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.
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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.
Nullius in Verba says:
November 16, 2010 at 1:15 pm
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 …
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 🙂
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/
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.
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.
Mike Hebb says:
November 16, 2010 at 11:37 am
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.
Willis Eschenbach says:
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 ).
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.
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.
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.
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.
Joel Shore says:
November 16, 2010 at 1:55 pm
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.
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.”
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
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.
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.
Bejan’s name is misspelled in the intro to this post. Adrian, not Andres.
[Thanks, fixed. ~dbs]
Willis Eschenbach:
Likewise.
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
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.
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.
Rocky Road:
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”.
@Willis Eschenbach November 16, 2010 at 1:17 pm:
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.
@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.
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?”
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
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.