Stochastic dynamical model of intermittency in fully developed turbulence

Abstract

A model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution of velocity increments is calculated explicitly and expressed in terms of generalized hypergeometric functions of the type (n)F(0), which exhibit power-law tails. The model predictions are found to be in good agreement with experiments on a low temperature gaseous helium jet. It is argued that distributions based on the functions (n)F(0) might be relevant also for other physical systems with multiscale dynamics.