Direct numerical simulation of distributed roughness induced transition in a supersonic boundary layer

Supersonic boundary layer transition induced by distributed roughness elements is studied via direct numerical simulation. Sinusoidal roughness patterns with different roughness heights are considered. Results show that the sinusoidal roughness pattern generates two types of counter-rotating streamwise vortex pairs in the wake. The stronger one is composed of two vortexes passing through the lateral portion of the last row of sinusoidal humps, and the weaker one is formed by the two vortexes shedding from the center of the sinusoidal humps. The roughness patch with a higher roughness height can induce the complete laminar breakdown to transition. Power spectral and flow stability analysis further identifies several types of instability modes, and the symmetric mode related to the lateral counter-rotating vortex pair is dominant and has a higher frequency. At a lower roughness height, no transition behavior is observed, and the low-frequency antisymmetric mode around each counter-rotating vortex pair becomes dominant and has a much lower growth rate.