Study of flow transition process induced by oblique wave instability in a supersonic flat-plate boundary layer

The spatial large eddy simulations of the transition process and the full turbulence in a supersonic flat-plate boundary layer at a free-stream Mach number M_∞=4.5 and a Reynolds number Re=10000 are carried out by solving the three-dimensional compressible Favre-filtered Navier-Stokes equations with a hybrid method of a fifth-order upwind compact difference and a sixth-order symmetric compact difference. The compact storage third-order explicit Runge-Kutta method is applied for the time-integration. The sub-grid scales are formulated according to the modified Smagorinsky eddy-viscosity model. Based on the linear stability theory, a pair of the most unstable oblique first mode disturbances is imposed on the inflow boundary and the evolution of flow from laminar transition to full turbulence, is simulated successfully. The instant and statistical parameters are obtained, and numerical results show a good agreement with the relevant flat-plate boundary layer theory. Especially the linear and weakly nonlinear growth of disturbance, the appearance of staggered Λ-vortex pattern, and the evolution of Λ-vortex into hairpin vortex are consistent with related findings in literature.