In this paper, we linearly investigate the compressibility effects on Gortler vortices, caused by the centrifugal instability along a concave surface, in an adiabatic supersonic turbulent boundary layer. The linear solution for such a problem can be used as an appropriate initial condition in the study of the nonlinear development of Gortler vortices. By using appropriate scaling for a compressible turbulent boundary layer together with Morkovin's hypothesis, the nonlinear three-dimensional parabolic governing equations for Gortler vortices are obtained. The linearized disturbance equations are then obtained and solved numerically using a finite-difference method with deferred corrections. The obtained stability diagrams are presented and interpreted. It is found that the flow becomes less stable as Mach number increases for turbulent boundary layer, this is due to the increase of the density and the effective viscosity destabilization effects as Mach number increases.
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