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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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…..
I think who is the nearest to what really happens with earth’s temperature is WUWT regular Vukcevic:
http://www.vukcevic.talktalk.net/GeoMagField.gif
Instead of massaged temperatures we can measure magnetic fields (and also the other fields).
G.L. Alston says:
November 15, 2010 at 10:55 pm
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.
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:
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?:
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:
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.
A vision of Arte Johnson’s character, Wolfgang, many years ago from Laugh In comes to mind,
“Verrrry interesting.”
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.
k winterkorn says:
November 16, 2010 at 10:15 am
Then you will enjoy:
http://www.scribd.com/doc/42018959/Unified-Field-Explained-9
k winterkorn says:
November 16, 2010 at 10:15 am
Let me tell you: You do not find truth, truth finds you.
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. 😉
“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.
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” 🙂
Need to go out there with a tuning fork..:-)
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?
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”.
😉
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. 🙂
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.
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.
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…
Jack Simmons says:
November 16, 2010 at 4:49 am
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.
Jose Suro says:
November 16, 2010 at 4:11 am
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.
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.
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:
Then Willis added:
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.
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.
Paul Birch says:
November 16, 2010 at 4:30 am
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:
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 …
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?
Enneagram says:
November 16, 2010 at 7:45 am
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:
READ THE BLOOMIN’ CITATIONS! People say “where are the testable predictions”? READ THE CITATIONS.