Numerical experiments in supersonic boundary-layer stability

The three-dimensional (3-D) time-dependent compressible Navier–Stokes equations are numerically solved by a Fourier–Chebyshev collocation method to study the stability of supersonic flows over a flat plate. Several direct simulations carried out in this study suggest the existence of a secondary instability that might provide a route to transition. The interaction of the modes involved in the secondary instability is possibly amenable to a Floquet-type analysis. Pertinent differences between this instability and the analogous incompressible K-type secondary instability are pointed out. Some preliminary results of a 2-D direct simulation of the nonlinear evolution of a second mode perturbation wave are also discussed.