ve never been comfortable with the idea that climate, with all its apparent symmetry, could be chaotic”
That’s because it is not – if it were the whole concept of ‘climate’ would not exist – you would just have weather.

56. Grey Lensman says:

Rivers, rivers of energy, the flow of the cosmos, Victor Schauberger had it nailed.
Come to think of it, even entropy is purely subjective, it depends upon the perspective.
The total availability of energy in a system is a direct function of the data density thus entropy is purely a manifestation of data flow.

57. Douglas Dc says:

John Hultquist and Pamela Gray- winds starting the Grande Ronde Valley, seemed to have calmed a bit, waiting for the front to get here.
Fond memories of flying scheduled air freight/courier this time of year, this is getting to
the point where the only reason to check weather is to see how scared yo are going to get…
As for the name of Grande Ronde, the name was from a French Fir Trapper, name of
Dawes, who described those meanders in the valley. Much like what Willis is talking about…[googlemaps http://maps.google.com/maps?q=Grande+Ronde+Valley&oe=utf-8&client=firefox-a&ie=UTF8&hl=en&hq=&hnear=Grande+Ronde+Valley,+La+Grande,+Union,+Oregon+97850&ll=45.402789,-117.905617&spn=0.058817,0.103512&t=h&z=13&output=embed&w=425&h=350%5D

58. Willis Eschenbach says:

Smokey says:
November 15, 2010 at 8:49 pm

I may be out of my depth here, but Prof Lindzen has written that the earth’s temperature at the equator has not varied by more than 1°C over the past billion years. So the large variations at the higher latitudes might correspond to oscillations above and below that temperature?

Thanks, Smokey. One of the advantages to analyzing the climate as a heat engine is that it allows us to to make sense of some of the differences between the tropics and the poles.
A heat engine is characterized in part by two temperatures, Th and Tl. Th is the high temperature of the hotter end of the heat engine. This is the area where the majority of the energy enters the system. Tl is the lower temperature of the colder end(s) of the heat engine. This is the area where excess heat is radiated from the heat engine. In the climate system, the hot end of the heat engine is the tropics and the cold end is the poles.
The Constructal Law says that there will be a constant change and evolution in Th and Tl, accompanied by changes in w, the power expended to circulate the fluid (which is also entropy, since it is all eventually converted to heat by a fluid brake), and Ql, the heat rejected from the tropics to the poles. These quantities will adapt and evolve constantly in such a way as to maximize the sum of w and Ql.
In the tropics, there is a strong governing system which keeps the tropical temperature within fairly narrow bounds. As a result, when there is excess solar energy entering the tropics, the tropics doesn’t heat up much. Instead, the rate at which energy is passing through the heat engine increases. In other words, more heat is exported to the poles rather than being used to warm the tropics.
This, of course, tends to warm the poles. However, because of the homeostatic nature of the Constructal Law, the net result of the changes in Tl and Th are such that the sum of w work done and Ql heat rejected tends to a maximum. As a result, there is no simple one-to-one relationship between forcing changes and changes in either Tl or Th.
Finally, please note that in addition to the climate as a whole, all flow sub-systems of the climate are governed by the Constructal Law. These include such things as the jet streams; the flow of energy into and out of the ocean, land and atmosphere; the oceanic currents; storms and hurricanes; and all types of winds. The complexity of the interplay of these flow systems, each of which is constantly evolving and reorganizing to maximize flow, and many of which form physical constraints for neighboring flow systems similarly evolving, is staggering.
However, please do not mistake this for an “argument from complexity”. I am not saying we cannot understand the climate simply because of its complexity. Quite the opposite.
I am trying to unravel the exact style and nature of the complexity, in order to better understand and model it. Our current generation of models don’t do any better at estimating the uncertainty in climate sensitivity than did the models of twenty years ago. I say it is because they are using the wrong paradigm, one which doesn’t contain the Constructal Law.

59. anna v says:

Willis, everybody who has had a course in theoretical mechanics will recognize:
Action minimization. From Wikipedia:
In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is joule-seconds in the International System of Units (SI). Generally, the action takes different values for different paths. Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more strictly, is stationary. The classical equations of motion of a system can be derived from this principle of least action. The stationary action formulation of classical mechanics extends to quantum mechanics in the Feynman path integral formulation, where a physical system follows simultaneously all possible paths with amplitudes determined by the action. It also provides a basis for the development of string theory.
I make a guess it is a thermodynamic manifestation of the action principle, though I would have to read up to make any better comparison, and even then. Have you not seen any such correlation in your readings?

60. JDN says:

Willis: The reason nobody’s heard of the ‘constructional law’ is because it isn’t useful. It isn’t useful because everything that might be concluded from it can be concluded from other sources. Where are the great accomplishments, the mind-blowing apocalypses from this law? It sounds like the latest socially-acceptable fraud to me. I give it 10 years before everyone figures out it’s like Michel Foucault all over again. I think you’ve been played. Why is this ‘law’ only showing up in relation to climate sites and the paranormal?: http://reporter.blackraiser.com/?p=909
Furthermore, you should know better than this: “PS – For those that think that the Constructal Law is some crackpot theory, it is not. Bejan is one of the 100 most cited engineering authors of our time, and the results of the Constructal Law have been verified in a host of disciplines. It is indeed a new fundamental law of thermodynamics, one which we cannot ignore. ” Have you lost your mind? The “top” 100 cited climate scientists are all warmists, right?

61. kuhnkat says:

Thank you Willis!!!

62. Terry Jackson says:

The accreting river is the source of oxbows. Some rivers cut and some accrete and most do both at various points, depending on the available gradient.
The accreting river needs to find a place to drop the sediment load, and that is on the bottom unless in periods of high flow. I seem to recall that a stream’s ability to carry debris increases as the square of the increase in velocity.
Rivers may or may not support or refute Willis’ formulation of law, but they quite clearly react to the external forces of available drop in elevation and composition of the terrain.
John McPhee has written about this in The Control of Nature.

63. kim says:

I suspect the heat engine just pumps heat a little further poleward when it’s got more energy to reradiate to space and not so toward the poles when it’s got less. The heat is more easily lost poleward. CO2 concentration somewhat irrelevant. A self-leveling mechanism without the need for a thermostat.
=============

64. Willis Eschenbach says:

anna v says:
November 15, 2010 at 10:09 pm

Willis, everybody who has had a course in theoretical mechanics will recognize:
Action minimization. From Wikipedia:

In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is joule-seconds in the International System of Units (SI). Generally, the action takes different values for different paths. Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more strictly, is stationary. The classical equations of motion of a system can be derived from this principle of least action. The stationary action formulation of classical mechanics extends to quantum mechanics in the Feynman path integral formulation, where a physical system follows simultaneously all possible paths with amplitudes determined by the action. It also provides a basis for the development of string theory.

I make a guess it is a thermodynamic manifestation of the action principle, though I would have to read up to make any better comparison, and even then. Have you not seen any such correlation in your readings?

Interesting, anna. I had only a vague idea of the action principle, so I read your citation and a couple others. Can’t say I’ve moved too far forwards … there are obvious similarities, although one is a minimization function and the other a maximization function.
Further deponent saith not …

65. anna v says:

Willis Eschenbach says:
November 15, 2010 at 10:56 pm
For a finite-size (flow) system to persist in time (to live), its configuration must evolve such that it provides easier access to the imposed currents that flow through it.
Sounds to me that “easier access to the imposed currents” means less energy expenditure. That is where minimization would come in.I cannot guess how to write an action integral for flow though. It needs a theoretician.

66. bubbagyro says:

Thank you Willis, for once again provoking our thoughts.
This phenomenon has been demonstrated and worked out in the statistics of bottlenecks in traffic patterns, applied at once to the traffic “humping along” or “caterpillar crawling” as a response to congestion and density of the traffic. The statistics were worked out for key variables including traffic density, i.e. numbers of cars on a road, width of the lanes, and maximum average speed, and others. Although the traffic, even with a total bumper-to-bumper density, would be physically able to go at the speed limit, say 65 miles per hour, the cars go in fits and starts around an average speed that is allowable under the constraints of the variables, but at a rate much lower than the maximum, and this new value is based on statistical principles.
This has also been applied to military congestion on a battlefield, and I have seen the papers on this years ago. The gist of it is that certain bottlenecks control the flow on a battlefield in a way that is counterintuitive, because the apparent bottlenecks or restrictions one could see as restricting flow are not the ones the statistics finds in practice, but the restrictions happen well ahead or behind or to side eddies of the eye-identified bottlenecks.
Has anyone remembered the work that I am trying to recall?

67. Peter Pond says:

The new law is also applicable to politicians expounding new policy initiatives. Their explanations become ever more convoluted as confounding issues are identified, until someone cuts through the “spin” with a simple policy explanation. Then, as other politicians add their “two bobs worth” (“five cents worth”), the “spin” process recommences.

68. steven mosher says:

Seems like observations are consistent with the law ( I’d like to see the math) they say that since the observations are consistent with the theory that this counts in favor of the theory. Same argument holds true for GCMs.

69. Roger Carr says:

JDN says: (November 15, 2010 at 10:25 pm) Willis: The reason nobody’s heard of the ‘constructional law’ is because it isn’t useful.
JDN: There is something very appealing to me in your line. It rings true; and I suspect it is.

70. Willis Eschenbach says:

Steve Mosher, thanks for the link. That appears to be an update and extension of the paper that I linked to above. I’m in the Solomon Islands at the moment, where the electrons move slowly, so I’ll wait until I get back to the US on Friday to download it … \$35.95 … grrr.

71. Grey Lensman says:

I am really enjoying this debate, even if it seems to be “flowing’ around me. Complexity and chaos, tow theories but how can they be linked with universal laws. That indeed is a question of our times.
My gut feeling, at the most basic level is that it makes a complete mockery of the claim that a single molecule, carbon dioxide, can be used as universal marker for climate behavior. QED, its dead and buried.

72. Alex Buddery says:

“If someone asked me if a river could be shortened, I’d say “Sure. Just cut through a meander.”. And if I cut through the bend I could physically measure the river length and prove that indeed, the river was shorter.
But would that really make the river shorter?
Of course not. Soon the relentless forces of flow would once again increase the length of the river until the next cutoff forms another oxbow lake, and the cycle repeats.
Net effect of my cut on the length of the river? None. The length of the river continues to oscillate around the same fixed value.”
If you were to cut through a meander in a city it might not make the dynamic system of the river any shorter in one sense but you would certainly have a huge impact on the lives of the people living in the city. The city has infrastructure in place which is designed to benefit off the current river system. The river system moves so slowly that we are able to adapt our situation easily in response to the slow evolution of the river. If the river system was suddenly artificially modified it would likely have a huge negative impact on the residence of the city.
Similarly a perfectly legitimate concern that warrants investigation is that while we may have not displaced the climate system outside of its normal variation it may be that artificially changing the point in the cycle will have a large negative impact on our population. Now I am sceptical that this effect is significant but it certainly doesn’t mean that just because you’re not displacing the dynamic system beyond its natural bounds that our actions can’t have a significant negative impact.
There are periods in the ‘meandering’ of the earths climate that I am certainly glad I wasn’t around for.

73. G.L. Alston says:

This sounds like parts of information theory or game theory where information entropy is discussed. And a touch of Wolfram where you have relatively complex behaviours resulting from the interaction of simpler underlying parts where these necessarily follow physical laws. Given that everything man can detect about nature — ranging from evolution to the birth and death of galaxies — can be seen from an informational perspective, it’s no big surprise that this theory is correct. Flow systems aren’t all that different than electricity, e.g. lightning will take the path it CAN take, even if it would prefer to be a straight line.
Similarly constructual law says only that rivers take the course they CAN take; nothing more, and nothing less. Large collections of H2O have preferences, but they don’t have arbitrary preferences. They are obedient to physical law.
Regarding climate though I’m unsure what you’re wanting to say. Posts here and other places can show climate response (a ‘signal’ if you will) to gross input e.g. AMO/PDO, solar output, volcanism, etc. One needn’t merely tease a signal out of that noise (I’m thinking Krakatoa here) to show that the system responds to stimuli and recovers to a “natural” state as fast as it can do so. That recovery even happens is evidence of constructual law (or any other similar descriptions of information.)

74. Neil Jones says:

As a Non-scientist I have a question. How does this apply to the Jet Stream?

75. Willis Eschenbach says:

steven mosher says:
November 15, 2010 at 11:19 pm

Seems like observations are consistent with the law ( I’d like to see the math) they say that since the observations are consistent with the theory that this counts in favor of the theory. Same argument holds true for GCMs.

Sorry, Mosh, I forgot to respond to your comment. The difference between GCMs and Bejan’s model is that Bejan’s is the mathematically calculated result of a theoretical understanding of the underlying nature of the system.
The other is the result of careful tuning of an iterative model by changing both inputs (modelers are free to select among a variety of historical estimates of aerosol variations) and internal parameters until the model reproduce past conditions.
Very big difference. The agreement of GCMs with observations doesn’t impress me to date. Given that they are tuned, and are operating in a climate which has been generally warming for three centuries, agreement of a tuned model with what it is tuned to reproduce has little probative value.
The real test of such models, which are trained on a steady diet of increasing temperatures, comes when the temperature fails to increase. As my brother once commented to me, the future is easy to predict … as long as it looks like the past. Which was the case for a while after their initial forecasts.
But in the event, all of the climate models failed to model the post-1995 lack of warming. This doesn’t mean the models are wrong, I am clear about that … but it can hardly be counted as “agreeing with observations”.

76. Gilbert K. Arnold says:

Willis: I believe I ran across a variation of the Constructural Law in a graduate course in Fluvial Geomorphology. The text we used was: “A View of the River” by Luna B. Leopold. In it Leopold says (paraphrase): “a river can best be described if it is considered as a system, in which the system tries to maintain an optimum condition regarding morphology and energy efficiency”. It may provide some insight to the Constructural Law. If nothing else you will gain an appreciation for how rivers (of all types) work. The book is available at Amazon.com

77. Gilbert K. Arnold says:

oops that should have been “Geomorphology”.

78. Willis Eschenbach says:

Alex Buddery says:
November 15, 2010 at 10:53 pm

“If someone asked me if a river could be shortened, I’d say “Sure. Just cut through a meander.”. And if I cut through the bend I could physically measure the river length and prove that indeed, the river was shorter.
But would that really make the river shorter?
Of course not. Soon the relentless forces of flow would once again increase the length of the river until the next cutoff forms another oxbow lake, and the cycle repeats.
Net effect of my cut on the length of the river? None. The length of the river continues to oscillate around the same fixed value.”

If you were to cut through a meander in a city it might not make the dynamic system of the river any shorter in one sense but you would certainly have a huge impact on the lives of the people living in the city. The city has infrastructure in place which is designed to benefit off the current river system. The river system moves so slowly that we are able to adapt our situation easily in response to the slow evolution of the river. If the river system was suddenly artificially modified it would likely have a huge negative impact on the residence of the city.
Similarly a perfectly legitimate concern that warrants investigation is that while we may have not displaced the climate system outside of its normal variation it may be that artificially changing the point in the cycle will have a large negative impact on our population. Now I am sceptical that this effect is significant but it certainly doesn’t mean that just because you’re not displacing the dynamic system beyond its natural bounds that our actions can’t have a significant negative impact.
There are periods in the ‘meandering’ of the earths climate that I am certainly glad I wasn’t around for.

An interesting question, Alex. What you are saying about a concern warranting investigation is certainly true. However, our current understanding of the climate is not sufficient to say what a small change of a few W/m2 in downwelling radiation will do. We can’t model it and can’t measure it and don’t understand it to that fine a detail.
Me, I don’t think it will do much. A change in forcing of less than 1% in a dynamic flow system as powerful and turbulent as the climate seems like it would be lost in the noise.
And if it does make a change, we can’t say whether that change will be beneficial or detrimental to the world.
So while your concern is legitimate, we simply don’t have the tools to answer your question. We are working on them, and this and other like discussions are an important part of that work … but we don’t have the answer. We can’t measure or model it to that fine a level, to an accuracy of a couple of W/m2. Here’s James Hansen on why:

2.4 Principal Model Deficiencies [in the GISS Model E GCM]
Model shortcomings include ~25% regional
deficiency of summer stratus cloud cover off the west
coast of the continents with resulting excessive absorption of
solar radiation by as much as 50 W/m2, deficiency in absorbed
solar radiation and net radiation over other tropical regions by
typically 20 W/m2, sea level pressure too high by 4-8 hPa in the
winter in the Arctic and 2-4 hPa too low in all seasons in the tropics,
~20% deficiency of rainfall over the Amazon basin, ~25%
deficiency in summer cloud cover in the western United States
and central Asia with a corresponding ~5°C excessive summer
warmth in these regions.

J. Hansen, Climate Simulations 1880-2003

79. G.L. Alston says:

Willis E — This doesn’t mean the models are wrong, I am clear about that ..
Ummm… yes, it does, and by definition. As Prof George E.P. Box puts it — “All models are wrong, but some are useful.” The question I have is “which models are are useful?”

80. Richard111 says:

Crazy world! I remember learning about river meanders and flood plains at school nearly 60 years ago. These plains have vast areas of flat fertile land easly farmed and built on. Especially for the more disadvantaged peoples. Of course when the inevitable flood happens crops and homes are destroyed. Coupled with increasing population each flood is more of a disaster. But then that is just global warming. You cure it by restricting access to fossil fuels so the poor of the world can’t get their produce to market. /sarc

81. Mike Edwards says:

Willis,
Can you cite some material that is critical of the Constructal Law, please?

82. Spector says:

I wonder if we are dealing here with an aspect of nature equivalent to turbulence. The shape of a meandering river is quite similar to a turbulent flow pattern. If the flow is slow enough so that all reactive effects are well damped we have laminar or uniform flow. Once the rate of flow reaches a given limit where local resonances can be excited by positive feedback derived from the force (more properly: energy) of the rate of flow we have a transition to turbulent flow.
In the case of this planet, a laminar flow climate might apply if the Earth orbited the sun, perhaps, as far out as Pluto.

83. If we want to understand the climate, or to model the climate, we have to explicitly take the Constructal Law into account.
It is very interesting that you model a river system as this is often quoted as the typical 1/f noise system, and you clearly show why. Unlike Gaussian noise where the variation is short variations away from a mean, the river flow is affected by the presence or absence of obstructions which cause a step change in flow as they occur or are removed.
The short cut of the Ox-bow lake is a clear step change in the flow causing a long term semi-irreversible change.

84. phlogiston says:

But as the speed increases further, the turbulence rapidly starts to interfere with the circulation. Soon, a condition exists where further speed increases actually decrease the total of work done and heat rejected. That is the point at which the system will naturally run. This is why nature has been described in the past as running at “the edge of turbulence”.
So Constructal Law states that dynamic systems converge at the Hopf bifurcation region where non-equilibrium pattern formation begins, but stopping short of outright chaos and turbulence which destroys emergent pattern.
So it could be said to be a law requiring a dynamic flow system to maximise richness of emergent nonlinear/nonequilibrium pattern.
Such a law could indeed have played a role in the emergence of life and biology, as well as climate.

85. John Marshall says:

Very interesting and likely to be very important. It may mean, in the climate scenario, that the hotter a system becomes the quicker it looses heat. This is a blow to the hypothesis of AGW.

86. Roger Carr says:
November 15, 2010 at 10:37 pm (Edit)
JDN says: (November 15, 2010 at 10:25 pm) Willis: The reason nobody’s heard of the ‘constructional law’ is because it isn’t useful.
JDN: There is something very appealing to me in your line. It rings true; and I suspect it is.

Maybe JDN should have googled ‘constructal’ rather than ‘constructional’.
Interesting post Willis, though I noticed something of a contradiction between the river “maximising it’s length” and “going as fast as it can”.
Isn’t it actually the cutting of the oxbows which is maximising the flow and the water’s rush towards entropy? Wouldn’t that mean that the turbulence introduced by the medium the flow moves through was somehow neg-entropic?
Is one of the problem of the theory that by ascribing intentions to the components we are effectively anthropomorphising the river and the land, and getting contradictory results from their ‘different points of view’?

87. Waffle says:

Let me see if I understand this constructal law correctly.
Catastrophism will always seek to run at its most alarming. Then, when the current doomsday scenario has been debunked, a new one will emerge. Thus, catastrophism is forever seeking its maximum form!

88. Willis Eschenbach says:

Thanks, tallbloke, interesting ideas and questions.
tallbloke says:

Interesting post Willis, though I noticed something of a contradiction between the river “maximising it’s length” and “going as fast as it can”.

I’m using “going as fast as it can” metaphorically to indicate that it runs at the limit of the maximization of length. Sorry for the lack of clarity.

Isn’t it actually the cutting of the oxbows which is maximising the flow and the water’s rush towards entropy? Wouldn’t that mean that the turbulence introduced by the medium the flow moves through was somehow neg-entropic?

Flow isn’t being maximized. Length is.

Is one of the problem of the theory that by ascribing intentions to the components we are effectively anthropomorphising the river and the land, and getting contradictory results from their ‘different points of view’?

It’s difficult to talk about an evolving system without some level of anthromorphic undertones creeping in, although I certainly meant to keep it clean. Bejan is better at that than I am.

89. Lindsay Holland says:

Very interesting discussion.
Could we arrive at a fractal dimention for the process which may give better results in predicting future states.

90. Dave Springer says:

John Marshall says:
November 16, 2010 at 1:19 am

Very interesting and likely to be very important. It may mean, in the climate scenario, that the hotter a system becomes the quicker it looses heat. This is a blow to the hypothesis of AGW.

OMG!
Does this also mean that the higher the water is behind a dam the faster the flow will be through a gate at the bottom?
/facepalm /sarcoff

91. brc says:

That’s not an oxbow lake. Any geography student will tell you that’s a Billabong!

92. Sound like “flow access” is a thermodynamic variable characterizing open systems, referenced in the Constructal Law as something that tends to increase with time. If so,
1. What is the formal definition of “access” as a physical quantity?
2. How is it measured? (operational definition)

93. Another Ian says:

Re Dave Springer says:
November 15, 2010 at 9:07 pm
This thought arose back when I was closer to citation indices. Conventional thinking would suggest that a CI would be maximised by writing the best paper on the subject.
I reckon that the maximum CI would be achieved by writing the worst paper on the subject that you could get published – you would be guaranteed citation by all those in the field to show how bad it was, plus you would pick up all the “me-too’s” that cited it to show that they’d heard about it.
Any hard data would be appreciated!

94. Ian E says:

I must be missing something here – how is the river system , which oscillates around a given length, evolving ‘such that it provides easier access to the imposed currents that flow through it’? Rather it would appear to be simply randomly walking around some quasi-steady state. In what way does the constructal ‘law’ help us understand the river system?
Perhaps someone can explain what I am missing?

95. Roger Carr says:

brc says: (November 16, 2010 at 2:11 am) That’s not an oxbow lake. Any geography student will tell you that’s a Billabong!
I thought that, too, brc; until I realised there were no swagmen or jumbucks pictured… but some of the flora does resemble the grasstree, so you may be correct after all.
If the topography showed some of the river was flowing uphill then we could be sure it was Australia; and Willis may well have a Twain quote to prove it… perhaps:

Australian history … does not read like history, but like the most beautiful lies; and all of a fresh new sort, no mouldy old stale ones. It is full of surprises and adventures, and incongruities, and contradictions, and incredibilities; but they are all true, they all happened.” Mark Twain from “More Tramps Abroad” (1897)

96. Richard S Courtney says:

jimmi says at November 15, 2010 at 9:26 pm
” “I’ve never been comfortable with the idea that climate, with all its apparent symmetry, could be chaotic”
That’s because it is not – if it were the whole concept of ‘climate’ would not exist – you would just have weather.”
Hmmmmm. No! Jimmy, I suggest you look up what chaos theory is.
This link will get you started
http://www.abarim-publications.com/ChaosTheoryIntroduction.html
And if you read the section in the on Attractors then you will understand why your assertion is an assumption. It is not a fact.
Richard

97. This seems to explain how some glaciers are melting, or sometimes some parts of glaciers, while others are growing. A more credible explanation that that they are melting & will all be gone by 2025.

98. Jose Suro says:

“What does the climate flow system maximize? Because it is a heat engine (converting sunlight into the physical work of the planetary circulation), Bejan says (pdf) that it is doing a dual maximization. It maximizes the sum of the work done driving the planetary circulation, and the heat rejected back to space at the cold end of the heat engine. Again in Bejan’s words:”
Hi Willis,
Thanks for posting this. I’m trying to read all the background on this but I’m getting a “403 Forbidden” to the PDF link in the above paragraph. Do you have another link? I for one believe the thermodynamics is one of the true last frontiers. There is so much we don’t know……
Thanks,
Jose

99. Ventana says:

It ties in with all of the above”
I really don’t see how that’s relative

100. 1) The so-called “Constructal Law” is not a scientific law, because it does not state what specific physical property of a system will be maximised or minimised. In general terms, it is a behaviour that can be seen in every conceivable “flow system”, because that is the mathematical nature of variables; in any mathematically definable differentiable process or procedure something (some variable, or some combination of variables) must be maximised (or its reciprocal minimised). In the expression a+b=c, what is being minimised is the difference c-(a+b). This is not some deep quiddity; it’s a tautology.
2) Nevertheless, it is often instructive, in considering complex physical or mathematical systems, to look for a variable that is maximised or minimised or conserved, or such that perturbations in its value will be opposed or damped. Identifying such a variable will aid analysis and often lead to valuable insights into the mechanism and behaviour of the system. There is nothing new in this; it is what physicists have always done.
3) The controlling variable(s) may be quite different in different systems; maximising entropy, maximising the rate of entropy change, maximising energy, minimising energy, maximising energy flow, minimising energy flow, maximising work done, minimising action, maximising length, minimising length, maximising volume, minimising volume; or something much more complicated, such as a particular combination of such variables, or the trajectory of a strange attractor.
4) Rivers do not maximise their lengths, nor their flow, nor the work done. Nor do they oscillate about a fixed mean. There is a process of meander formation that would increase the length of the river without limit for as long as meanders do not intersect. When they do, the length discontinuously shortens. The actual length of the river is never stable; it varies on all timescales, with a large-tailed (fractal) distribution, between the upper limit of a plain as completely covered by non-intersecting meanders as possible, and the lower limit of a straight line to the sea. It is not oscillating about an average (it is quite likely that the distribution will be so long-tailed that no statistical average exists; and highly likely that no standard deviation will exist); it is doing a drunkard’s walk. Not all rivers do the same thing, and the same river can switch abruptly from one mode to another; for example, from meandering slowly to running straight and fast. River engineers have long known that in some circumstances, when you cut through a meander to shorten a river, the new cut scours a deep straight navigable channel to the sea, without trying to regain its length by new meanders.
5) I’m afraid that Bejan, in falsely believing he has found a great new organising principle, is indeed promoting something of a “crackpot theory”, and Willis, in attempting to apply that notion to the climate, is falling into the same error.

101. jimmi says:

John Marshall says,
“Very interesting and likely to be very important. It may mean, in the climate scenario, that the hotter a system becomes the quicker it looses heat. This is a blow to the hypothesis of AGW.”
Er, a hotter object does radiate more heat, faster – that is a necessary part of the greenhouse gas theory – it is how the planet gets back into equilibrium.

102. Jack Simmons says:

Very interesting.
Now, can someone make some testable predictions using this new law?

103. Spector says:

It would seem that the structure of a meandering river, much like turbulent flow, would tend to impede the flow of water through the system. My understanding is that these curves develop as a result of positive feedback between the rate of erosion and the degree of curvature and this persists until the link becomes isolated. I am not sure that the Constructal ‘Law’ is properly stated; as in this case, ease of flow seems to be equivalent to maximizing the amount of erosion.

104. Alexander K says:

Willis, you have done it again with another brilliant exposition. Just when I think I know something, you arrive here with another set of stuff that gives me a headache trying to get sorted and categorised to my personal satisfaction. The complexity of the utterly simple is sometimes a little difficult for me to understand, but if I continue to work at it, comprehension eventually arrives.
Thanks!

105. JDN says:

tallbloke says:
November 16, 2010 at 1:26 am
JDN says: (November 15, 2010 at 10:25 pm) Willis: The reason nobody’s heard of the ‘constructional law’ is because it isn’t useful.
> Maybe JDN should have googled ‘constructal’ rather than ‘constructional’.
I guess I’ll have to wait until the gmail spell-checker recognizes ‘constructal’. I do this exercise of asking ‘what would be lost if it never existed?’ with everything that people claim is a ‘great’ thing or somehow central to thought or life. If the answer is that nothing but a cottage industry dedicated to the thing would be lost, then you have something basically unconnected to the greater reality.

106. I’m old school and your post is my introduction to this new “law”. To me it seems that it has more to do with kinetics than it does with thermodynamics. They are related but the first deals with rates and the the second equilibrium. What we observe is the transport of momentum, energy, and mass. It will be a great contribution if it helps us to better understand these processes what ever name you give it. Also, these phenomena may be studied with statistical wave analysis.

107. Fred Harwood says:

I first saw a description of this in Tucson, AZ, at a riparian display at the Desert Museum, if memory serves, now perhaps three or four decades ago. Surely this knowledge is not new?

108. John Day says:

Correct me if I’m wrong, but I don’t see anything new here. I’m not saying it’s useless or wrong, but merely a collection of wise principles and truisms that are either obvious or derivatives of other theories:
Obvious:
“According to the Constructal law, every system is destined to remain imperfect, i.e. with flow resistances ” http://www.constructal.org/en/theory/presentation.html
The meandering of a river is completely explained in terms of natural kinetic and thermal forces and minimizing energy (Principal of Least Effort).
The way numbers accumulate e.g. Zipf Distribution is also claimed (by Zipf himself) to be an example of the Principal of Least Effort.
Minimizing Entropy => decompose entities until they are pure (i.e. splitting a handful of dirt into minerals and then elements etc, minimizing the information needed to explain each collection)
Maximizing Entropy => Don’t assume (avoid bias) unless you are compelled to (i.e. use the least informative distribution until you know better).
I have also found similar, useful, wisdom in the Bible:
Deuteronomy 18:21-22 => Don’t believe in (or fear) a Model that gives you incorrect predictions (Alarmists take heed of this 🙂
1 Thessalonians 5:21 (St. Paul) “Test everything and keep what is good.” => (Supervised Machine Learning)
So, I merely want to know: has Bejan’s theory presented any new law of nature that is not obvious or derived from somebody else?

109. Pamela Gray says:

This law should be studied by anyone building a house within the plain of a river. While your chosen plot may be miles from the river bank, anything that happens up stream to its banks can result in the river, within a short period of time, knocking on your door. This is also why serious sounding riprap attempts to control river erosion are only temporary measures. An upstream diversion will simply result in a walk around by the river, all the while thumbing its nosy waves at the downriver riprap now sitting dry as pie crust off in the distance.
Weather systems do the same thing. We get Pacific systems coming in from the coast, and depending on where they choose to flow towards the East, can result in either a New England Nor’ Easter, Washington DC closing its snow bound streets, or lay dry as a bone while Florida’s manatees shiver in their all together in a driving cold rain.
I would imagine that this law is easily studied by a classroom experiment: The tilted sand table with a flow of water at the top.
By the way, that damned wind woke me up in the middle of the night with a BANG! It had jiggled my backyard gate latch open and banged the heavy gate against the house. Both dogs rose from their slumber on full barking/growling/jumping alert. I landed on the ceiling finger and toenails firmly embedded.

110. Tim Clark says:

kcrucible says: November 15, 2010 at 6:50 pm
That’s not really what I’m seeing. I’m seeing a constant attempt to MINIMIZE the length of the river, which fits in with thermodynamics quite nicely. The original elongation was an aberation. Once in the lowest energy state possible between two points (straight line) there’s absolutely nothing to cause it to create additional corners.

Not true.
In an open system, unrestrained by ACOE dikes, erosion from the land surrounding the defined bed and bank river path will creat gulleys and perennial or intermittent streams. Concommittantly, siltation from upstream erosion occurs in eddy areas near bank obstructions (commonly trees) reducing flow rate and further increasing deposition of siltation. Over time. the flow rate decreases and water level increases (via slope reduction) in those areas. Under periodic episodes of flooding, the water overflows the banks and will erode riverlets into the adjoining intermittent gullys, then return to the original streampath. Subsequent episodic flooding will cause the river to establish a new watercourse in these eroded areas.
What you are seeing is an artificial, channelled, dredged and diked river.

111. James Sexton says:

Jack Simmons says:
November 16, 2010 at 4:49 am
Very interesting.
Now, can someone make some testable predictions using this new law?
========================================================
Absolutely Jack! See my post, I’ve already made one. Or, watch a river.

112. The UNIVERSAL generation of configuration, or the generation of ‘design’ in nature is the FIBONACCI SERIES

113. Billy Ruff'n says:

Like the comment above on the jet stream, ocean currents may provide a better illustration of the principle under discussion, particularily as it relates to climate. The Gulf Stream is a huge heat dispersion mechanism. The meanders (and the warm and cold eddies on either side of the axis created a meander is cut off) are clearly visible on the image at
http://www.k12science.org/curriculum/gulfstream/images/eastcoast.gif .

114. …And The FIBONACCI SERIES…is originated by the movement of the resultant force of the two forces (charges) existing and operating in Nature; in other words, by the variation in size of the Pythagorean hypotenuse, or what is the same: WAVELENGTH, whether increasing or decreasing.
Then, if we think it simply, it is the generalization of Max Planck’s equation:
E=h*v
to, E=(Sin y+Cos y) x v x 10
See:
http://www.scribd.com/doc/42018959/Unified-Field-Explained-9

115. George E. Smith says:

“”””” Enneagram says:
November 16, 2010 at 7:52 am
…And The FIBONACCI SERIES…is originated by the movement of the resultant force of the two forces (charges) existing and operating in Nature; in other words, by the variation in size of the Pythagorean hypotenuse, or what is the same: WAVELENGTH, whether increasing or decreasing.
Then, if we think it simply, it is the generalization of Max Planck’s equation:
E=h*v “””””
I believe that is what Albert Einstein actually got his Nobel Prize in Physics for; not for E= mc^2

116. kagiso says:

Way behind the curve here.
Dynamic systems come to an equilibrium flow when entropy production is maximised, and explains the creation of dissipative structures.
Paltridge first noted this with the earths circulation a few decades ago, lots of other work on ‘Maximum Entropy Production’ by Dewar, Ackland, Gallagher, Levy & Solomon, and many others.
Lots of hardcore effective maths for those who don’t like this ‘constructual’ approach.

117. John Day says:

@George E. Smith:
> I believe that is what Albert Einstein actually got his
> Nobel Prize in Physics for; not for E= mc^2
Einstein received the Nobel Prize in 1921 for his explanation of the Photoelectric Effect, the elastic scattering of photons by electrons.
http://en.wikipedia.org/wiki/Photoelectric_effect
[FYI, Arthur Compton received a Nobel Prize a few years later (1927) for his discovery of the inelastic scattering of photons by electrons (Compton Effect)]

118. George E. Smith says:
November 16, 2010 at 8:18 am
How did he dare to SQUARE C?….fortunately it was wrong, was it not, the first A Bomb would have blown up our whole planet ! 🙂

119. George E. Smith says:
November 16, 2010 at 8:18 am
…Btw: the shorter the wavelength, the higher the energy. Now, let’s talk about nanoparticles…..

120. Dave Springer says:

G.L. Alston says:
November 15, 2010 at 10:55 pm

This sounds like parts of information theory or game theory where information entropy is discussed. And a touch of Wolfram where you have relatively complex behaviours resulting from the interaction of simpler underlying parts where these necessarily follow physical laws. Given that everything man can detect about nature — ranging from evolution to the birth and death of galaxies — can be seen from an informational perspective, it’s no big surprise that this theory is correct. Flow systems aren’t all that different than electricity, e.g. lightning will take the path it CAN take, even if it would prefer to be a straight line.
Similarly constructual law says only that rivers take the course they CAN take; nothing more, and nothing less. Large collections of H2O have preferences, but they don’t have arbitrary preferences. They are obedient to physical law.

Yes. You can boil everything down to information flow if it suits your fancy.
Bejan really trivializes living systems which have a unique charateristic in that they store information about present states and retrieve information about past states using an abstract code. Nothing else in nature that we know of does this which is what makes living things quite different from other dynamic systems. Rivers aren’t “living”. Rivers are matter and energy obeying the immediate dictates of immutable physical law. Living things are matter and energy following recipes and procedures in a book that is being constantly updated as better recipes are discovered.

121. nofate says:

Several thoughts relating to “climate change”:
1. Leaving out the fact that ice core proxies from Antarctica and Greenland show non-linkage of CO2 and temperature, CO2 cannot act as the warmists have proposed – the constructal law guarantees that the system will eventually change the “direction” of the current trend.
Ditto temperature – if we give Mr. Mann his hockey stick, nature (no pun intended), via the constructal law and a whole host of other influences will eventually chop off the blade and, given enough time, send it in the other direction.
2. Natural cycles, i.e. geological, solar, and cosmic continually influence the current state of the atmoshere over long (sometimes millenial) periods of time. Some that come to mind include:

a) volcanic eruption “events” such as the Siberian or Deccan traps.
b) changes in the earth’s magnetic field such as when the poles flip.
c) changes in the magnetic fields in the sun, such as when sunspots decline (which, if I understand what I have read correctly, is a visible result of large changes in the magnetic fields inside the sun).
d) cosmic influences, i.e. the increased level of cosmic rays able to breach the solar wind/magnetic field (terminology may be poor) during periods of decreased solar activity causing increased low level cloud formation and subsequent cooling.

3. The curent warm period is but a maximal warm “swing” that, due to “global constraints”, will eventually be swinging back the other direction, i.e. ice age. As a matter of fact, looking at the 400,0000 year ice core graph and an 800,000 year graph again, ice ages seem to be the more normal position of the atmosheric condition and the warm periods appear to be the overshoot, or the “oxbow lake” left behind when the atmosphere normalizes temperatures again.
4. Using the model given by D. Patterson @7:02 P.M. at Constructal Theory Web Portal, does this seem like a possibility?:

Application Millenial Temperature
What Flows Heat
Tree Channels ????Atmosheric influences-Water vapor, solar activity, geologic activity, low level cloud formation, etc.???
Interstitial spaces ????Earth’s Atmosphere???Earth’s Rotation????

Not enough of a scientific thinker to be able to fill this in correctly, but it does seem that the millenial atmospheric model does seem to follow this idea: “The natural constructal tendency then is to distribute the imperfections of the system, and this distribution of imperfection generates the shape and structure of the system.”
5. From a comment by Willis Eschenbach, 11-15-10, 10:02 PM:
The complexity of the interplay of these flow systems, each of which is constantly evolving and reorganizing to maximize flow, and many of which form physical constraints for neighboring flow systems similarly evolving, is staggering.
Especially when throwing in solar and cosmic influences pointed out by Svensmark, and others.
Disclaimer: I realize I am out of my league here, as I don’t understand a bit of comments like this:

Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more strictly, is stationary. The classical equations of motion of a system can be derived from this principle of least action. The stationary action formulation of classical mechanics extends to quantum mechanics in the Feynman path integral formulation, where a physical system follows simultaneously all possible paths with amplitudes determined by the action. It also provides a basis for the development of string theory.
I make a guess it is a thermodynamic manifestation of the action principle, though I would have to read up to make any better comparison, and even then. Have you not seen any such correlation in your readings?”

I think Grey Lensman said it best (@10:47):
“I am really enjoying this debate, even if it seems to be “flowing’ around me…My gut feeling, at the most basic level is that it makes a complete mockery of the claim that a single molecule, carbon dioxide, can be used as universal marker for climate behavior. QED, its dead and buried.”
Ditto. I really enjoy reading and learning from this site, as well as the level of the ensuing debate.

122. Warren in Minnesota says:

A vision of Arte Johnson’s character, Wolfgang, many years ago from Laugh In comes to mind,
“Verrrry interesting.”

123. k winterkorn says:

The Constructal Law seems to me a brilliant insight into the nature of things.
I think some of the wording used to describe the Constructal Law is unfortunate: many of the words carry usage burdens that mislead the reader. For example, “design” in common usage calls for a “designer”. This is the problem in the “intelligent design” debates. Perhaps saying systems “adapt” in such and such a manner, rather than are “designed” would be an improvement (off the top of my head).
The constructal law indicates that all systems that “live” (another forced, unfortunate word choice) over time will seem to be “intelligently designed”, that is they will develop what I would call a topology of complexity that appears strategic, the result of a designer achieving a goal.
Teleology or goal-directedness is an important issue in science. I like the discussion in Herbert A. Simon’s “Sciences of the Artificial”, a gem of a short book. If Bejan and others in the field would revisit their arguments using Simon’s word choices and paradigms to make their more general case, a certain fuzziness would be scrubbed away, and the central brilliance of the Constructal Law would shine more clearly.
A Taoist might say, “To know the shape of the Tao (the Way of All Things) in all dimensions, that is enlightenment”. The Constructal Law is the science of the shape of all things in which there is energy and movement. A good start toward enlightenment.

124. k winterkorn says:
November 16, 2010 at 10:15 am
Let me tell you: You do not find truth, truth finds you.

125. JDN says:
November 16, 2010 at 5:49 am
I do this exercise of asking ‘what would be lost if it never existed?’ with everything that people claim is a ‘great’ thing or somehow central to thought or life. If the answer is that nothing but a cottage industry dedicated to the thing would be lost, then you have something basically unconnected to the greater reality.

Mulling over pet theories is fun, educational, promotes lateral thinking, and serves to stir the pot. Very occasionally the cottage industry booms into a new school of thought which makes real strides in understanding. If these things bore you, or you feel the odds are too low to bother, feel free to go and get cynical about the next thread along the line. 😉

126. “All thermodynamic systems in nature are flow systems (i.e. live, non-equilibrium systems), and they all have configuration. If they do not have it, then they acquire it,”
-Bejan-
Seems a reasonable proposition to me. I’ve been having similar thoughts about the solar system, and how feedback from the planets in their orbits might have affected solar activity levels, which in turn have influenced the locations of those planetary orbits. There are just too many neat whole number harmonic resonances and similarities between subsystems within the solar system for it to be otherwise.

127. tallbloke says:
November 16, 2010 at 11:11 am
There are just too many neat whole number harmonic resonances and similarities between subsystems within the solar system for it to be otherwise.

That’s very interesting. And what about disharmonies, I just suspect a few as far as the presence of some “scars” in it, like the asteroids ring or the moon itself. Some “Velikovskian” past perhaps?. We are living in interesting times, but I hope not “too much” 🙂

128. Need to go out there with a tuning fork..:-)

129. Mike Hebb says:

How come this is a Constructal Law and not a Constructal theory or hypothesis having only been around about 14 years when Einstein’s “theory of relativity” hasn’t graduated to the law of relativity in almost 100 years? Is this an example of space time compression?

130. Mike Hebb says:
November 16, 2010 at 11:37 am (Edit)
How come this is a Constructal Law and not a Constructal theory or hypothesis

Some things are “just plain self evident”.
😉

131. Mike Hebb says:
November 16, 2010 at 11:37 am
…..it’s because we are living in “Interesting Times”, and, BTW WUWT did not exist in those “good days”, so we have managed to find the contradictions. No “flying pigs” in sight. 🙂

132. Laurence M. Sheehan, PE says:

What I am trying to do is see the point of this exercise. I fail to see any predictive qualities in it. River systems are hugely variable, the characteristics of the underlying and bank material varies widely, as do the flow rates.
Water will flow from a higher elevation to a lower elevation, always following the path of least resistance for the quantity of flow involved, eroding as it flows to create a path of lesser resistance for said quantity of flow, which quantity can widely vary. Material eroded will be deposited (due to the force of gravity) where it can be deposited.
Where there is erosion, what is there is destructed. Where there is deposition of eroded material, there is new construction . Looks as if it were a “push” to me.
“Constructal/destructal” Depends on whose ox is being gored.

133. Feet2theFire says:

Willis – Sir, I think you’ve picked the exact wrong example to argue this “Law.” I had written several points disagreeing with the illustration and your description of it, but the “Law” itself is far more interesting to write about here.

We pursue this from the constructal point of view, which is that the circulation itself represents a flow geometry that is the result of the maximization of global performance subject to global constraints.
…There is a most fascinating interplay between those two. When the speed of the planetary circulation is low, so are the turbulent losses. So as speed increases, up to a certain point the sum of work done (circulation speed) and heat rejected is also increasing.
But as the speed increases further, the turbulence rapidly starts to interfere with the circulation. Soon, a condition exists where further speed increases actually decrease the total of work done and heat rejected.

This threw my head into a really interesting place:
Yes, this is what the clouds do. We have looked at clouds from lots of different perspectives, but has anyone looked at them as intrinsically turbulence, instead of collections of water vapor?
Speculating here: That is perhaps why – and HOW – they (which we have seen and treated as merely water vapor) act as thermostats, as negative feedbacks sometimes and positive ones other times. The more turbulence, the more negative the feedback. They’ve tried to model water vapor and so far failed. But if they modeled it as turbulence – a totally understood feature of thermodynamics – would it work better?
And perhaps the water vapor is not the driver in itself. Perhaps it is only the outer manifestation of the underlying turbulence. That is iffy in my thinking here, but should be speculated on, I think: what is the relationship of water vapor and turbulence? Which should we be modeling?
If heat energy flow is the reality of climate (this really hearkens my mind to something called heat pipes), then perhaps temperature is not what we should be looking at as a measure of climate, but heat flow. And if heat flow is the flow we are looking at, then heat flow turbulence would be the braking mechanism, what keeps the system running optimally.
This would possibly have ramifications of the Faint Young Sun Paradox, too. Maybe the heat (in this case, temperature) would not be any different if we are only looking at heat flow and the turbulence engendered by it. It may, in fact, not be dependent on the specific elements present.
Now, some may argue, “But look at Venus.” Yes, but Venus’ system is not Earth’s. With this kind of system, we don’t know if there are discrete states that dictate the maximization optimum of such systems. Perhaps like electron shells, the system can only be in discrete “shells” – energy states, not something in between.
Therein lies a possibility: Once in an energy state (shell), the climate will create the proper level of turbulence that keeps the system at that energy state. Perhaps ice ages occur only when some gross (external?) effect slips the system into a new discrete energy state. But within that (fairly wide) state, turbulence keeps the overall energy level (heat flow) within narrow limits, no matter what occurs…

134. Willis Eschenbach says:

Jack Simmons says:
November 16, 2010 at 4:49 am

Very interesting.
Now, can someone make some testable predictions using this new law?

The new law has made a whole host of these, by mathematically deriving a number of previously empirical relationships. Please read the references that I gave.

135. Willis Eschenbach says:

Jose Suro says:
November 16, 2010 at 4:11 am

Hi Willis,
Thanks for posting this. I’m trying to read all the background on this but I’m getting a “403 Forbidden” to the PDF link in the above paragraph. Do you have another link? I for one believe the thermodynamics is one of the true last frontiers. There is so much we don’t know……
Thanks,
Jose

My apologies. That’s the public folder of my iMac account, and I haven’t a clue why it is giving the 403, never happened before. I’m in the Solomon Islands right now, I’ll see what I can do, but it may have to wait until Friday when I return to the US.

136. Willis Eschenbach says:

OK, Jose, try this link …
files.me.com/williseschenbach/y1gqp0
It seems they have decided to password protect all my public files … I am very unhappy about that.
w.

137. Feet2theFire says:

This is a pain. I wrote this out, then posted it and it disappeared. I will try again.
As to the Constructal Law, and as to Willis’s example, I think both are wrong – a wrong self-important self-declared “Law” and not even a decent example of what Willis’ words were saying. In that area, I agree with Paul Birch at 4:30 am.
But wow, did this part get my mind in action:

We pursue this from the constructal point of view, which is that the circulation itself represents a flow geometry that is the result of the maximization of global performance subject to global constraints.

There is a most fascinating interplay between those two. When the speed of the planetary circulation is low, so are the turbulent losses. So as speed increases, up to a certain point the sum of work done (circulation speed) and heat rejected is also increasing.
But as the speed increases further, the turbulence rapidly starts to interfere with the circulation. Soon, a condition exists where further speed increases actually decrease the total of work done and heat rejected. That is the point at which the system will naturally run. This is why nature has been described in the past as running at “the edge of turbulence”.
What does that mean for understanding the climate? This is a new area of scientific investigation. So I don’t know what all of that means, there’s lots of ramifications, some of which I may discuss in a future post. However, one thing I am sure of.
If we want to understand the climate, or to model the climate, we have to explicitly take the Constructal Law into account.

First of all, I will give the Constructal Law a bit of breathing room, by looking at it as an organizing principle. Too often science believes that the whole is the sum of the parts, and then take that to mean that if we understand the parts we can understand and even build the whole. The early history of science was what it needed to be: Begin with simple things and try to understand them, and perhaps that will allow us to understand a larger whole. Necessary, yes, but at some point we have to begin also trying to see the systems from the top down, to wee what organizes them. Perhaps that is what the Constructal Law is attempting to do. If so, by the gods, he needs to re-word it in something intelligible.
One might glimpse such a thing in terms of stem cells, which we don’t know what the heck they are doing, but we are beginning (yes, only still in the earliest stages) of understanding them, even as we use them in more and more ways. (Hey, we use electricity, too, and claim we know what it is, but at the most fundamental levels we are still clueless.)
As it applies to the SYSTEM of climate, we perhaps need to do what Willis is suggesting, look at the heat flows. But look at it in terms of turbulence – turbulence as a governor, so that the heat flow does not get excessive, nor fall too low. Enough studies have been done that suggest clouds do this for the weather/climate. But perhaps it is not the water vapor per se that governs. Perhaps it is the turbulence (which we SEE as clouds) that is the real reality, the rel governor. Perhaps when we measure water vapor in clouds we are missing the bigger picture. What if the upwelling, the electrical that makes lightning, the gestalt of clouds is the real governor?
Now turbulence is something well studied in thermodynamics. It is incorporated into weather, certainly. I have no idea how it is modeled in GCMs. I know they don’t have water vapor modeled properly. But maybe turbulence is a good proxy – or the exact thing to be putting into the models in the first place.
But this is not about models. This is about seeing how the system self-regulates. Too much heat flow? Kick up the heat flow to turbulence levels. Too low of heat flow? Decrease the heat flow turbulence. (by lowering the heat flow velocity to laminar levels, so heat can be distributed more quickly.)
Turbulence may always be present. Vertically we see it as clouds and experience it as thermals/convection. Horizontally it is wind, from Coriolis Effect and other factors. But it isn’t JUST convection. As the warm air rises, clouds are formed when it bursts through into colder layers. But this also creates turbulence, which we always see as the roil of rising clouds. The turbulence adds to heat transfer, of course, but is there more to it than that? Heat transfer is actually best at laminar velocities. Just as airfoils need laminar flow to work best, so does heat transfer. So the turbulence we see in clouds is perhaps the most important part of what is going on, instead of the chemical and UV/IR blocking.
…just wonderin’…
Thanks for the mental exercise/glimpse, Willis.
I’ve found that when complex things are going on and we need to figure them out, we often ask questions that seem to be the right ones to ask, but after progressing through the situation we see that another level of questions arises, that are not apparent from the starting point. The old questions are no longer the right ones to ask. Those new questions comes about only because we recognize that some other factor exists that we had not considered important. With the new questions, a new level of insight arises. Sometimes this step up process has more than one step to it. But if we keep asking the same questions, we may never get to the right questions, the ones that do tell us what is going on.

138. Crispin in Johannesburg says:

In Bejan’s book Convective Heat Transfer there is a section on the heat transfer between two flat, horizontal plates, the bottom one being hotter than the one above. The heat is transferred by water. As the distance between the plates is increased, different forms of flow manifest and are copied throughout the area making pretty patterns. The forms are dictated by the properties of water at that temperature and pressure and the vertical distance. It is interesting that certain patterns repeatedly emerge and stabilize. As the distance between the plates increases, different complex, stable states repeatedly emerge and disappear.
It is often said that systems have chaotic elements in them. David Garcia-Andrade the mathematician said if you look into the nature of the chaos you will find a lower level of order that only looks like chaos. Looking closely at that lower level or order, you will again find what appear to be other chaotic elements, themselves experiencing an even lower level of order.
Each description of a system that eventually sees ‘chaos’ may be described as an order of complexity. I do not know how many orders of complexity exist in the atmosphere. Constructal law seems to be shorthand for saying that systems with multiple levels of complexity are ergodic in nature: specifically unpredictable but always behaving in a manner clustered around familiar behavioural nodes, and that these nodes are maximising the values of certain system variables.
We know there are multiple behavioural modes for oceanic and atmospheric systems. We also know from studying the transitions from one to another that ‘tipping points’ are a fact. But CO2-induced a tipping point for thermal runaway is not one of them or it would have tipped long ago when the CO2 was at a far higher concentration. It seems with the Earth as one plate and space the other, the multiple modes of heat transfer away from the equator and upwards into space prevent the global average temperature from rising above 25 deg C.

139. Willis Eschenbach says:

Paul Birch says:
November 16, 2010 at 4:30 am

5) I’m afraid that Bejan, in falsely believing he has found a great new organising principle, is indeed promoting something of a “crackpot theory”, and Willis, in attempting to apply that notion to the climate, is falling into the same error.

Sometimes you guys crack me up. First, Bejan applied the idea of the Constructal Law to the climate, not me, and has written several papers on it. More to the point, Bejan has a PhD from MIT and is a full professor at Duke University. He is one of the most cited scientific authors on the planet. He has over 400 peer reviewed papers. He is the recipient of (among others) the following awards:

Donald Q. Kern Award from the American Institute of Chemical Engineers (AIChE), 2008, for “seminal contributions to heat exchange design based on two original methods: entropy generation minimization, and constructal theory.”
Fluid Science Research Award of the Institute of Fluid Science, Tohoku University, Japan, 21 January 2008.
James P. Hartnett Memorial Award, 2007, International Center of Heat and Mass Transfer.
Luikov Medal, 2006, International Heat Transfer Conference, Sydney.
Edward F. Obert Award, 2004, American Society of Mechanical Engineers, for the paper “Thermodynamic Formulation of the Constructal Law” written with Prof. S. Lorente.
Charles Russ Richards Memorial Award, 2001, American Society of Mechanical Engineers, for “outstanding achievement in mechanical engineering by an engineer twenty years or more following graduation.”
Ralph Coats Roe Award, 2000, American Society of Engineering Education.
Max Jakob Memorial Award, 1999, awarded jointly by the American Institute of Chemical Engineers and the American Society of Mechanical Engineers, “for highly imaginative and inspiring ideas in the thermal science and design of engineering and nature.”
Worcester Reed Warner Medal, 1996, of the American Society of Mechanical Engineers, “for originality, challenges to orthodoxy, and impact on engineering thermodynamics and heat transfer, which were made through the first three books: Entropy Generation Through Heat and Fluid Flow (1982), Convection Heat Transfer (1984), and Advanced Engineering Thermodynamics (1988).

Here’s a hint, Paul. On this planet, when a man gets awards for the excellence of his work on the Constructal Law both from the American Society of Mechanical Engineers and the American Society of Chemical Engineers, you are not looking at a crackpot scientist nor a crackpot theory … you are looking at a very unusual mainstream scientist whose theoretical work has proven valuable in a variety of fields. On your planet that may be called a “crackpot” … here, not so much …

140. Nullius in Verba says:

I had a look at the linked reference, and I couldn’t work out what the theory was supposed to be, besides that the appearance of design appears as a result of some variable being maximised or minimised – but besides the many anecdotal statements of relationships that “constructal theory has predicted…” I can’t see where the derivations actually are. How do you determine which variables are to be optimised?
I’m guessing here, but the nearest I could get to the gist being conveyed was that dynamical systems tend over time towards attractors, trajectories of stable or pseudo-stable behaviour, the general shapes of which are usually determined by the symmetries of the dynamics. If the dynamics happens to have a scale symmetry, then you often get fractal, branching structures.
The tendency towards dynamical attractors is indeed a general law, somewhat distinct from (but related to) the 2nd law of thermodynamics. We can certainly work out from the dynamics what the symmetries and attractors are, and get many of the same sort of predictions, but I get the feeling that more is being claimed than that.
I’m not interested that Bejan is a world-famous engineer, or that he’s well-respected, widely cited, or that the theory “has made many successful predictions”. Climatology has claimed the same. I want to know how it works, in detail. Do you have any better sources?

141. Willis Eschenbach says:

Enneagram says:
November 16, 2010 at 7:45 am

The UNIVERSAL generation of configuration, or the generation of ‘design’ in nature is the FIBONACCI SERIES

The Fibonacci series indeed appears many times in nature, and people have often wondered why. However, the appearance of the Fibonacci Series is a derivable result from the Constructal Law. Google “constructal fibonacci” for a host of references. It is also specifically mentioned in one of the works I cited in the head post:

Comparisons with the empirical correlations and
formulae based on ad hoc models support the constructal
vegetation design, which also predicts and
unifies classical empirical ‘rules’ such as Leonardo
da Vinci’s rule, Huber’s rule (the proportionality
between leaf specific conductivity and the specific conductivity
of the stem), Zipf ’s distribution and the
Fibonacci sequence. These empirical rules are no
longer statistical ‘coincidences’ because one of the predicted
features of the tree trunk and canopy is the
proportionality between the vertical spacing between
two sequential branches along the trunk and the distance
from the branching point to the tip of the
trunk. For example, from this proportionality follows
Leonardo da Vinci’s rule, which is the observed conservation
of wood cross-sectional area during
branching (the lower trunk cross section equals the
upper trunk cross section plus the cross section of
the branch).

READ THE BLOOMIN’ CITATIONS! People say “where are the testable predictions”? READ THE CITATIONS.

142. Willis Eschenbach says:
November 16, 2010 at 12:37 pm
files.me.com/williseschenbach/y1gqp0

Thanks Willis, just downloaded and had a look. If the Earth model in fig 1 is right then my engineers eyeball tells me that solar variation is most easily going to be dealt with by a change in the angle theta. This means Stephen Wilde might be on the rght track with his polewards and equatorwards shifting of the jetstreams being the primary feedback mechanism for maintaining equilibrium.
Very interesting, thanks again.

143. Willis Eschenbach says:

Nullius in Verba says:
November 16, 2010 at 1:15 pm

I had a look at the linked reference, and I couldn’t work out what the theory was supposed to be, besides that the appearance of design appears as a result of some variable being maximised or minimised – but besides the many anecdotal statements of relationships that “constructal theory has predicted…” I can’t see where the derivations actually are. How do you determine which variables are to be optimised?

If you have indeed read all of the host of papers given in the very first citation in the head post, and you still don’t understand the Constructal Law, I’m afraid you are beyond any assistance I have to offer.
If you haven’t read all of those papers, and you are still interested, I suggest that you read them. There are also good instructional videos listed there, including Bejan explaining the Constructal Law. Dig in, knowledge is not easily gained …

144. Crispin in Johannesburg says:
November 16, 2010 at 1:02 pm
Each description of a system that eventually sees ‘chaos’ may be described as an order of complexity
Chaos is usually found in the mind of the beholder 🙂

145. Willis Eschenbach says:
November 16, 2010 at 1:17 pm (Edit)
Enneagram says:
November 16, 2010 at 7:45 am
The UNIVERSAL generation of configuration, or the generation of ‘design’ in nature is the FIBONACCI SERIES
The Fibonacci series indeed appears many times in nature, and people have often wondered why. However, the appearance of the Fibonacci Series is a derivable result from the Constructal Law.

Yep, we’ve been getting a lot of Fibonacci numbers turning up in planetary – solar relationships too. Further down the comments in this thread we cover some of the ground.
http://tallbloke.wordpress.com/2010/07/28/gray-stevens-planetary-effects-on-solar-activity/

146. Willis Eschenbach says:

There’s more on the Constructal Law and the Fibonacci Series here, including the mathematical derivations. You folks that want math, you folks that want testable predictions, that citation is a good place to start.
w.

147. Chaos is a fact whenever some intelligent “cancer cells” think they can improve nature’s functioning. Of course Nature has a remedy for that: Enforcing the Law the body dies taking with it those “intelligent’ cells.

148. Willis Eschenbach says:

Mike Hebb says:
November 16, 2010 at 11:37 am

How come this is a Constructal Law and not a Constructal theory or hypothesis having only been around about 14 years when Einstein’s “theory of relativity” hasn’t graduated to the law of relativity in almost 100 years? Is this an example of space time compression?

I suspect that it is a law because of the generality of the application. Gravity applies to all objects the same, whether cows or cannonballs. Similarly, the Constructal Law applies to all flow systems, whether they are flows of water or of information.
The theory of relativity, on the other hand, only gives different answers from our normal Newtonian worldview in special circumstances which most of us never encounter.
That’s my guess, anyhow. YMMV.

149. Joel Shore says:

Willis Eschenbach says:

Here’s a hint, Paul. On this planet, when a man gets awards for the excellence of his work on the Constructal Law both from the American Society of Mechanical Engineers and the American Society of Chemical Engineers, you are not looking at a crackpot scientist nor a crackpot theory … you are looking at a very unusual mainstream scientist whose theoretical work has proven valuable in a variety of fields. On your planet that may be called a “crackpot” … here, not so much …

Just out of curiosity, how would this same sort of logic apply to someone who is an extremely widely-cited scientist in his field, has won awards from a range of scientific organizations and also has a theory that some people think is important and others seem to think of as “crackpot”? I am referring of course to James Hansen (cv here: http://www.columbia.edu/~jeh1/HansenCV_200912.pdf ).

150. Nullius in Verba says:

Hi Willis,
Thanks, but I’ve just had a look at three of those articles/papers and they were all the same.
I appear to beyond help. Thanks anyway.

151. kadaka (KD Knoebel) says:

Ah Willis, it still makes sense, just like it did last year. From the start of flow, the flow rate will increase until it starts to destabilize (turbulence), which will reduce the flow rate. You end up “on the edge” barely below turbulence.
For rivers, at that flow rate, there is an issue of dispersing excess energy. Rivers flow downhill, the gravitational potential energy is transformed to kinetic energy, of which only part of that can be expressed as the water flow at that flow rate. The rest is dispersed during the flowing, mainly by viscous (frictional?) forces that exist between the water and the river channel. Thus the river becomes long enough to lose enough energy by those forces, maintaining the flow rate, and is resistant to changes in that length.
There is another possibility, that may be confusing some people about the Constructal Law, the hard polished path. This is seen in plumbing. Things that can cause turbulence, like edges at joints, will erode away. When possible, features will fill with sediment, as in gaps between parts that extend beyond the straight sides of the pipe (the straight path). The path becomes smoother, capable of higher flow rates. This is seen with rivers that flow over rock, giving us results like the Grand Canyon.
It is ultimately not sustainable. With increased flow rates come increased erosion. Pipes wear through. The river keeps cutting deeper into the rock, basically continually making a new river channel in a downward direction. To note it, erosion is also a method whereby a flowing fluid loses kinetic energy. Then when the fluid escapes the pipe, it will flow downhill at a certain flow rate, obeying the Constructal Law. The sides of the Grand Canyon weather, crack, pieces break off and there are rock slides, the material ends up in the river where it restricts flow and the flow rate decreases.
It’s actually a very simple law to comprehend, well seen in Nature if not in computer models.

152. kadaka (KD Knoebel) says:
November 16, 2010 at 2:04 pm
Things that can cause turbulence, like edges at joints, will erode away. When possible, features will fill with sediment, as in gaps between parts that extend beyond the straight sides of the pipe (the straight path). The path becomes smoother, capable of higher flow rates. This is seen with rivers that flow over rock, giving us results like the Grand Canyon.
It is ultimately not sustainable. With increased flow rates come increased erosion.

When I worked as a design engineer on centrifugal pumps, we took into account attrition rates on the pump casting materials when specifying flow rates.
“How long do you want this pump to last”
“20 years”
“We’ll make it twice as big and spin it slower. It’ll cost 4 times as much as one that’ll last 10 years but performance will be maintained better towards the end of it’s life span”
“We’ll buy two of the smaller faster ones.”
For a while I worked at a refurbing place where I got to pull apart some of the pumps I’d machined the new castings for 10 years previously. The inside of the involutes looked like the surface of the moon.

153. Joel Shore says:
November 16, 2010 at 1:55 pm
I am referring of course to James Hansen

Joel, hahahaha, good one. Lets keep an eye on whose theory is still regarded as important in twenty years time.

154. Willis Eschenbach says:

Joel Shore says:
November 16, 2010 at 1:55 pm

Willis Eschenbach says:

Here’s a hint, Paul. On this planet, when a man gets awards for the excellence of his work on the Constructal Law both from the American Society of Mechanical Engineers and the American Society of Chemical Engineers, you are not looking at a crackpot scientist nor a crackpot theory … you are looking at a very unusual mainstream scientist whose theoretical work has proven valuable in a variety of fields. On your planet that may be called a “crackpot” … here, not so much …

Just out of curiosity, how would this same sort of logic apply to someone who is an extremely widely-cited scientist in his field, has won awards from a range of scientific organizations and also has a theory that some people think is important and others seem to think of as “crackpot”? I am referring of course to James Hansen (cv here: http://www.columbia.edu/~jeh1/HansenCV_200912.pdf ).

Joel, good to hear from you. I’ll let you know how the logic would apply as soon as Hansen discovers a new fundamental law of thermodynamics, or he gets awards from both the American Society of Mechanical Engineers and the American Society of Chemical Engineers … engineers are not impressed by Hansen’s kind of doubletalk. They give awards for real achievements, unlike Hansen’s award from the Heinz Ketchup Foundation, or his Szilard Award for the promotion of physics (not for doing physics, but for “promotion” of physics). That’s an award for PR, not for physics.
See “Bejan number” for another part of what Adrian has achieved. When Hansen starts getting fundamental physical dimensionless numbers named after him, we’ll compare them again.

155. Hansen’s fame will last about as long as the late C20th warming.
How long his infamy will last is anyones guess.
“Who is this guy telling us the sky is falling?”
“Don’t worry about him, he’s just doing a Jimbo.”

156. Willis Eschenbach says:
November 16, 2010 at 3:29 pm
See “Bejan number” for another part of what Adrian has achieved. When Hansen starts getting fundamental physical dimensionless numbers named after him, we’ll compare them again.

Willis, you’re forgetting Hansen’s work on the hyperbolic function.
It’s to do with the amount of hyperbole you can fit into a congressional hearing.
Turns out it’s inversely proportional to the amount of supportable scientific fact.

kcrucible says:
November 15, 2010 at 6:50 pm

Willis:
“That leaves the river shorter. Again the lengthening process continues, until the river cuts through some other bend and shortens again. And as a result, the length of the river oscillates around some fixed value. It is constantly evolving to maximize the length, an ideal which it never attains.”
That’s not really what I’m seeing. I’m seeing a constant attempt to MINIMIZE the length of the river, which fits in with thermodynamics quite nicely. The original elongation was an aberation. Once in the lowest energy state possible between two points (straight line) there’s absolutely nothing to cause it to create additional corners.
The “generation of configuration” in this case is the lowest-energy path between two points. Once it has the optimal configuration there’s no reason for it to change.

All one has to do is look at the number of natural rivers (essentially ALL of them) in that great outdoor laboratory that defy your explanation and you can see that such is NOT the case. A breakthrough will temporarily shorten the length but the river will immediately begin the lengthening process again, with greater vigor, I might add. And certainly, sufficient geologic time has passed for this straighening/shortening to be adequately observed in rivers if that were the base natural state. But again, it is not.

158. Phil. says:

Willis Eschenbach says:
November 16, 2010 at 1:41 am
I’m using “going as fast as it can” metaphorically to indicate that it runs at the limit of the maximization of length. Sorry for the lack of clarity.
Isn’t it actually the cutting of the oxbows which is maximising the flow and the water’s rush towards entropy? Wouldn’t that mean that the turbulence introduced by the medium the flow moves through was somehow neg-entropic?
Flow isn’t being maximized. Length is.

Are you sure, isn’t the river attempting to achieve a brachistocrone profile and thereby maximize flowrate? If at a suboptimal profile it might achieve that by lengthening. If the meandering river is already at the optimum flowrate then shortening it or lengthening it will slow down the flow.

159. concerned_citizen says:

Bejan’s name is misspelled in the intro to this post. Adrian, not Andres.
[Thanks, fixed. ~dbs]

160. Joel Shore says:

Willis Eschenbach:

Joel, good to hear from you.

Likewise.

I’ll let you know how the logic would apply as soon as Hansen discovers a new fundamental law of thermodynamics, or he gets awards from both the American Society of Mechanical Engineers and the American Society of Chemical Engineers … engineers are not impressed by Hansen’s kind of doubletalk. They give awards for real achievements, unlike Hansen’s award from the Heinz Ketchup Foundation, or his Szilard Award for the promotion of physics (not for doing physics, but for “promotion” of physics). That’s an award for PR, not for physics.

Willis,
This reminds me of the old technique of writing job descriptions for jobs that must be advertised but for which there is already a candidate in mind so that only the specific candidate can fill them. You originally made a statement based on general principles but now seem to basically just be setting up arbitrary standards so that the people you like fill them and those you don’t don’t!
Hansen has won numerous prestigious awards from his employer, NASA, as well as prestigious awards from the AGU, the APS, the AMS, and AAAS. But, of course, that won’t be enough because he hasn’t won the specific awards that “People who Willis has decided are scientific revolutionaries and not crackpots” have won or done the specific things that such people have done. (And, by the way, I am certainly not claiming that Bejan is a crackpot. Far from it…I am merely pointing out some double-standards that seem to be applied.)

Phil. says:
November 16, 2010 at 3:57 pm

Are you sure, isn’t the river attempting to achieve a brachistocrone profile and thereby maximize flowrate? If at a suboptimal profile it might achieve that by lengthening. If the meandering river is already at the optimum flowrate then shortening it or lengthening it will slow down the flow.

We assume the elevation difference between two points along a river is fixed, whether the stream is meandering or not–hence the river would have a steeper gradient the shorter it is, reaching maximum gradient in a straight course.
Water flow would be fastest for the steepest gradient; it would be slower for anything less than the steepest gradient. Hence, decreasing the length between two points by straightening the river will speed the river up (it corresponds to the steepest gradient); increasing the length will slow it down (it corresponds to less than the steepest gradient), provided the same volume of water is passing through.
I like to think of it this way: Fast water has more energy to impart on the riverbed, whereas slow water has less energy to impart. An energetic river will quickly form meanders whereas a meandering river does so in a slower fashion until equiplibrium is reached.
This whole theory pretty much destroys those “tipping points” the CAGW folks like to bandy about since “tipping points” violate the Constructal Law.

162. A lot of confusion here. So let’s cut through the cake, since I’ve been struggling with this concept for the past 20 years. In the process I formulated two more useful hypotheses:
1) any (dead) system that derives low quality energy from the environment (like gravity, wind) behaves like a living system. Waves, tides and winds form moving dunes that rise out of the sea and undulate landward. http://www.seafriends.org.nz/oceano/beachgo.htm. It led to the formulation of the six laws that define beaches and dunes everywhere. These ‘new’ laws also make falsifiable predictions.
Likewise rivers meander like snakes do, and something similar is seen in glaciers. Likewise climate and weather may exhibit qualities found in living systems.
Thermodynamics is the logic of dead systems which tend to go towards chaos (=loss of information/quality). But life defies these laws as it also defies the laws of quantum physics. According to physics, life is not possible. Yet it is there, capable of organising itself against the trend towards chaos, because it derives low quality energy (Brownian motion and solar energy) from the environment. It also developed free will, against the tenets of quantum mechanics. So where life is involved, we can expect other (pseudo-physical) laws.
2) I have always wondered why landscapes are so predictable and I formulated the Least Loss Landscapes Law (LLLL) where life organises the landscape for minimal losses. That is losses in life and thus life’s processes and needs (water, nutrients, soil, information, biodiversity, etc.). So life tends to make terraces, deep soils, slow river flows, higher biodiversity, etc.
This law is easy to prove, because any point on the landscape that defies it, will soon be drawn in line by sustained losses, until a new least loss equilibrium results.
http://www.seafriends.org.nz/enviro/soil/erosion3.htm. The law also makes falsifiable predictions, which all appear to be in line with observations.
The confusion about the constructal law of thermodynamics is that it does not sufficiently distinguish between the behaviour of life and that of a dead system. The meandering of rivers is greatly determined by the life in and around it, yet a dead river also meanders, but less so. It does not recognise that the kind of behaviour it predicts, is that found in living organisms. The way it is formulated, does not make falsifiable predictions either. So it is a bit useless.

163. Joel Shore says:

This whole theory pretty much destroys those “tipping points” the CAGW folks like to bandy about since “tipping points” violate the Constructal Law.

So, are you saying that the climate is incapable of rapid changes…or reaching points of instability under some forcing? That’s a pretty strong statement and seems to be at odds with the paleoclimate record.
My guess is that statements like “tippings points violated the Constructal Law” have about as much validity as statements like “the greenhouse theory violates the 2nd Law of Thermodynamics”.

164. Feet2theFire says:

@Willis Eschenbach November 16, 2010 at 1:17 pm:

The Fibonacci series indeed appears many times in nature, and people have often wondered why. However, the appearance of the Fibonacci Series is a derivable result from the Constructal Law. Google “constructal fibonacci” for a host of references.

I have to ask:
Do the Fibonacci numbers themselves appear in nature, or does the Golden Mean appear in nature? They are not quite the same thing.
1,1,2,3,5,8,13,21,34,55,89… Is THIS what appears in nature?
Or is it the ratio 0.618033988… (or 1.618033988…) that appears?
There is a difference.
I’ve never seen anyone else put this out, but no matter WHAT the two starting numbers are in a sequence – if you add each consecutive pair then divide by the first, you very quickly arrive at the 0.681033988… as a limit.
Try it. There is nothing magical about the 1,1,2,3,5,8,13,21,34,55,89… sequence of Fibonacci. Starting with 102367 and 645, you still end up with 0.681033988…
So it is NOT those particular numbers that are incorporated into the ratio – it will be there WITH ALL NUMBERS. That is why it is in nature. It is growth. Growth is adding something – anything possibly – to what exists. Certainly with numbers.

165. Feet2theFire says:

@Floor Anthoni –
Very well thought out comments, trying, it seems, to go to the essence of things and doing it well.
I do see some value in the Constructal THEORY. But no matter what they are calling it, I agree with Mike Hebb that 14 years is WAY too short a time to be calling something a Law.
But I see a close parallel between what you are saying about live and dead systems. I am wondering if the Constructal whatever is actually talking about what MAKES life – which I refer to as an organizing principle. If it IS talking about such a thing (No, Willis, I have not yet had time to read all the links), then something LIKE the Constructal whatever is long overdue, because SOMETHING is working in opposition to entropy and the “deadness of physics.”
I don’t care whatever else comes out of this discussion. I am seeing a glimpse of something pretty deep and involving. Perhaps Constructal is touching on it, but my god, the language is enough to choke William F Buckley.

So life tends to make terraces, deep soils, slow river flows, higher biodiversity, etc.

It is as if all the life is acting in concert, to enhance its own chances of continuity. You are right – physics has no room for life. It is perhaps even at the solar system level that life acts on its own behalf, creating the environment for life. In some ways we haven’t yet considered as part of the process. We are still waiting for a lightning bolt to create life in some muck somewhere – but life is being created around us all the time. Perhaps the claimed universality of this Constructal thingy is attempting to fill that void. SOMETHING DOES.
Entropy was always something I thought, “WTF? There is stuff going opposite of entropy all the time! What are they talking about? And what are they smoking?”

The meandering of rivers is greatly determined by the life in and around it, yet a dead river also meanders, but less so.

I agree. For one thing, show me a straight arroyo or wadi. But the flora around a river affects its meandering, especially when trees fall in and form snags or wash up and protect a meander shore. It is NOT only about maximizing some parameter. In science there is a tendency to believe that the tree fell at random, yet the river washing out its underlying soil means the river itself moved the tree into the flow in the first place.
In some ways Constructal seems to suggest – heavens! – Intelligent Design/Creationism. In other ways it seems to suggest the James Lovelock’s and Liberals’ Gaia. Are we all meeting on the far side of the discussion? hahahaha

166. Feet2theFire says:

Willis –
Nullius in Verba has good points about Hansen and your cherry picking of Hansen’s creds. Here on a climate skeptic site all of us are only too aware of the shortcomings of people who have TONS of papers and awards – and you know it. It is the wrong venue to pull that rabbit out of the hat and wave it around. Here the rabbit’s neck is likely to be wrung out. Enter Nullius in Verba…
One or more papers being correct does not mean that the next one is correct, or wrong, either one. Each one has to stand on its own. There are certainly papers Michael Mann has written that we cannot fault – but it doesn’t make the Hockey Stick any more correct. You are arguing that Bejan’s “Law” is correct – and it may well be. But waving credentials around? Here? Wow! . . Interesting, to say the least.
Better maybe to have gone into the links you’ve pointed everyone to and actually brought back arguments of substance. No one likes it when someone argues by, “Go see the links.” Honestly.
I will go see the links, but not to see how your points pan out. It honestly seems like something that may have expanded science. With all our myriad little improvements in science in my lifetime (excluding computers from that “little” class), we have had a real dearth of big ones. Most of the claimed ones have yet to stand the test of time, at least in my opinion. And I do reserve the right to have an opinion. While many advances in Science have been made, it is also true that few have survived. So, it is with no hesitance that I expect few of today’s “truths”, “laws” “theories” or “hypotheses” to still be standing in 2100. All the scientists of 1875 were as adamant about their state of knowledge as scientists are today, and what good has it done? Modern scientists still ignore almost any findings over 20 years old. How much gets replaced in the next 90 years? And what will that mean about what we accept as fact/true today? Today’s peer reviewed papers – most will be toilet paper by 2100. And the rate they are publishing, they will be as plentiful.

167. Pamela Gray says:

Joel, it isn’t a double standard. It’s human nature to instinctively listen to and follow a person that strikes a chord in your own brain. The trick is to know whether or not you are being led around by a ring in your nose. That includes questioning the nose ring someone else may have put there, as well as your own brain you put there.

168. Willis Eschenbach says:

Joel Shore says:
November 16, 2010 at 4:18 pm

….
Hansen has won numerous prestigious awards from his employer, NASA, as well as prestigious awards from the AGU, the APS, the AMS, and AAAS.

And you are impressed by awards from someone’s employer and AAAS and APS? I guess we live in parallel scientific universes … Hansens’s science is good. But it is not stellar. It is not extraordinary. He is not even listed on the ISI HighlyCited site, and Bejan is in the top 100.
If you can’t see the difference … well, perhaps that’s why you believe so strongly in the AGW hypothesis.

169. Willis Eschenbach says:

Feet2theFire says:
November 16, 2010 at 6:10 pm

Willis –
Nullius in Verba has good points about Hansen and your cherry picking of Hansen’s creds. Here on a climate skeptic site all of us are only too aware of the shortcomings of people who have TONS of papers and awards – and you know it. It is the wrong venue to pull that rabbit out of the hat and wave it around. Here the rabbit’s neck is likely to be wrung out. Enter Nullius in Verba…

There are plenty of people with papers and awards. What Bejan has is achievements that have led to breakthroughs. I respect that more than Hansen’s Heinz Ketchup Award, but you are free to differ …

170. Willis Eschenbach says:

Feet2theFire says:
November 16, 2010 at 6:10 pm

Better maybe to have gone into the links you’ve pointed everyone to and actually brought back arguments of substance. No one likes it when someone argues by, “Go see the links.” Honestly.

I know people don’t like it.
But I don’t like it when people ask questions without first investigating what they are talking about. If you want to be spoon-fed, you’ve come to the wrong place. Either do your homework or move on. I’m not here to force anyone to learn something. If you are interested in e.g. the math of the Constructal Law, as some people have asked about, then all I can tell you is to read the relevant documents so we can have an interesting discussion. This is not a course in the mathematical or other details of the Constructal Law. It is intended as a discussion of the implications of the Constructal Law for climate science.

171. Phil. says:

November 16, 2010 at 4:21 pm
Phil. says:
November 16, 2010 at 3:57 pm
“Are you sure, isn’t the river attempting to achieve a brachistocrone profile and thereby maximize flowrate? If at a suboptimal profile it might achieve that by lengthening. If the meandering river is already at the optimum flowrate then shortening it or lengthening it will slow down the flow.”
We assume the elevation difference between two points along a river is fixed, whether the stream is meandering or not–hence the river would have a steeper gradient the shorter it is, reaching maximum gradient in a straight course.
Water flow would be fastest for the steepest gradient; it would be slower for anything less than the steepest gradient.

Not true, the fastest descent would be down the brachistocrone, not the steepest gradient, it will be slower for any curve not conforming to the brachistocrone.
Hence, decreasing the length between two points by straightening the river will speed the river up (it corresponds to the steepest gradient); increasing the length will slow it down (it corresponds to less than the steepest gradient), provided the same volume of water is passing through.
Since the foregoing isn’t true this doesn’t hold either.

Phil. says:

Not true, the fastest descent would be down the brachistocrone, not the steepest gradient, it will be slower for any curve not conforming to the brachistocrone.

I love your weightless, massless, frictionless explanation regarding a brachistocrone, Phil.
I find the definition of a brachistocrone, or “a curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and is constrained to move along the curve to the second point, under the action of constant gravity and assuming no friction.”
http://en.wikipedia.org/wiki/Brachistochrone_curve
However, you conveniently forget that streams are real world environments with intial velocity, have significant mass, and also considerable friction. Indeed, that’s where it all starts to fall apart, since the definition of a brachistocrone also includes the disclaimer that if the body we’re considering (the stream) is given an initial velocity or if friction is taken into account, the curve that minimizes time will differ from a brachistocrone.
So you can stay in your hypothetical world and believe in brachistocrones all you want. Not me. I’ll take a straight river course with steepest gradient any day–but then, that’s just the engineer speaking.

173. JDN says:

@tallbloke
…if these things bore you, or you feel the odds are too low to bother, feel free to go and get cynical about the next thread along the line. 😉
witty but unfair. I did consider it & I’m not a cynic. I don’t want to be a me-too poster on topics I and everyone else likes. I just read it and move on when I like something.

174. Oliver Ramsay says:

This brachistochrone would appear as a curve to the east or west of a river flowing due south???
Or, is it a curve in the vertical profile of the river? Id est carving a deeper bed in the upper stretch and depositing sediment for a shallower course lower down.
If all that’s being claimed is the latter, then its course would still be a straight line from north to south.
I would love to hear of an actual river that exhibits anything like this characteristic. Even a diagram with dimensions would be impressive.

175. @Feet2theFire –
I forgot to mention that the Constructal law talks about maximising its processes, but what I’ve observed in nature is that it attempts to minimise losses. The two are not the same even though they may have similar outcomes.

176. Malaga View says:

So I guess GDP is like a hot air balloon… you have to keep burning fuel to stay aloft.
This is where the Constructal Law becomes interesting because it facilitates change… usually small variations around the optimum as the flow peaks and trough…. like the bends in the Mississippi river… but sometimes the changes may be more catastrophic – like Hurricane Katrina breeching the levees in New Orleans… so it is important to remember that flow systems are subject to Destructive Events… especially manmade flow systems.
If you take inland transportation, as an example, then the increasing utilisation of fuels has enabled societies to evolve from using horse and carts… first they built canals… then railways… then tarmac roads… and finally airports… this is the evolutionary history of the industrial revolution which has steadily increased the flow of people and goods to every corner of the land.
The point being that it has taken generations for this system to evolve and that, by definition, there is no fallback plan… we drive cars to the supermarkets – not horse & carts… the supermarkets are restocked by road – not railways. The system is only as resilient as its weakest link… this resilience can be counted in days on one hand… so it is always good to remember that our energy dependent society is always only five days away from collapse…. Man Proposes But Nature Disposes.

177. Willis Eschenbach says:
November 16, 2010 at 1:02 pm
Paul Birch says: November 16, 2010 at 4:30 am …
5) I’m afraid that Bejan, in falsely believing he has found a great new organising principle, is indeed promoting something of a “crackpot theory”, and Willis, in attempting to apply that notion to the climate, is falling into the same error.
“Sometimes you guys crack me up. First, Bejan applied the idea of the Constructal Law to the climate, not me, ”
You are quite obviously attempting to apply his ideas to the climate through your own pet theories. I never said Bejan didn’t do much the same.
“More to the point, Bejan has a PhD from MIT and is a full professor at Duke University … … … … [ and more and more ad nauseam)].”
I’m astonished you have the gall to perpetrate so egregious an example of the fallacy of “argument by authority”. The number of PhDs and respected scientists who have promoted “crackpot theories” (your words) is legion. Even the great Newton, Einstein and Galileo were not immune.
As stated, the so-called Constructal Law is not a scientific law. It is not falsifiable, because one can pick and choose what flow variable is the one it maximises. The specific example you gave (that of a meandering river) was false. Rivers do not do what you claim, as many commenters have pointed out to you. Nor does the climate. To treat this vague “organising principle” as a newly established fundamental law of thermodynamics is “crackpot”. At most, it is a potentially enlightening way of looking at old problems.

178. Dave Springer says:

@Willis
“What Bejan has is achievements that have led to breakthroughs.”
I can’t find any specifics on those “breakthroughs”. I even did a patent search which turned up empty. That’s highly unusual in engineering.
Surely you must know some specific practical things that have come about due to these breakthroughs. Please share some examples with us.

179. Spector says:

I believe there may indeed a Constructal thermodynamic principle in nature that perhaps explains why radiation from the sun and the stars eventually caused the construction of all the intricate complexities on our planet, but I am highly skeptical that Adrian Bejan’s wording is the proper expression of the principle of that process.

180. Jose Suro says:

“Willis Eschenbach says:
November 16, 2010 at 12:37 pm
OK, Jose, try this link …
files.me.com/williseschenbach/y1gqp0
It seems they have decided to password protect all my public files … I am very unhappy about that.
w.”
That worked, thanks for your time.
Jose

181. “In an open system, unrestrained by ACOE dikes, erosion from the land surrounding the defined bed and bank river path will creat gulleys and perennial or intermittent streams.
In a straight system, erosion along all sides of the stream should happen equally, maintaining straightness. This is the principle. If areas of erosion differ (hard rock in one section as opposed to soil) then that’s the river reacting to the environment and attempting to find a new optimum.
As described by willis the river WANTS to be as long as possible. BS. The river doesn’t desire to meander. It MAY meander due to the nature of the physical systems and what it runs into, but ultimately the river follows topography. The river WANTS as easy a system as possible to get from a high energy level to a low energy level. The environment change change, causing the optimum path to vary over time, but that’s not because the river desires to be longer and take a circuitous siteseeing path.
It does not WANT to maximize length. If that were true then instead of a single river you’d have an entire landscape covered with streams spreading out in every direction. The construction law is basically a BS rule-of-thumb, that merely observes that order can arise out of even chaotic systems. No great observation there.

182. phlogiston says:

Could Bejan’s Constructal law just be describing the Lyapunov stability of attractors in the phase space of a non-equilibrium non-linear pattern system? Phase space can be almost anything, thus the universality of the statement that “certain parameters are maximised”.
On the other hand, what if attractors are themselves an attractor? One of the outcomes of Lyapunov stability is the unexpected pervasiveness and persistence of emergent pattern at the boundary of linearity and chaos, where Willis states that Constructal law tends to confine a dynamic flow system. For instance why are all coastlines fractal, rather than just a subset of them? Why also do most rather than just some biological structures show fractal and emergent nonlinear pattern? Why do nonlinear interactions between clouds make them more persistent than they “should” be?
There is something there, we are smelling the smoke but maybe haven’t quite found the fire.

183. Phil. says:

November 16, 2010 at 9:00 pm
Phil. says:
Not true, the fastest descent would be down the brachistocrone, not the steepest gradient, it will be slower for any curve not conforming to the brachistocrone.
I love your weightless, massless, frictionless explanation regarding a brachistocrone, Phil.
I find the definition of a brachistocrone, or “a curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and is constrained to move along the curve to the second point, under the action of constant gravity and assuming no friction.”
http://en.wikipedia.org/wiki/Brachistochrone_curve
However, you conveniently forget that streams are real world environments with intial velocity, have significant mass, and also considerable friction. Indeed, that’s where it all starts to fall apart, since the definition of a brachistocrone also includes the disclaimer that if the body we’re considering (the stream) is given an initial velocity or if friction is taken into account, the curve that minimizes time will differ from a brachistocrone.

It will still be a brachistocrone, just a different one (an additional friction term), it will not be a straight line!
So you can stay in your hypothetical world and believe in brachistocrones all you want. Not me. I’ll take a straight river course with steepest gradient any day–but then, that’s just the engineer speaking.
One who ignores the discoveries of Newton, Bernoulli et al., I would hope that most engineers know that a straight channel is not the fastest way to conduct water from A to B. Here’s an illustration for you: http://curvebank.calstatela.edu/brach/Straight2NickForever.gif

184. Jose Suro says:

“Paul Birch says:
November 16, 2010 at 4:30 am
1) The so-called “Constructal Law” is not a scientific law, because it does not state what specific physical property of a system will be maximised or minimised. In general terms, it is a behaviour that can be seen in every conceivable “flow system”, because that is the mathematical nature of variables; in any mathematically definable differentiable process or procedure something (some variable, or some combination of variables) must be maximised (or its reciprocal minimised). In the expression a+b=c, what is being minimised is the difference c-(a+b). This is not some deep quiddity; it’s a tautology.”
files.me.com/williseschenbach/y1gqp0
Paul, read the paper – the link is now open (above). Yes it does, the “specific physical property” can be called Optimal Flow. I think the confusion is coming from the word “maximized” which after reading the paper I believe it to mean “optimized”, and as such it makes complete sense. What I get now is that flow systems, as in heat engines, are constantly “hunting around” for this optimal flow. As such then “optimal flow” is not rhetorical. The earth atmosphere is a perfect analog for testing this because it has all the necessary components, with ample descriptors supplied by other previous studies that can all be expressed mathematically.
From the horse’s mouth (the last two paragraphs – but read the whole paper):
“To see why the constructal law of optimization of flow architecture is distinct from the second law, let us review the essence of thermodynamics. Thermodynamic theory was developed in order to account for the functioning and improvement of heat engines. The first law accounts for the conservation of energy, and serves as definition of energy as a concept. The second law accounts for the generation of entropy (irreversibility), on the one-way nature of currents that overcome resistances, and serves as definition of entropy as a concept.
The first law and the second law account for the functioning of a given (observed, assumed) heat engine configuration. The history of flow systems (e.g. heat engines) shows what the first law and the second law are not covering: the case-by-case increase in performance, in time. Every class of flow systems exhibits this behaviour, from river basins to animals and heat engines. Each system in its class represents a flow architecture. New flow systems coexist with old systems, but persist in time if they are better, while older systems gradually disappear. This never-ending parade of flow systems represents the generation of flow architecture-the generation of geometric form as the clash between objective and constraints in flow systems. This is the phenomenon summarized in the constructal law.”

Paul Birch
November 16, 2010 at 4:30 am
Good Post.
This so called “Constructal Law of Flow Systems” is not a real physical law derived from accepted principles of physics and mathematics, as far as I can tell. There is no mathematical proof of anything.
In fact there are examples where the flow of a river has been altered in a significant way. The construction of a dam can do this. The flow rate of the river will not be the same. A dam can create a situation where evaporation reduces the flow rate of the river downstream.
In fact, the dam analogy is appropriate here because John Tyndall, who discovered the role of greenhouse gases 150 years ago, by measuring the IR absorption of gases, made the analogy that the earth’s atmosphere was a dam which causes the level of water behind the dam to rise. The water level is analogous to the temperature. Arrhenius pointed out in 1896, that the burning of coal would make the dam higher and increase the water level behind the dam.
If we are going to use a river as an analogy this would seem to be the one to use.
Every scientist knows that an analogy is a means of explaining the results of a physical and mathematical theory to laymen, and is not the basis of a scientific theory.

186. George E. Smith says:

“”””” Phil. says:
November 17, 2010 at 6:07 am
November 16, 2010 at 9:00 pm
Phil. says:
Not true, the fastest descent would be down the brachistocrone, not the steepest gradient, it will be slower for any curve not conforming to the brachistocrone.
One who ignores the discoveries of Newton, Bernoulli et al., I would hope that most engineers know that a straight channel is not the fastest way to conduct water from A to B. Here’s an illustration for you: http://curvebank.calstatela.edu/brach/Straight2NickForever.gif
Well why use a two syllable word; when a four syllable one will do just as well .
I’ll stay with Cycloid.
If memory serves me (you guys keep on dredging up ancient memories); it doesn’t matter where you start on the cycloid; or even on the brachistochrone; the time it takes to reach the bottom is exactly the same.
So if you did start with the straight line steepest slope, and the water was able to erode the bottom; we might as well make the material homogeneous, in line with all the other ideals: What shape would the water end up carving out for itself; assuming (another ideal) that it is constrained in the vertical plane ?

187. George E. Smith says:

November 16, 2010 at 9:00 pm
Phil. says:
Not true, the fastest descent would be down the brachistocrone, not the steepest gradient, it will be slower for any curve not conforming to the brachistocrone.
I love your weightless, massless, frictionless explanation regarding a brachistocrone, Phil.
I find the definition of a brachistocrone, or “a curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and is constrained to move along the curve to the second point, under the action of constant gravity and assuming no friction.”
http://en.wikipedia.org/wiki/Brachistochrone_curve
However, you conveniently forget that streams are real world environments with intial velocity, have significant mass, and also considerable friction. Indeed, that’s where it all starts to fall apart, since the definition of a brachistocrone also includes the disclaimer that if the body we’re considering (the stream) is given an initial velocity or if friction is taken into account, the curve that minimizes time will differ from a brachistocrone. “””””
Well I presume that the reason the word “brachistochrone” even exists; lies in that “curve of fastest descent”. (izzat Greek ?)
So the brachistochrone for the zero velocity start, and the frictionless fall happens to be the cycloid. Presumably under other non -ideal conditions the brachistochrone is still a brachistochrone ! Isn’t it ??

188. bubbagyro says:

Interesting dialogs (polylogs?)
I think that we are not dealing with a law, but an example. or corollary to existing laws.
Fick’s First and Second Laws of Diffusion are overriding my thoughts about the Constructal Law. Fick says that diffusion, or trafficking of molecules from one place to another depends on the initial concentration of the particles. The initial concentration is a special example of average chemical potential, or enthalpy of the individual particles, driving things from high to low energy. According to thermodynamics, things move naturally from areas of high potential to low potential. For Fick, that is high concentration to low concentration, and for rivers, areas of high gravity potential to low. On the molecular scale, each particle moves in a random walk, or drunken sailor walk, as has been mentioned above. Since we have trillions of particles, or molecules, these statistically average to marching in a straight line until the chemical potential reaches equilibrium.
What is different here, is that we do not have an almost infinite number of rivers, although they are surely composed of particles, so we do not have a good statistical number to estimate the population (p) of all rivers possible. We only have (n) a singular case. We do not have (p-n) even, but we can approximate what (p) looks like if we imagine a hundred or a thousand rivers starting out spaced a few hundred yards apart. Ignoring coalescence for a moment, assuming each river stays separate, they proceed to the low potential river delta, each doing the random walk. On average, though, they move in a straight line. A Fickian result.
The random walks of droplets on a window pane have also been statistically modeled, [I think in Nature or somewhere recently]. Each droplet meanders like a river down the glass, but eventually each loses potential energy when it gets to the bottom. On average, with a million droplets, these average a sheet of water moving in a straight line from top to bottom.
So why do we call the Constructal Case a Law?

189. Phil. says:

George E. Smith says:
November 17, 2010 at 9:01 am
Well I presume that the reason the word “brachistochrone” even exists; lies in that “curve of fastest descent”. (izzat Greek ?)

Indeed it is, ‘shortest time’.
So the brachistochrone for the zero velocity start, and the frictionless fall happens to be the cycloid. Presumably under other non -ideal conditions the brachistochrone is still a brachistochrone ! Isn’t it ??
Quite so, it’s more difficult to solve but can be done analytically for friction, you end up with the cycloid plus an additional friction term:
x=0.5k^2((Θ-sin(Θ) + mu(1-cos(Θ))
y=0.5k^2((Θ-cos(Θ) + mu(1+sin(Θ))
In the problem of the eroding river bed you referred to I’d expect optimization al la Bejan to tend towards the brachistocrone.

190. Jose Suro says:
November 17, 2010 at 6:25 am
Paul Birch says: November 16, 2010 at 4:30 am
1) The so-called “Constructal Law” is not a scientific law, because it does not state what specific physical property of a system will be maximised or minimised.
“Yes it does, the “specific physical property” can be called Optimal Flow.”
This is not a physical property. It is a subjective quality. “Optimal” means a state that a person prefers. Optimisation is economics, not physics. Rivers aren’t “trying” to flow fast or slow down, or to remove material from the river bed, or even to reach the sea. They just follow the mechanical laws of physics and do whatever they happen to do; even when this process maximises some interesting parameter (such as river length), it is not a universal law; other rivers will do something else, or maximise some other parameter. There is no such thing as an “optimal flow” for rivers – it is a meaningless descriptor, a particularly pathetic case of the pathetic fallacy!

191. Eric J Rees says:

Here is one counter-example which (perhaps) shows that the “Constructal Law” is not generally applicable to all ongoing, finite processes: growth of a protective oxide film on the surface of freshly-cut metal.
The driving force for this process is the free energy of oxidation of the metal. The “current that flows through the it” must be the rate of combination of oxygen with the metal. This rate declines over time (because oxygen and metal are separated by an ever-thickening layer of protective oxide), but does not necessarily tend to zero.
I daresay there is some explanation as to why such counter-examples don’t apply to the “Constructal Law”; and I expect that Warmists would be keen to get there hands on such a piece of reasoning.
By the way, there seem to be quite a few self-citations in Bejan’s paper – does the “Constructal Law” have anything to say about that? Does “flow” (rate of publication?) lead to “form” (having a lot of citations?), because this increases access to the flow (i.e. more self-citations become possible?). I think we should be told.

192. George E. Smith says:

“”””” John Day says:
November 16, 2010 at 8:38 am
@George E. Smith:
> I believe that is what Albert Einstein actually got his
> Nobel Prize in Physics for; not for E= mc^2
Einstein received the Nobel Prize in 1921 for his explanation of the Photoelectric Effect, the elastic scattering of photons by electrons.
http://en.wikipedia.org/wiki/Photoelectric_effect “””””
Well as is typical wiki gets it all wrong again; and you seem to have not even cited wiki correctly.
The photo-electric effect has nothing whatsoever to do with the elastic scattering of photons by electrons.
Long before Einstein it was known that when light (photo-)fell on certain materials; notably the alkali metals, and some others like Selenium; electrons (-electric) were emitted from the metal surface. The more light that shone on the surface, the more electrons that were emitted but the spectrum of emitted electron energies was unrelated to the intensity of the light.
Then it was discovered, that no matter how much the light beam was attenuated, electrons were still emitted and still with the same electron energy spectrum.
Classical explanations for the photo-electric effect were attempted using the electromagnetic wave theory of Maxwell. It was simple to calculate the energy density one would get in an electromagnetic field such as light, and they assumed there was some kind of “work function” that said how much energy was required to eject an electron from the surface. So if you could make some assumption about what that work function energy was, you could calculate how long it would take to absorb enough energy out of an electro-magnetic wave field to cause an ejected electron.
Unfortunately all attempts to demosntrate this by using ultra low intensity light sources, and trying to time the delay to emission, failed; because the electrons; even though small in number were ejected instantaneously; and there was NO measurable (in those days) delay. But it was also shown that light consisting of only longer wavelengths ejected NO electrons; no matter how bright the light source was; but shorter wavelenghts did cause emission, and moreover the shorter the wavelenght the more the electron energy was found to be.
Einstein; who simply hated the notion of a quantum theory; reasoned that the observations could only be explained if the energy was delivered to the material in “packets” rather than as a continuous energy stream, and if a packet of energy was big enough an electron would be ejected immediately, and that any energy left over from the minimum required to get any emission would be manifest in the kinetic energy of the ejected electron; and since that energy incresed inversely as the wavelength of the light; Einstein came up with the Formula E= h.nu as the energy of a wave packet of wave number nu.
Well he didn’t use h; but the constant he postulated ended up being identical to Max Planck’s h.
That is what Einstein got his Nobel Physics prize for discovering.
So far as I know; to this day; nobody has ever devised any Classical Physical explanation for the Photo-Electric effect; even Einstein couldn’t, and it was this failure that led him to accept that energy had to be quantized; as there was simply no other possible explanation for the photo-electric effect; it is entirely a quantum effect.
If you talk to Anna; she uses the particle Physicist’s system of Units where the value of (c) = 1.
Then E= m.c^2, and voilla! (that’s not Greek) Energy and mass are identical.
Well the other part of that system of units is that hbar (h/2pi) is also equal to one.
Then E = h.nu also says Energy = wavenumber ( well they use radians per sec rather than cycles per sec for the frequency; hence the hbar rather than h).
The photo-electric effect is an emission process; not a scattering process. Cesium is a preferrred photo-cathode material for photo-multiplier tubes; but the III-V componds like GaAs and GaAsP are also very efficient photocathode materials; and especially useful for (short) infrared detection (not LWIR).
The commonest IR photo-cathode is the so-called S-1 PC which is AgOCs, and is good out to almost 1100 nm (extreme) but peaks at about 800. Well it also has a UV peak at around 360 nm; but there are much better UV photo-cathodes. S-1 is very noisy and needs to be cooled to be of much use.
GaAs has a relatively flat response going down to as short as 150 nm and as long as 900 with 3-10% quantum efficiency. GaAsP has a smaller spectral range; 150 nm to 750 max, but it has about 20% QE.
NaKCSSb has a very good visible range from about 300 nm up to 850 nm and 25-30% QE.
And some weird materials like CsTe work in the 100-300 nm UV range.

193. Dinostratus says:

This newly named “law” is not “One of the most fundamental and far-reaching discoveries in modern thermodynamics.” Anti-entropy theories have been around for a long time, ever since some physicist mistakenly said “Entropy is randomness”. Their grad students are then surprised as physical laws don’t force everything from order to randomness and believe they’ve discovered some sort of truth.
Physical laws are still physical laws and don’t contradict the fundamental laws of thermodynamics.

194. Jose Suro says:

“Paul Birch says:
“November 17, 2010 at 12:23 pm
Jose Suro says:
November 17, 2010 at 6:25 am
Paul Birch says: November 16, 2010 at 4:30 am
1) The so-called “Constructal Law” is not a scientific law, because it does not state what specific physical property of a system will be maximised or minimised.
“Yes it does, the “specific physical property” can be called Optimal Flow.”
This is not a physical property. It is a subjective quality. “Optimal” means a state that a person prefers. Optimisation is economics, not physics.”
Sorry Paul, I can’t buy that. Did you read the paper? From the tone of your response it seems to me that you have an axe to grind. I don’t. And you’re hung up on the river analogy, which as a matter of fact, is not about rivers, but “river basins”. I won’t get into this any further except to say that: Optimization in nature, as in the universe, is indeed, Natural.

195. Dave Springer says:

@George Smith
“So far as I know; to this day; nobody has ever devised any Classical Physical explanation for the Photo-Electric effect; even Einstein couldn’t, and it was this failure that led him to accept that energy had to be quantized; as there was simply no other possible explanation for the photo-electric effect; it is entirely a quantum effect.”
Conversely, as far as I know, interference patterns cannot be explained by quantum effect. You might be interested in this:
Wave–particle duality of C60 molecules
Carbon-60 (a Fullerene configuration of 60 carbon atoms) is a pretty big chunk of matter yet when fired singly through double-slit apparatus it produces an interference pattern that cannot be explained in terms of the molecule being a particle.
There are more things in heaven and earth, George, than are dreampt of in your philosophy of science.
The trick with understanding electromagnetic radiation is knowing when to treat it like a particle and when to treat it like a wave. A general rule of thumb is to treat it as a wave except when it interacts with matter and then in some circumstances it might act like a particle as in the photo-electric effect. In other situations, like in waveguides and radio antennas, it must still be treated as a wave.
The mistreatment of electromagnetic radiation in atmospheric physics is astounding. The scale and density of matter in the atmosphere relative to the wavelengths of the radiation involved makes it entirely a matter of classical electrodynamics not quantum mechanics. The confusion that results from trying to treat EM as discrete particles in what’s clearly a wave domain is sad and entertaining at the same time.

196. Dave Springer says:

re; constructal law
I’ve got a house with some old plumbing in it. The flow has become restricted due to calcification in the pipes. According to constructal theory the pipes should evolve to optimize the flow so I guess I just have to wait longer and the problem will fix itself.
What a bunch of bullsht.

197. Dave Springer says:

Entropy is a cruel mistress. Dynamic systems can run from it but they cannot hide. Every river will eventually die. Nothing is spared.

198. Dave Springer says:

@George Smith
“I would hope that most engineers know that a straight channel is not the fastest way to conduct water from A to B.”
I would hope that most scientists know that straight channels cost far less to produce than curved channels. Engineering is all about cost/performance tradeoffs.

199. Dave Springer says:

phlogiston says:
November 17, 2010 at 5:44 am
“Why also do most rather than just some biological structures show fractal and emergent nonlinear pattern?”
Cells don’t have fractal shapes. Bi-lateral symetry is quite common and that isn’t fractal either.

200. Jose Suro says:
November 17, 2010 at 5:18 pm
“Sorry Paul, I can’t buy that. Did you read the paper? From the tone of your response it seems to me that you have an axe to grind. I don’t. And you’re hung up on the river analogy, which as a matter of fact, is not about rivers, but “river basins”. I won’t get into this any further except to say that: Optimization in nature, as in the universe, is indeed, Natural.”
The only axe I have to grind here is the the fine-honed axe of truth. The river analogy was directly from the OP, so it is quite appropriate for me to criticise it here. It would also be false even as applied to whole river basins. As for optimisation, it would appear that you do not know (or refuse to admit) what the word means. It is intrinsically a value judgement or preference, the process of approaching a desired goal, not merely something that just happens to be an end result. A physicist can optimise; physics cannot. Physics can only maximise or minimise. Whether that extremum is “good” or “bad” is something physics cannot say. That lies in the domain of economics or aesthetics or morality – the subjective world of persons. It would just about be legitimate to talk of a system falling into an optimal configuration for maximising some variable, but only if you first specify that variable. If you don’t, or if you have to specify different variables for different scenarios, you don’t have a scientific law. One of the signs of a “crackpot theory” is the over-use of such inappropriate, anthropomorphic, language.

201. Ron Powell says:

Second law of thermodynamics: U = Q – W

202. Jimv says:

Thanks Willis, for yet another brilliant post that us laymen can understand. I’ve always been fascinated by meandering rivers and often thought of the jet stream as a river in the sky redistributing energy all over the earth and cleaning up the atmosphere in the process, much like a meandering river cleans up its bed and keeps the ecosystem in the gravel healthy. A river that doesn’t meander is a dead river.
People who fish in deep water lakes often talk of the time in the spring when the lake “turns over”; the water and the fish at the bottom come to the top and the fishing is good. The surface water becomes much warmer. Most people would say that the lake has just warmed up, but in fact, the lake is actually giving up its heat.
I have to think that when the surface of the ocean heats up in some cases it is not a sign that the the waters are heating, but rather the ocean is giving up heat. Counterintuitive, but perhaps worth consideration.

203. Another excellent post Willis, thank you. This really is thinking about things at a fundamental level. Weird how nature always seems to want to form circles.

204. Brian H says:

G.E. Smith;
“and voilla! (that’s not Greek) ”
Nor is it proper French. The correct word is “voilà”. Literally, “look there!”
😉

205. Brian H says:

Dave Springer says:
November 17, 2010 at 5:35 pm
re; constructal law
I’ve got a house with some old plumbing in it. The flow has become restricted due to calcification in the pipes. According to constructal theory the pipes should evolve to optimize the flow so I guess I just have to wait longer and the problem will fix itself.
What a bunch of bullsht.

They will indeed. The pipes will burst or split or crack, and the flow will optimize itself in a new channel through your walls. Enjoy!