The wall region of a turbulent boundary layer

Abstract

An analysis is undertaken of a nominally two-dimensional turbulent boundary layer in zero pressure gradient. In accord with Yajnik [J. Fluid Mech. 42, 411 (1970)], the well known law-of-the-wall similarity relationship for the mean velocity, Reynolds stress, and turbulence fields in the wall region is shown to be only the leading term in an expansion, the higher-order terms of which are dependent upon streamwise Reynolds number. The asymptotic behavior of the streamwise velocity, Reynolds stress, and turbulence intensities is deduced to leading order for two parts of the wall region, one immediately next to the wall and the other far enough from it for the effects of viscosity to be unimportant. A continuous function is then deduced for the velocity that precisely satisfies and links the asymptotics in each region; the corresponding distributions of Reynolds stress and turbulence intensities follow. Agreement with experiment at high Reynolds number is excellent. No ad hoc turbulence assumptions are made.