Abstract
The stability of supersonic boundary layer flow on a semi-infinite flat plate and the growth of Tollmien-Schlichting waves are investigated numerically. At a Mach number of 2.2, the two-dimensional periodic disturbances are introduced into the flow as the upstream boundary conditions and the boundary layer response is studied by directly solving the 2D Navier-Stokes equations using a TVD scheme. The suitability of the numerical method for the investigation on the stability and the initial growth of disturbances is demonstrated for small amplitude fluctuations. The numerical results are shown to be in close agreement with linear stability theory. Furthermore, using the present direct simulations, we find the non-parallel flow effects to cause the profiles of disturbances, especially the streamwise velocity fluctuations, to deviate slightly from those obtained from the linear stability theory.
