Nonlinear Stability of Supersonic Nonparallel Boundary Layer Flows

This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations (NPSE). An accurate numerical method is developed to solve the equations and march the NPSE in a stable manner. Through computation, are obtained the curves of amplitude and disturbance shape function of harmonic waves. Especially are demonstrated the physical characteristics of nonlinear stability of various harmonic waves, including instantaneous stream wise vortices, spanwise vortices and Λ structure etc, and are used to study and analyze the mechanism of the transition process. The calculated results have evidenced the effectiveness of the proposed NPSE method to research the nonlinear stability of the supersonic boundary layers.