THE COMPRESSIBLE GORTLER PROBLEM IN 2-DIMENSIONAL BOUNDARY-LAYERS

In this paper the authors investigate the growth rates of Gortler vort ices in a compressible flow in the inviscid limit of large Gortler num ber. Numerical solutions are obtained for 0(1) wavenumbers. The furthe r 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 di sturbance mode can appear in this problem. The first is a wall layer m ode, so named as it has its eigenfunctions trapped in a thin layer nea r the wall. The other mode investigated is confined to a thin layer aw ay 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 w hich occurs in each of the limits mentioned. The inviscid limit does n ot predict a fastest growing mode, but does enable a most dangerous mo de to be identified for 0(1) Mach number. For hypersonic flow the most dangerous mode depends on the size of the Gortler number.