Fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic turbulence

Abstract

A compact expression of fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic, incompressible turbulence is obtained as a function of its invariants and of generic components of the velocity gradient. This single, compact expression is in full agreement with the four different expressions previously obtained by Siggia as functions of the same invariants and of generic components of the vorticity vector and the strain tensor; however, some discrepancies arise with respect to a similar, single expression obtained by Phan-Thien and Antonia. The used algorithm may be easily extended to handle higher order statistical moments of the velocity gradient.

This article may be downloaded for personal use only. Any other use requires previous permission of the authors and AIP publishing.This article appeared in Physics of Fluids 15 (2003) 3434-3442 and may be found at doi:10.10630/1.1613648