Statistics of Velocity Increment in Turbulence Predicted from the Kolmogorov Refined Similarity Hypothesis

Abstract

The Kolmogorov refined similarity hypothesis for isotropic turbulence is reformulated from a viewpoint of probability. As a result, the probability density function (pdf) of velocity increment across a domain of a certain scale is entirely related to the pdf of dissipation rate averaged over the domain. With the recent experimental evidence that the ratio of velocity increment and (cubic root of) dissipation rate in the same domain is similar to a Gaussian distribution and with some good models for isotropic turbulence, it can be explained that the pdf of velocity increment varies continuously from Gaussian to stretched-exponential as the scale of domains decreases.