A Two-Region Model of the Turbulent Boundary Layer, With Emphasis on Interfacial Conditions

Abstract

Presented herein is a turbulent boundary-layer analysis which is based on a two-region characterization for eddy viscosity. The eddy viscosity for the inner region is described with the usual wall law whereas the outer region, which is characterized by large eddy scales, is treated through an application of Prandtl’s eddy viscosity model for free shear flows. A similarity solution for the outer region is obtained for a linearized motion equation and suitably joined to the inner solution by requiring continuity of shear stress and eddy viscosity. The present matching criteria for the two regions result in the preservation of the velocity profile shape in the defect plane while simultaneously yielding the correct longitudinal development of all layer parameters. It is shown that interfacial conditions are, collectively, the particular feature of incompressible flow which can serve as the point of reference for variable density transformations. A simple, parametric density scaling of the eddy viscosity is employed to demonstrate that the inner layer is much less sensitive to the density variation than the outer region. An improved compressibility transformation, based on ρε = ρ̄ε̄, is advanced.