Effects of wall disturbances on the statistics of supersonic turbulent boundary layers

In the present study, we perform direct numerical simulations to investigate the spatial development and basic flow statistics in the supersonic turbulent boundary layers at the free-stream Mach number of 2.0 over smooth and disturbed walls, the latter of which enforces extra Reynolds shear stress in the streamwise direction to emulate the drag increment and mean streamline curvature effects of rough walls. Such disturbances escalate the growth rate of turbulent boundary layer thickness and the shape factor. It is found that under the rescaled global coordinate, the mean velocity, Reynolds stress, and pressure fluctuation variance manifest outer-layer similarity, whereas the average and fluctuation variances of temperature and density do not share such a property. Compressibility effects are enhanced by the wall disturbances, yet not sufficiently strong to directly impact the turbulent kinetic energy transport under the presently considered flow parameters. The generalized Reynolds analogy that relates the mean velocity and temperature can be satisfied by incorporating the refinement in modifying the generalized recovery coefficient, and that associates the fluctuating velocity and temperature work reasonably well, indicating the passive transport of temperature fluctuations. The dispersive motions are dominant and decay exponentially below the equivalent sand grain roughness height ks, above which the wall disturbances are distorted to form unsteady motions responsible for the intensified density and pressure fluctuations in the free-stream traveling isentropically as the acoustic radiations.