THE COMPRESSIBLE GORTLER PROBLEM IN 2-DIMENSIONAL BOUNDARY-LAYERS

In this paper the authors investigate the growth rates of Gortler vortices in a compressible flow in the inviscid limit of large Gortler number. Numerical solutions are obtained for 0(1) wavenumbers. The further limits of (i) large Mach number and (ii) large wavenumber with 0(1) Mach number are considered. It is shown that two different types of disturbance mode can appear in this problem. The first is a wall layer mode, so named as it has its eigenfunctions trapped in a thin layer near the wall. The other mode investigated is confined to a thin layer away from the wall and termed a trapped-layer mode for large wavenumbers and an adjustment-layer mode for large Mach numbers, since then this mode has its eigenfunctions concentrated in the temperature adjustment layer. It is possible to investigate the near crossing of the modes which occurs in each of the limits mentioned. The inviscid limit does not predict a fastest growing mode, but does enable a most dangerous mode to be identified for 0(1) Mach number. For hypersonic flow the most dangerous mode depends on the size of the Gortler number.