I agree with you that turbulence in general is problematic. However, there are several procedures and methods to solve turbulence problems. The examples being turbulent flow in conduits, turbulent flow in heat exchanging equipment etc. Even though, several equations are given to solve, still the real problems will be persisting and developing the new solutions is becoming a continuous process.

Certainly something is missed if look carefully into the fine structure of a fluid flow .

For example, there are transverse thin surfaces reflecting white light in inside a growing splash after water drop impact into the quiescent tap water.

May be somebody can indicate another interesting features in "ordinary flows of ordinary fluids"?

The question is actually whether we have today a principle understanding of developed high-Re turbulence under ideal conditions in incompressible fluids.

I.e.: no gimmicks like stratification or complex geometries or even internally structured or non-Newtonian fluids or interaction with sound or complex thermodynamics et cetera, et cetera.

Higher-order phenomena are interesting but we first had to ask the most simple questions, e.g. for the Karman constant in simple turbulent fluids at PLANE walls. I have asked his question in the spirit of the english monk Isaac Newton who e.g. took our planet Earth as a point mass: a typical idealization which is standard in physics today and used by Maxwell, Einstein and many others. When these colleagues presented their equations, did they solve all the problems of gravitation or electricity? Not at all, the contrary is true.

I also elaborated an idealized theory of turbulence which is based on old ideas of Lord Kelvin (= Willliam Thomson, 1867: "On Vortex Atoms"), of Anrej N. Kolmogoroff (1942: "Equations of turbulent motion of an incompressible fluid"), and on a newer work by Hans J. Herrmann (1990: "Space-filling bearings"). I only took these pieces and added sort of "dipole chemistry" to find an astonishingly simple description of turbulence as far as the above questions are concerned. This theory will hopefully be called KKHB (2005, 2011, 2013) and gives five elementary non-trivial features of developed turbulence without any empirism or parameterization: (1) the Karman constant, (2) the spectral prefactor of the frequency spectrum, (3) same for the wavenumer spectrum, (4) the decay exponent of the turbulent kinetic energy and (5) the decay exponent of the r.m.s. vorticity --- all astonishingly close to the observations/measurements.

Actually, now we have what smart brains have searched for more than 100 years and longer. If I am irror, dear colleagues, correct me please! Applications of the idealized picture mentioned above were published for the non-Newtonian case, which implicitely contained finite Reynolds numbers (rather than Re=\infty as in the original KKHB theory) and has recently been elaborated by Chinese colleagues, adding an approach to an understanding of intermittency observations (still to come). I personally am planning to apply the theory to the problem of curved surfaces and namely to the case of pipes Princeton superpipe and namely in Cottbus/Brandenburg, the CoLa pipe.

Dear Yuli D. Chashechkin , you surely have insight into other such pribory (experimental pipes) where data might be available, and any hint is welcome!

I personally leave the much more complex topics of fluid dynamics to the smarter brains of your institute or to APS DFD heroes and prefer to quote Lew Landau (may be it was Lifshitz rather than Landau ?) who still stated in their 6-volume textbook series on theoretical physics that a theoretical derivation of the Karman constant is impossible and only measurements can make it. This indicates a more general problem in the "physics sciences business" in some countries: fluid dynamics is taken to be too trivial to count seriously. Last year Katepalli Sreenivasan consequently mentioned on the BACKPAGE of APS News 6/2018 something sensu that "we" were on the moon ... but ordinary pipe flow is still a general issue. And APS has its DFD and has got nice support, at least in the past! Courtesy does actually not allow to talk about Germany whereby the country actually has contributed heroes like Euler, Helmholtz, Prandtl, Karman, et alii to the field, but in a distant past. I better stop my walk about a mine field here but would like to add a serious statement by Falkovich & Sreeni (2006) that "The diversity of problems in turbulence should not obscur the fact that the heart of the subject belongs to physics." And here I come back to the "list of unsolved problems" mentioned at the beginning of our debate by Jouni Jokela: The original text of question #3 under Condensed Matter posed by John Baez was: "How can turbulence be understood and its effects calculated?  One of the oldest problems of them all.  A vast amount is known about turbulence, and we can simulate it on a computer, but much about it remains mysterious." A very good question, and the answer is : KKHB (2005, 2011, 2013). The answer is not to spend another century on speculations/manipulations of aspects of the Navier-Stokes eqns. Hugh! ( :--)))

Maybe the problem is that for turbulent flow we have an equation of motion but no probability distribution for the fluctuating velocity. This can be checked by rederiving the hydrodynamic equations from statistical mechanics of the fluid as a cloud of molecules. It can be argued that in this case the velocity variable, if the flow is turbulent, is already the mean velocity. The resulting equation shows a nonlinear dissipation force; in linear approximation, the Navier-Stokes equation is rederived. In its present form, the equation is for small Reynolds numbers only, just outside the Navier-Stokes regime. Moreover, it is for flow with no boundaries. Unlike laminar flow, boundaries will change the form of the equation; this problem is still unsolved.

Only to explain the universality of the problem, I attach a note by Feynman and two actual talks by a Chinese colleague to illustrate the further way to go.

Dear Sirs,

Thank you very much for all these Contributions.

Dear Yuli D. Chashechkin Again I read with great interest your few words. I would be very happy if you could share some picture about this observation, as I believe you are now the first one, who also sees that a reflection of a light is a proof for existing surface inside a fluid. My own observations about "ordinary flow's of ordinary fluids" are mostly in Youtube. This play of vortex-shades is one I consider the most beautiful.

https://www.youtube.com/watch?v=hiye-tTpibw&list=PLgUc9kJnDMMExJivT2dWh9dAjdYYUgOFE&t=0s&index=8

Here is the same vortices visualized better with a color-dye;

https://www.youtube.com/watch?v=iXfkaFmpnL4&list=PLgUc9kJnDMMExJivT2dWh9dAjdYYUgOFE&index=20

At 5:20-> in this video there is somehow visible, how the color and it's shade in the river bed are actually creating the picture, and the most interesting thing, that the surface is actually very smooth.

Dear Helmut Ziegfeld Baumert

With great interest I read your "dipole chemistry" but due to my complete different approach-angle to the issue I currently can't follow it completely. If the Answer is KKHB, then what does it predict? With plane walls you have a smooth solution and the closure is not a problem no matter what is the velocity? Ok, but this must be similar like the case described by Juergen Piest describes, as isn't about the same if there are no boundaries, or if there are plane walls?

I also want to thank you for your second comment, as it made me thought about this pipe flow.

In my mind I combined

1. this old MIT-video;

https://www.youtube.com/watch?v=1_oyqLOqwnI&list=PLgUc9kJnDMMExJivT2dWh9dAjdYYUgOFE&index=13

(from 8:00 to 8:20)

2. the words of Feynman "What we really cannot do is deal with actual, wet water running through a pipe"

3. This Q&A from physics stackexchange which I have written open;

https://physics.stackexchange.com/questions/227309/air-core-vortex-physical-explanation-of-the-air-entrainment-hook-at-f-co-0

4. The Letter which I wrote to Prof. Andreas Malcherek to München about the Torricelli -factors, related to his article in "Wasserwirtschaft 7-8/2016"

The sad thing is I don't have the copy of this letter in hand. But the idea in it was, that I was able to calculate the exact loss-factor of such a (pipe) flow out from tank directly with the math which is presented here;

Data Navier-Stokes existency and smoothness problem, -The Answer (word-txt)

And now I just thought this further, and this obviously means that if the "dead-points" of the flow is reduced and the flow velocity is calculated like shown in 3. then it's actually also possible to calculate the 2. and all this without (almost) any relation to Reynolds number (surface roughness) like said in 1, but yet with all possible boundary shapes and forms similarly like I already did in 4.

...Interesting...

Dear Jouni Jokela , you wrote

"If the Answer is KKHB, then what does it predict?"

Well, it predics

(i) the Karman constant,

(ii, iii) the two pre-factors of both spectra and

(iv, v) the two decay exponents (the latter for the freely decaying developed turbulence) - all this in nice agreement with data. There is no other study which gives us such consistent picture of turbulence. Need to mention that the party is not over, similarly like in electrodynamics or quantum mech the party just began when their fundamental eqns of Maxwell and Schroedinger were discovered. Now we have KKHB and the party may just begins and one of the next steps is who John Z. Shi has recently presented, and Princeton superpipe and/or Cottbus' CoLa-pipe are the next (see https://books.google.ru/books?id=7OywCwAAQBAJ&pg=PA216&lpg=PA216&dq=Cottbus%27+CoLa.&source=bl&ots=IHUZ65T0Hn&sig=ACfU3U1adF19S_6IgzpBjcukjIfK0APWyg&hl=de&sa=X&ved=2ahUKEwiOip3sjIXhAhWRr6QKHVauDb8Q6AEwC3oECAIQAQ#v=onepage&q=Cottbus'%20CoLa.&f=false).

Besides, we need to classify or discriminate the notions in our debate. If I talk about turbulence, I always mean not the multitude and beauty of phenomenae where low-Re number turbulence plays its important roles like e.g. in air flights or

in paintings by Van Gogh (https://de.euronews.com/2015/01/30/das-leben-van-goghs-als-gemalter-film)): I mean exclusively developed high-Re number turbulence in larger fluid volumes, much beyond the critical Reynolds number. THIS branch of science since long missed a closed theory answering the above most simple questions (i - v).

Thank you for hinting again at optical phenomenae related with turbulence. Maybe it was Archimedes who was the first to sketch a vortex dipole ? The Greek were great seamen like Celtic people too ...

Dear Mr. Jokela,

in Fig. 8a in paper:

Чашечкин Ю.Д. Капли: короны, всплески, звуки… // Природа. 2016. № 11. С. 13-23.

Chashechkin Yu. D. Drops: crowns, splashes, sounds // Nature (Priroda, Russia). 2016. No.11. P. 13-23. (In Russian).

one can see bright transverse reflecting surface separating upper cylindrical part of the the splash jet (dark) and low conical part of the jet covered by banded envelope.

I did not described this flow component in details in the paper but especially select to print this photo taking in mind intention to inspect this phenomenon more carefully, but "the hands did not reach." Maybe circumstances and your interest will help come back to the further study of this flow component...Original photo is attached.

With best regards,

Yuli D Chashechkin

Sorry, cannot attach photo but can send personally.

Yuli

Dear Sirs,

It's seems that the very foundation must be laid to this interesting conversation.

I can easily adapt some other meanings too, but when I talk about "Turbulence", I mean the same as ie the wikipedia;

"turbulence is any pattern of fluid motion characterized by chaotic changes in pressure and flow velocity."

I also prefer the "syndrome" discription of the old MIT video linked above at it's beginning (@2:57);

1. Disorder

2. Effcient Mixing

3. Vorticity

This approach actually already tells us few physical things about Turbulence;

1. Disorder; tells us that turbulence is not reproducible in detail, so there must be similar aspects in play as in Kinetic gas. Particles are moving very freely.

2. Efficient mixing. This also tells us the same story; the material is not attached to each others, and the molecules can choose their positions freely.

3. Vorticity; This is interesting, as it tells us the opposite. According to wiki-definition, vorticity is local spinning motion of a continuum near some point. This spinning must include multiple molecules, and it must mean that these molecules are attached to each others. In the case of rigid body vortex, they rotate like a solid object. And in the case of irrotational vortex, these particles move like in laminar flow.

This is my basic approach to this issue;

Why disorder?

Why Mixing?

Why Vorticity?

Dear Helmut,

So you are basically talking about the concept of Boundary layer. (Karman constant)To me this concept is another simplification about the reality. It might be mathematically sound and mostly agree with experiments. But what is the true physical background behind this concept? I mean if we think a single atom/molecule in fluid. How do they know where do they belong? This is the same question Feynman made about cold welding; single atom have no change to know which object do they actually belong.

When I think this there are practically two basic options;

1. Atoms are bound together in organised predictable and irreversible manner, (solid matter, fluid in laminar flow)

2. Atoms are not bound together, and all interactions are based on collisions, meaning chaos and irreversibly. (Ideal gas)

And then there is this "in the between" of these two basic options, but for a single atom, what could that possibly mean? Can there really be any other options besides these two, for a single atom?

Your results must be telling us something interesting about this. But what?

Dear Yuli,

Thanks for sharing this beautiful picture 8a in high quality;

Article Чашечкин Ю.Д. Капли: короны, всплески, звуки…Природа. 2016. ...

...Now I even found this paper from your collection; hope the link works!

I don't consider the white transverse "collar" as a surface. (This picture must be done without a ink?) Because Surface is also a point of a broken continuity.

Rather I consider this picture as a verfication of my previous thoughts about water vortex and the surface between it and it's surroundings. Here I have made a contribution about it;

https://physics.stackexchange.com/questions/190414/the-optics-of-vortex-in-water-why-there-is-a-bright-ring

There in my question is a three pictures-serie, and the third shows the bright ring which I mean here. The first shows how the surface deformation deflects light in the middle and makes the shade. The second shows how this deformation makes a neutral shade. But the third shows how the surface inside the fluid collects all these reflections and makes them parallel. This was easy to observe, as though the shade were mostly there. This "light goes on" at the same moment when the vortex rotation stabilizes it self.

So your picture shows this same water pillar standing alone, without the surrounding water.

.... But I don't bother to write this all here again now, because this beautiful picture has even more...

Below this collar there can be seen like vein's. White lines like roots. And these I do consider as a "broken fluid", or at this case the water is like a drawn wire, and this single water "wire's" are separated from their neighbours...

I think I just open a beer now, and just enjoy the beauty of the nature in it.

Edit:

...forget to say; I also see the pattern of these transversal vortices on the surrounding waves, and also on the splash pictures of your paper;

https://www.youtube.com/watch?v=EVbdbVhzcM4