Effect of Compressibility on the Growth of Spatially Developing Free Shear Layers

Abstract

In this paper, the effect of compressibility on the growth of a spatially developing plane free shear flow was studied for various values of the convective Mach number. The linear stability equations of compressible shear layers are solved using a direct spectral method. The mapped spectral method (mapped Fourier method) for the free shear flow of the unbounded boundary conditions was employed. Numerical results reveal that oblique modes (3-D modes) are significant in the mixing layer as the convective Mach number M_c increases. Above M_c = 0. 6, the most unstable modes are oblique waves. The unstable modes at M_c. = 0. 6 are found to be characterized by sobsonic and supersonic fast/slow waves. The fundamental eigenfunctions at M_c =0. 3 and M_c = 0. 6 are presented in this paper, whose profiles are affected by the magnitude of the convective Mach number. Finally, we find that the maximum growth rate of the spatial instability mode is approximately proportional to the Pitot-thickness growth rate obtained by Papamoschou and Roshko.