Our research group works with non-Newtonian density currents generated by high concentration of sediments. Due to rapid deposition and modification of flow characteristics, can not perform spectral analyzes.

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However, as observations and analysis of other studies (recently: Spectral analysis of Newtonian and viscoelastic turbulent channel flows) gives to infer that the law of decay, proposed by Kolmogorov, does not apply in the case.

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But rest assured that leads us to affirm the non-application of decay -5 / 3 spectrum of turbulence is the origin of the theory of Kolmogorov. This theory is based on dimensional analysis has defined the dimensions of the smallest structures from a constant viscosity. In non-Newtonian fluids the viscosity is variable as a function of velocity gradients. The question to be answered is: How can you define a dimension of a microstructure through a relationship with the viscosity which is a function of its own size?

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Thus, we can conclude that it is not possible to employ the theory of Kolmogorov-Oboukhov for non-Newtonian fluids! Analogies, perhaps, but mainly in the region of dissipation, no.

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In the first hipothesis of similarity (The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, AN Kolmogorov 1941), there is a footnote on page clearly says that the scale lambda should be independent from viscosity.

I may possibly not be in the position to comment appropriately and not theoretically enough. The only non-Newtonian fluids I have studied in more depth are polymer melts and especially multi-phase polymer melts (and their solid counterparts). Therefore I somehow doubt (but only intuitively) that the scale lambda should be independant from viscosity - maybe roughly correct for a certain low viscosity range, but beyond some higher range?

What we observe in polymer melts, when turbulence sets off, is a phenomenon called "melt fracture". I believe that is the polymer melt equivalent to cavitation.

also I do not believe that polymer melts will have a real scaling of vortices, but maybe I am wrong - how to analyze?

(in my RG pages, one can find some publications about viscosity and other non-equilibrium phenomena, especially dispersion, in multi-phase polymer melts / systems, if of any interest for the group here)

Bernhard.

What I proposed was made ​​from some test results (which was not measuring the energy spectrum) and also from considerations of fundamental vortices Kolmogorov.

I also made clear that they are initial hypotheses that should be confirmed and enhanced by physical simulations. I think this issue is completely open.

Rogerio and Bernhard.

Excuse my quiteness for couple days, I was on the road.

Thanks for the interesting hints into a completely open region of physics! I will intensively study your papers! Yes, we know almost everything about the extremely small scales (recent Nobel) and the extremely large ones of our world, but don't understand many human-world scale phenomena, seemingly simple things like blood (non-Newtonian), and many other complex fluids which are of industrial ($$$) weight.

Possibly the difference between Newtonian and non-Newtonian dissipation spectra is the behaviour outside the universal (Kolmogorov) range where the character of the friction should become most clearly visible.

Hi Rogerio,

thanks for your interesting advice. Your studies are extremely interesting although non-Newtonicity and stratification are possibly too much of unknowns in one question, I fear. I studied neutrally stratified turbulence for a while and found a purely geometric solution, see http://arxiv.org/abs/1203.5042 (appeared in 2013 in Physica Scripta, may send you a copy if you are interested). I also studied stratified shear flows and found also here a solution - as far as we talk about the laboratory because under geophysical conditions other forces come into the game: the (internal) tides, i.e. the solar system. We can't switch these forces off so that we have a permanent and uncontrollable background mixing. A solution is given here: http://arxiv.org/abs/1207.1633

I am now happy to tell that also non-Newtonian turbulence is no longer a miracle.

However, at present I have not the right to publish details. Bernhard knows why.

But your results sound extremely interesting and I would love to read more about them. If you have published material than please send me copies. All my data you also may find here: www.iamaris.org

Thank you! Helmut.

If dilute polymer solutions are counted as one example of non Newtonian fluids, then the evidence suggests that this viscoelastic fluids exhibit a lot of behavior similar to the Newtonian ones - spectra, structure functions, etc. This is not to say that this example can be extrapolated to all the non Newtonian fluids.