The inviscid compressible Goertler problem

The growth rate is studied of Goertler vortices in a compressible flow in the inviscid limit of large Goertler number. Numerical solutions are obtained for 0(1) wavenumbers. The further limits of large Mach number and large wavenumber with 0(1) Mach number are considered. It is shown that two different types of disturbance modes can appear in this problem. The first is a wall layer mode, so named as it has its eigenfunctions trapped in 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. The near crossing of the modes which occurs in each of the limits mentioned is investigated