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.
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.
“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.
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.)
As a Non-scientist I have a question. How does this apply to the Jet Stream?
steven mosher says:
November 15, 2010 at 11:19 pm
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”.
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
oops that should have been “Geomorphology”.
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:
J. Hansen, Climate Simulations 1880-2003
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?”
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
Willis,
Can you cite some material that is critical of the Constructal Law, please?
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.
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.
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.
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.
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’?
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!
Thanks, tallbloke, interesting ideas and questions.
tallbloke says:
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.
Flow isn’t being maximized. Length is.
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.
Very interesting discussion.
Could we arrive at a fractal dimention for the process which may give better results in predicting future states.
John Marshall says:
November 16, 2010 at 1:19 am
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
That’s not an oxbow lake. Any geography student will tell you that’s a Billabong!
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)
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!
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?
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: