Stability of a compressible boundary layer

Abstract

The problem of stability in a compressible boundary layer, as opposed to an incompressible layer, involves many parameters and requires consideration of three-dimensional perturbations. The transverse component of the velocity, the thermal regime at the wall, etc., take on great significance. Investigation of all aspects of this problem requires systematic calculations performed by electronic computers. There do exist a few calculations of stability of a compressible boundary layer with respect to three-dimensional disturbances for particular cases. It follows from those studies (see, for example, [1]) that consideration of three-dimensional perturbations and of the transverse component of the basic flow velocity is important. Many aspects of this problem remain uninvestigated. Aside from the sheer cumbersomeness of the problem, there exist purely mathematical difficulties connected with the presence of a small parameter with higher derivatives in the differential equations for the perturbations, which causes losses in accuracy of calculation. In this present study an algorithm will be developed for solution of the problem of stability of a compressible boundary layer relative to three-dimensional disturbances with consideration of the transverse component of the basic velocity. Calculations are performed for a boundary layer on a plane thermally insulating plate, and the effects of the transverse velocity component and the three-dimensionality of the perturbations on stability at various Mach numbers are demonstrated.