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.
“”””” 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.
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.
“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.
@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.
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.
Entropy is a cruel mistress. Dynamic systems can run from it but they cannot hide. Every river will eventually die. Nothing is spared.
@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.
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.
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.
Second law of thermodynamics: U = Q – W
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.
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.
G.E. Smith;
“and voilla! (that’s not Greek) ”
Nor is it proper French. The correct word is “voilà”. Literally, “look there!”
😉
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!