The Favre–Reynolds average distinction and a consistent gradient transport expression for the dissipation

Abstract

Two equation and higher order closures for compressible turbulence fail to capture the compressible wall layers’ log scaling. Accounting for the distinction between Favre and Reynolds averaged variables in the compressible moment equations indicate that turbulent transport expressions obtained using the ‘‘variable density approximation’’ are in error. The error is related to the enstrophy, a Reynolds averaged variable appearing in the equation for the Favre averaged k; recognizing this fact an expression for the transport of dissipation consistent with simple mixing length arguments is obtained. Within the (limited) context of a gradient transport hypothesis a rational form for the turbulent transport of the dissipation is found. Modestly better agreement with the well established compressible Van Driest log scaling is found in a k−ε calculation.