Stochastic Dynamical Model of Intermittency in Fully Developed Turbulence

Abstract

A novel 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.

10 pages, 2 figures. To appear in Physical Review E