Spectral link of the generalized Townsend-Perry constants in turbulent boundary layers

Abstract

We propose a minimal spectral theory for boundary layer turbulence that captures very well the profile of the mean square velocity fluctuations in the stream-wise direction, and gives a quantitative prediction of the Townsend-Perry constants. The phenomenological model is based on connecting the statistics in the streamwise direction with the energy spectrum of the streamvise velocity fluctuations. The original spectral theory was proposed earlier to explain the friction factor and the von Kármán law. We generalized it by including fluctuations in the wall-shear stress and the streamwise velocity. The predicted profiles for the mean velocity and mean square fluctuations are compared with velocity data from wind tunnel experiments.