THE LINEAR EVOLUTION OF CENTRIFUGAL INSTABILITIES IN CURVED, COMPRESSIBLE MIXING LAYERS

The linear development of Gortler vortices in a curved compressible mi xing layer is studied. It has been shown both experimentally and theor etically that the curved mixing layer can support a centrifugal mode, which is believed to be similar to the Gortler vortex mode. This study follows the corresponding incompressible study of Otto, Jackson, and Hu, and attempts to demonstrate the effects compressibility has on the growth of such modes [J. Fluid Mech. 315, 85 (1996)]. The ultimate do wnstream fate of the modes is studied in the high Taylor/Gortler numbe r regime. The problem of the third boundary condition inherent to the mixing layer model is addressed using the set of boundary conditions f or both subsonic and supersonic flows derived by Ting [J. Math. Phys. 28, 153 (1959)]. A class of modes is discussed that have no counterpar t in the uniform temperature incompressible case. (C) 1997 American In stitute of Physics.