Turbulence Approximation for Inhomogeneous Flows: Part I. The Clipping Approximation

Abstract

A modification of the quasi-normal theory is proposed for the study of inhomogeneous turbulent flows. In this approximation realizability conditions for third-order correlations are enforced. These conditions are based on generalized Schwarz' inequalities which limit the growth of triple correlations and the approximation consists in “clipping” these last quantities when they violate their respective inequalities. By requiring that the inequalities be satisfied, we take into account the damping effect of fourth-order correlations. The equations corresponding to this approximation are derived for the case of inhomogeneous turbulence in a Boussinesq fluid with the aid of a recently proposed hypothesis for pressure correlation terms.