The Boundary-Layer Growth Equation with Reynolds Averaging

Abstract

A local interfacial boundary condition between a turbulent and non-turbulent layer is constructed in a manner that allows local entrainment. The Reynolds average of this equation produces a mean boundary-layer growth rate that contains additional terms not heretofore included in boundary-layer growth models. One of these terms represents the net effect of fluctuating horizontal entrainment and can be absorbed into the usual net entrainment term. The other two terms may become important in horizontally inhomogeneous boundary layers: one represents mean horizontal entrainment across an interface which slopes in the mean, and the other is a divergence of a small-scale horizontal flux of boundary-layer height which presumably acts to smooth variations in the mean boundary-layer height.