THE STABILITY OF A TRAILING-LINE VORTEX IN COMPRESSIBLE FLOW

We consider the inviscid stability of the Batchelor (1964) vortex in a compressible flow. The problem is tackled numerically and also asympt otically, in the limit of large (azimuthal and streamwise) wavenumbers , together with large Mach numbers. The nature of the solution passes through different regimes as the Mach number increases, relative to th e wavenumbers. At very high wavenumbers and Mach numbers, the mode whi ch is present in the incompressible case ceases to be unstable, whilst a new 'centre mode' forms, whose stability characteristics are determ ined primarily by conditions close to the vortex axis. We find that ge nerally the flow becomes less unstable as the Mach number increases, a nd that the regime of instability appears generally confined to distur bances in a direction counter to the direction of the rotation of the swirl of the vortex. Throughout the paper comparison is made between o ur numerical results and results obtained from the various asymptotic theories.