Is circulation real?

The difference is between mathematics and physics.
A "no-slip boundary condition" for air over a sail might make sense in the mathematics of continuous functions, but I just don't understand how it can exist in nature.

 

Physics is all theory. It uses mathematics to represent these theories. Nature is on its own. However, a no-slip boundary indicates a discontinuous function.

 

I’m pretty sure that discontinuous functions do not exist in the nature that we experience. And that explicitly excludes quantum mechanics and black holes.

 

There are discontinuous functions all over the Universe. For example, boundary conditions, which by definition are discontinuous functions. One function covers the behavior between one or two limits. From the limit, a different function covers the new behavior. A good example is the material properties as it changes physical states: ice, water, steam.

 

Can we get back to the core questions?

1. How thick is the stationary part of the boundary layer?
2. (If the no-slip boundary layer is not fundamental aerodynamic theory then) to whose version of aerodynamic theory do you subscribe?
3. Please provide a reference to one or two experiments validating no-slip boundary.
4. Where's a) the theory or b) evidence that the air comes to rest at the interface?

 

You have been provided with references ad nauseam, so I won't add any more. This link to NASA has a basic explanation and the equation to solve the thickness of the boundary layer. We have discussed to exhaustion theories and evidence. All evidence is based on theories, as all science is, and you refuse to accept any theory so we go around in circles.

 

Question 1 is: How thick is the stationary part of the boundary layer?
That has not been answered.

 

2 articles (If I can get them to post…) that I think adds quantum theory into the mix of particles vs flow, much as the two slit quantum experiment shows light to be both particles and waves.

Mathematical problems lurk here, as well as scientific cultures resisting entanglement. But something else to tear asunder?

Here goes…

http://physics.ucsc.edu/~ccrummer/aero1.pdf

hah! There’s one….

damn, can’t get the other one to paste- it concerns triple deck theory, ‘An explanation and understanding of the triple deck theory of aerodynamic lift’ (I think my sleepy memory got close there), Schaffarczyk, Kiel university, not peer reviewed, but some grist for thought if you want to Google it. Apparently some changes have been made since….

 

I have started to read your first reference. Who is C .Crummer? Where was it published? And when?

 

I approached the Crummer paper with an open mind, but on Page 3, encountering :
"Even though these momentum transfers occur only in the boundary layer that appears to be “dragged along” by the surface, they are responsible for the whole of lift and drag.", my ******** antennae started ringing.
And then, on Page 4:"In reality, the fluid particles in a layer around a surface boundary seem to be carried along with the surface", I knew this was a hoax.
He is suggesting that the "particles", (air molecules?) are "carried along with the surface". As we all know from molecular theory, the molecules in a gas whiz around at about Mach 1. He is asking us to swallow the idea that they are slowed down (to zero relative to the surface).
I know I will be roundly criticised for behaving to form and rejecting authorities, but come on @Paul Scott! This is fantasy.

 

Read the link I posted and use the equation.

 

Let's analyze this by your standards. Where is you evidence that that theory is wrong? It has nothing to do with authority, but with being consistent on an argument.

 

Thanks for letting me know you started the Crummer article. I will alert the press.

I did warn that mathematical problems lurk, but that is a hallmark of quantum theory.

Do you consider the dual slit light experiment fantasy?

 

But you didn’t provide the requested details. Who? Where? When?

 

Which one?

I'm just paraphrasing the Kinetic Theory of Gases. It is pretty well established. It is in my high school physics textbook (Nelson & Parker 1958 ).