ON SPATIAL EVOLUTION OF LONG-WAVELENGTH GORTLER VORTICES GOVERNED BY A VISCOUS-INVISCID INTERACTION .1. THE LINEAR CASE

The generation of long-wavelength Gortler vortices is studied in the linear regime by numerically solving the time-dependent governing equations. It is found that time-dependent surface deformations, which assume a fixed non-zero shape at large times, generate steady Gortler vortices that amplify in the downstream direction. Thus, the Gortler instability in this regime is shown to be convective in nature, contrary to the earlier findings of Ruban and Savenkov. The disturbance pattern created by steady and streamwise-elongated surface obstacles on a concave surface is also examined in detail and contrasted with the flow pattern on a flat surface, due to roughness elements with an aspect ratio of order unity. Some difficulties in applying the Briggs-Bers criterion to unstable physical systems of this type are pointed out.