Is circulation real?

The final paragraph of the above link is:-
"This historical note is added to emphasize how difficult it was to
understand the motion of a fluid in contact with a solid body. In
the next part we will discuss how the question of boundary
condition at a fluid-solid interface was finally resolved."

Do you know where we could find Part 2?

 

I stand corrected, poor speed reading on my part, my apologies. I will correct the post.

 

here it is.
https://www.ias.ac.in/article/fulltext/reso/009/05/0061-0071

 

Thank you. Anyone interested in the no-slip boundary condition should take time to carefully read this.

 

Thank you.

 

Kind of begs questions of sub atomic aspects of the boundary layer (stresses within molecules, among other things) ? Have to Google that.

so I did, and got this

? Subatomic-Level Solid/Fluid Boundary of Lennard-Jones Atoms: A Molecular Dynamics Study of Metal-Inert Fluid Interface https://www.mdpi.com/2076-3417/9/12/2439

(3.2.2 gets interesting, but mainly in consciously ignoring it)

(4, conclusions, gets interesting, esp last sentence…)

 

Is circulation real?



Deterministic chaos, fractals, and quantumlike mechanics in atmospheric flows https://arxiv.org/html/physics/0010046

 

Very interesting article. I was not able to follow much of the detail and scanned it for the historical references and in particular the conclusion.
It seems that there was a lot of theoretical and experimental research about the nature/existence of the no-slip boundary condition through C18 and C19 which in the end was a bit inconclusive.
When attempting to extract an understanding of the thickness of the no-slip portion from the article, I struggled to interpret his symbol which decodes as "A" in the following quote, and appears to be the mean free path "In air at normal atmospheric temperature and pressure A is 0.065 μm"
But then he muddies the water in this paragraph by speculating on the size of A:
"Maxwell (1879) who has done pioneering work in the kinetic theory of gases, concluded that slip takes place according to the equation of Navier and the length μ/β is comparable to A, and it may be 2A. In the continuum theory A is zero. But in a real gas A is non-zero but extremely small. In air at normal atmospheric temperature and pressure A is 0.065 μm. In liquids it is still smaller. This non- zero but small value of A was where probably one faced the difficulty, both conceptual and practical."

The concluding statement: "It is these collective experimental observations that should give us great confidence in the validity of (the N-S equations and) the no-slip condition at the wall." (my emphasis) comes down on the side of the existence of no-slip condition.

I think he is telling us the the scale of the thickness of the no-slip portion is something smaller than the mean free path.
But, as I pointed out in #497 two weeks ago, that can't be true.
The temperature and pressure of a gas determines the mean velocity of the molecules. The mean velocity can only be zero at 0°K, and at that temperature air will be a liquid or a solid. The wind over my sails is warm air, not frigid liquid/ice.

 

Yes, 3.2.2 is interesting:"If the thermal energy is very small, the fluid atoms may form a perfect FCC (Face Centered Cubic) structure near the surface"
Does this very small thermal energy mean very cold, like near 0°K?
Like I said, the wind over my sail is warm air. That's not a frigid FCC.

 

Nope!

 

I have to spend time doing some maths with this very well explained article... Gosh... It remembers me so much of my courses in Fundamental Physics. But from my fading memories, it just pops out that a macroscopic equivalent of the Heinsenberg inequality can be established for a particular mechanical system, but I cannot remember which.... Have you got an idea ?

A shiver ran down my spine when I saw the diagram representing the geometrical progression of the growth of the circulation in a turbulent eddy. This is Penrose's pavement (1974, non-periodic pavement). In my humble opinion, eddies are the true manifestation of our current mis-understanding of fluid flows. Prantl's theory, Kutta-Joukowsky's theory, Navier-Stokes theory...you name it... All fail at the point where laminar flow conditions no longer applies. Of course, as long as the momentum conservation and mass conservation are respected, closing equations and gauge functions can be found to overcome and replicate the flow turbulence, but without any true explanations of the physics behind, their integration domain are always arbitrary choosen for the values of Lift or Drag to convergence, at the end of numerical iterations. Change a little bit the integration domain of your code and the Lift and Drag values can be very different. How disapointing.

In the other hand, I think that the approach used by the author of this article deserves a particular attention, because it may content a vital clue to get rid of our different conceptualization for laminar and turbulent flows. Great article. Yet I understand how the QM approach may be fertile, even at macroscopic scale.

 

0.01 eV / ps means 1,60218e-19 J / 10E-12 second. So, ok to say that these phenomenon won't occur on your wing. Nevertheless, so much funny phenomenon can be observed at atomic scale .

 

Can you stay focused on the matter at hand. Sailing, theoretical aerodynamics, circulation, no-slip boundary.

 

Yes....Sorry... I think that observations of the Lennard-Jones potentials effects are also to be seen at room temperature. This article makes a zoom on what happens at molecular level. So why not on your wing, as long as you fly in no rarefied pressure region.

I agree there is a kind of elusive jump here, that is opened to interpretation. Still, this article emphasizes the role of the continuum. So, in every situations where this continuum hypothetis can be verified, the non-slip condition given by Navier-Stokes is given at wall surface (null distance). If the continuum hypothetis cannot be verified, for instance when you look at phenomenon at molecular scale AND when the number of these molecule is very low,then this non-slip condition do not apply. Strictly speaking, there is no theories in Physics, only principles and laws, bound to their domain of application. What is referred to in physics as law and theory is man's understanding of physical phenomena. With the advancement of knowledge, man gets closer to the facts, but he cannot understand all the truth. The coexistence of a relevant non slip condition AND an irrelevant non slip condition do not lead to contradiction, as long as their field of application are distincts. The fact that, in a particular domain, the non slip condition is not relevant DO NOT IMPLY that its application in another domain is also irrelevant, and that the principle that applies this non slip condition, in this other domain, is wrong.

This is how I understand this.

 

Ha! That floor reminds me of the Purple Methyl People Eater at MIT Building #1! (Before some mysterious men in black wiped it down and painted over it….). Reading the article I have to admit I had a similar flashback to yours back to my days with Papaliolios (early 70’s) when he would bang me over the head with a problem and I’d know the answer but I didn’t know why, and he’d just grin and we’d get on with it.

Anyway, so much in your reply! I can’t remember the term for it off the top of my head, but the concept of cohesive reverberations at different sizes (states?) radiating (coming into focus?) from an observer’s supposed singular event came to mind reading the article. More general (amorphous?), I’m afraid, than the Heisenberg Inequality. (Although parallel wave clouds appeared and dissipated above the house just a couple of weeks ago, so maybe I’m stuck in the macro?) A von Karman vortex street also popped into my mind’s eye while reading the article. But I had been staring at while listening to a Gabrielli cello Ricercare just before I got on line. Physics for distracted but searching poets/ musicians anyone?

Somebody asked Feynman what he would ask God when he got the chance, and he is said to have answered “why turbulence?”. So, as you’ve pointed out upstream ^ a bit, down here, we smooth things out and some argue how many vortices dance on the head of a pin?

A satisfyingly, meaty article by a very smart woman. I wish I were more awake.