Homogeneity constraints on the mixed moments of velocity gradient and pressure Hessian in incompressible turbulence

Abstract

We derive a relation for the correlation between pressure Hessian and velocity gradient in homogeneous flows. This relation provides restrictions to the parameters in the closure models of pressure hessian in velocity gradient dynamics, and together with the Poisson equation, we could obtain an integral expression for the fourth-order moment of velocity gradient in isotropic flows. Furthermore, this relation could be generalized to shear flows, and it is approximately satisfied even in the presence of a shear and of a wall, as occurs in turbulent channel flows.