# How do Kolmogorov scales work in shear thinning fluis?

My understanding of Kolmogorov scales doesn't really go beyond this poem:

Big whirls have little whirls that feed on their velocity,
and little whirls have lesser whirls and so on to viscosity.

The smallest scale according to wikipedia* would be $\eta = (\frac{\nu^3}{\epsilon})^\frac{1}{4}$

But can I assume the same shear across all scales, and hence (for a shear thinning liquid) the same apparent viscosity?

Update: Maybe I need to clarify my question. I'm not so much interested in the theory as in one real physical phenomenon this theory describes: That there is a lower limit to the size of a vortex for a given flow, and this size can at least be estimated using above equation. Now, a lot of real fluids are non-Newtonian in one way or the other, I'm asking about shear because the apparant viscosity is (also) shear dependent.
While the theory of Kolmogorv may be hard to translate for non-Newton flow, the actual physical phenomenon of an observable (or evenmeasureable) lower limit for vortex size should still hold - are there any measurements or observations?

• Is there any way to make this question more clear? – mart Jul 16 '12 at 8:04
• As I said. The Kolmogorov theory and therefore the minimum size of a vortex does NOT apply to non Newtonian fluids. It is not hard to use it, it is impossible. You can't use a theory in a domain where it is known to be invalid. – Stan Won Jun 19 '13 at 9:00
• So, when the fluid is non-Newtonian, you can have eddies of indefinitly small size? Is that what ou are trying to say? – mart Jun 19 '13 at 9:43
• No. I am saying that the statistical eddy theory which posits a cascade of eddies from L to µ (aka Kolmogorov) doesn't work for non Newtonian fluids. There is no general Kolmogorov like theory for non Newtonian fluids so nothing general is known about scaling and eddy size properties. As viscosity is variable, the behaviour must be studied case by case with Navier Stokes + rheology considerations. For many plastic like non Newtonian fluids there is no eddy cascade at all so the question about their "size" is not even well defined. – Stan Won Jun 24 '13 at 9:03