Direct numerical simulation of the transition to turbulence in a supersonic boundary layer on smooth and rough surfaces

Direct numerical simulations of instability development and transition to turbulence in a supersonic boundary layer on a flat plate are performed. The computations are carried out for moderate supersonic (free-stream Mach number $\mathrm{M}=2$) and hypersonic ($(\mathrm{M}=6)$ velocities. The boundary layer development is simulated, which includes the stages of linear growth of disturbances, their nonlinear interaction, stochastization, and turbulent flow formation. A laminar-turbulent transition initiated by distributed roughness of the plate surface at the Mach number $\mathrm{M}=2$ is considered.