Mixing length and kinematic eddy viscosity in a compressible boundary layer.

Abstract

The effect of Mach number on the mixing lengths and kinematic eddy viscosities in the turbulent, flat-plate boundary layer has been evaluated. Using the generalized velocities suggested by Van Driest, it was possible to correlate measured boundary-layer profiles, for a range of Reynolds numbers and Mach numbers from 0 to 5, on a single curve. From this correlation, velocity profiles at desired Reynolds and Mach numbers were generated, and the boundary-layer equations of motion were then integrated, using these profiles, to obtain the local turbulent shear stress. The local mixing lengths and kinematic eddy viscosities were subsequently evaluated from the computed shear-stress distribution. The results of this study show that within the Mach number range of 0 to 5 the effect of compressibility on the normalized, turbulent shear stress and mixing length distribution is quite small, in keeping with Morkovin's hypothesis concerning the structure of compressible turbulent shear flow. The kinematic eddy viscosity displays a more pronounced sensitivity to Mach number, but a normalizing length scale can be found such that this sensitivity is all but eliminated.