There is a new theory making previous "models" obsolete -- but only if we talk about asymptotically high Reynolds numbers, Re -> infty. See attachment. A solid approximation of this theory for finite Re has just been presented orally at the IEEE 2014 in Tallinn, last week.

Sum paper about this question I putted in Attachment. Main feature of this closure,- Ri critic does not exist.

Nathan made an important point: In the context of stratified fluids there is a certain (variable) co-existence of turbulence and waves. As (ideal) waves are non-local and turbulence is local, we have problems to get a simple local theory like in the non-stratified case. However, if we have no turbulence at all and only a stochastic field of weakly dispersive waves, then we would also expect a sort of mixing. I.e. while the neutrally stratified case is more or less trivial, the challenge is the stratified case where in the geophysical case (oceans, atmospheres) the forcing is governed by internal tides and  thus of long-wave character.

Truth Helmut. In very close time wee will publish our new results about theory of energies transport by long-wave  buoyancy  wave, which can create turbulence without any wind.  

On the principle of independence of the boundary conditions of structure direction of turbulence

Lu Panming

Abstract

This is an introduction to the turbulence modeling theory of the present author, which can take the boundary conditions of turbulence structure into consideration ( the main contents have either not been published in normal journals or only published in chinese papers).   It is included that： (I)。Difficulty Problems Encountered in “Second-Moment-Closure” turbulence modelling ，i.e.  “Gao-Ge Anomaly” ;  (II)。The improvement  to the ”Second-Moment-Closure” turbulence modelling in order to allows the boundary conditions of turbulence structure direction could be prescribed;  (III)。An explanation to the principle of  independence  of  the boundary conditions of

turbulence structure direction ;  (IV)。Six suggestions to the possible future work directions;  (V)。 An explanation to the ”Gao-Ge Anomaly”.

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4. The principle of the independence of the boundary conditions is not only to the turbulence modelling, but also suitable to the other subject, because it is frequently meet the equations are not easy to solve, so there is often a need of modelling or predigestion.  For example, both the D‘Alembert anomaly (~1752) and the Stokes anomaly (~1856), are due to breach the  principle of independence  of the boundary conditions, according to today`s point of view .This is because, first, by using the inviscid potential flow`s dynamic equations it is not possible to affiliate the slip-less condition of the real fluid at the wall, and  second, using the Stokes equation it is not possible to affiliate the boundary conditions both at the wall of cylinder and at the infinite to the cylinder.  The first anomaly lead to the discovery of the Prandlt`s boundary layer theory（1904）, and the  second anomaly  was solved by Oseen（1910）with introducing a modification. All these reflect the scientific worthiness and broad latency of the present principle   of the independence of the boundary conditions.

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above is an example paragraph,for more details or need the full text, please go to the end of this letter, where will be an web address existed.

http://staff.ustc.edu.cn/~pmlu/ 

nathan, r u afraid of the work of alexander babanin of turbulence generation of long waves? I am interesting in this work I will be in Israel at the Technion and Tel Aviv University. Cheers

panming u work is very interesting have u considered code it up in openfoam, which I found is a good platform?

Dear Panmin, 

I couldn't get an english version of your text  as PDF or WORD from http://staff.ustc.edu.cn/~pmlu/. But this only as an aside.You should check this point if you wish to become known in the community.

The solid wall in turbulent flows is most easily understood when you take the picture I derived in the paper attached earlier and COMBINE it with a laminar low-Re friction layer of size delta - just in the  spirit of Ludwig Prandtl. (He still knew it but all the todays "turbulence modellers" are missing the solid grounds of physics. They know math, delphi and fortran, but (as Sreenivasan once mentioned): "The diversity of problems in turbulence should not obscur the fact that the heart of the subject belongs to physics." Indeed!

What you could wish do is: take my mechanical picture of turbulence (attached again) with the rotating spaghetti dipoles as elongated particles, and combine this picture for near-wall boundary with a laminar viscous fluid wherein all topics including inner-frictional vorticity loss, heat conduction up to turbulent mixing and intermitteny are correctly predicted without modelling - simply new arrangement of more or less classical knowledge. (If you wish consultations on this topic you may contact me directly. I worked for a company in China...) You'd be welcome as I see that you have a solid background which here "in the West" not all students have today: you still know D‘Alembert, Stokes, Prandtl ...

above is the web address of my paper .