Taylor-Goertler instability of compressible boundary layers

The purpose of this paper is to consider analytically how compressibility of a fluid will affect the instability of laminar boundary layers along slightly concave walls leading to the onset of longitudinal vortices. Neutral stability curves representing the relation of the Gortler parameter to the dimensionless wavenumber of the longitudinal vortices and also distributions of the disturbances at the onset of the vortices are presented. The results show that the critical value of the Gortler parameter increases about 1.6 times as the freestream Mach number varies from 0 to 5 in the case of a thermally insulated wall. Effects of temperature ratio (wall temperature to freestream temperature) in cases of an isothermal wall are also discussed.