Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence

Abstract

Obukhov, Kolmogoroff and Yaglom, and in effect (independently) the geologist deWijs, have argued that energy dissipation in intermittent turbulence is lognormally distributed. However, this hypothesis will be shown to be probably untenable: depending upon the precise formulation chosen, it is either unverifiable or inconsistent.The present paper proposes a variant of the generating model leading to the lognormal.This variant is consistent, appears tractable, and for sufficiently small values of the parameter μ, (in Yaglom' s notation) it yields the lognormal hypothesis as a good approximation.As μ increases, the approximation worsens, and for high enough values of μ, turbulence ends by concentrating in very few huge “blobs”.Still other consistent alternative models of intermitt,ency yield distributions that diverge from the lognormal in the opposite direction; these various models in combination suggest several empirical tests.