The outer region of a turbulent boundary layer

Abstract

Matched asymptotic expansions are used as a framework from which to derive differential equations that describe the mean velocity and turbulence fields in the outer region of a zero-pressure-gradient turbulent boundary layer. Attention is focused upon solutions to these equations in the very outer region or superlayer, where the boundary layer merges with the outer flow. It is found that both the velocity and turbulence fields approach their free-stream values exponentially fast as Townsend [The Structure of Turbulent Shear Flow (Cambridge U.P., Cambridge, 1976)] had foreseen, but not necessarily in the detailed manner he conjectured. These details are used to help construct approximate solutions for the mean velocity and turbulence fields in the outer region that display the correct asymptotic form both in the logarithmic region and the superlayer. The resulting solution for mean velocity is closely in accord with Coles’ law of the wake and accurately reproduces data over the complete Reynolds number range for which the boundary layer is turbulent; likewise the profiles for the turbulence intensities. It is further shown that the turbulence intensities conform to a law analogous to the law of the wake.