Prandtl mixing length vs Isotropic assumption
 

Hi:

In Prandtl mixing length hypothesis, which is almsot the background of all zero equation models, the turbulent fluctuataions throughout the whole computational domain are modeled as:

u' =. v' =. l*du/dy (=. is appoximation sign)

But ( u' =. v' ) is exactly the definition of isotropic turbulent.

My question: Does not this a violate the anisotropicicity fact of the turbulent close to the wall? i.e. how the Prandtl mixing length hypothesis justifies the anisotropic turbulent close to the wall?

Thanks for your comment.

MJ

Re: Prandtl mixing length vs Isotropic assumption
 

If this were true, and the only weakness of the mixing length hypothesis, it would be doing pretty well. The mixing length hypothesis is not meant to be any sort of rigorous derivation by any means.

That being said, I think the development is only contingent upon \overline{u'} and \overline{v'} being related by a constant. That constant doesn't have to be particularly small. In fact, it doesn't even have to be constant, since the mixing length is a function of y. You could split off any portion of the y dependence in l and consider it to be part of the relationship between u' and v' if you like.

Bob