An invariant representation of mean inertia: Theoretical basis for a log law in turbulent boundary layers

Abstract

A refined scaling analysis of the two-dimensional mean momentum balance (MMB) for the zero-pressure-gradient turbulent boundary layer (TBL) is presented and experimentally investigated up to high friction Reynolds numbers, . For canonical boundary layers, the mean inertia, which is a function of the wall-normal distance, appears instead of the constant mean pressure gradient force in the MMB for pipes and channels. The constancy of the pressure gradient has led to theoretical treatments for pipes/channels, that are more precise than for the TBL. Elements of these analyses include the logarithmic behaviour of the mean velocity, specification of the Reynolds shear stress peak location, the squ..