CROSS-FLOW EFFECTS ON THE GROWTH-RATE OF INVISCID GORTLER VORTICES IN A HYPERSONIC BOUNDARY-LAYER

The effects of crossflow on the growth rate of inviscid Gortler vortices in a hypersonic boundary layer with pressure gradient are studied in this paper. Attention is focused on the inviscid mode trapped in the temperature adjustment layer; this mode has greater growth rate than any other mode at the minimum order of the Gortler number at which Gortler vortices may exist. The eigenvalue problem which governs the relationship between the growth rate, the crossflow amplitude and the wavenumber is solved numerically, and the results are then used to clarify the effects of crossflow on the growth rate of inviscid Gortler vortices. It is shown that crossflow effects stabilize Gortler vortices in different manners for incompressible and hypersonic flows. The neutral mode eigenvalue problem is found to have an exact solution, and as a byproduct, we have also found the exact solution to a neutral mode eigenvalue problem which was formulated, but unsolved before, by Bassom and Hall (1991).