Generation of supersonic flow disturbances by a two-dimensional surface roughness in a turbulent boundary layer

We investigate the generation of disturbances in a supersonic wind-tunnel flow by a two-dimensional surface roughness element located on the test section wall. The study focuses on the case where the roughness height is small relative to the thickness of the on-wall turbulent boundary layer. The investigation combines numerical simulations, which resolve the turbulent boundary layer, and experimental measurements using hot-wire anemometry. We examine the effects of the roughness height and width, as well as the flow Mach number, on the generated flow disturbances. The results show that the presence of the two-dimensional roughness induces a stationary N-wave disturbance in the freestream, accompanied by a region of elevated unsteady fluctuations across a broad spectrum. An increase in roughness height is shown to amplify the disturbance amplitude and enlarge its spatial scale. For small roughness widths, the freestream disturbance maintains an N-wave profile. As the width increases, the disturbance amplitude remains constant, but the N-wave bifurcates into two distinct shock waves. Finally, we compare the spatial scales of the mean-flow disturbance for a fixed roughness geometry at Mach numbers of 2.0 and 2.5.