A consequence of the zero-fourth-cumulant approximation in the decay of isotropic turbulence

Abstract

This paper is a continuation of previous work (Ogura 1962a, b) on the dynamical consequence of the hypothesis that fourth-order mean values of the fluctuating velocity components are related to second-order mean values as they would be for a normal joint-probability distribution. The equations derived by Tatsumi (1957) for isotropic turbulence on the basis of this hypothesis are integrated numerically for specific intitial conditions. The initial values of the Reynolds number, There is no evidence of the energy distribution tending to become negative for Rλ = 7·2 and 1·8. It is observed that inertial effects are relatively weak at Rλ = 7·2 and the decay process is largely controlled by viscous effects. For Rλ = 1·8 a purely viscous calculation is found to be adequate to account for the numerically integrated results.