Stochastic Dynamical Model of Intermittency in Fully Developed Turbulence

TL;DR

This paper introduces a stochastic dynamical model for turbulence intermittency, deriving explicit velocity increment distributions with power-law tails, validated against experimental data and potentially applicable to other multiscale systems.

Contribution

The paper presents a new hierarchical stochastic model for turbulence intermittency, deriving explicit distributions using hypergeometric functions, and demonstrating agreement with experimental data.

Findings

Distribution fits experimental data well

Power-law tails observed in velocity increments

Model potentially applicable to other multiscale systems

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.