Nonlinear interaction mechanisms of disturbances in supersonic flat-plate boundary layers

Due to the complexity of compressible flows, nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient. In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers, the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5, 6 and 8 are analyzed by numerical simulations. It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level. The most rapidly amplified 3-D disturbances are Klebanoff type (K-type) disturbances which have the same frequency as the 2-D disturbance. Among these K-type 3-D disturbances, the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher. Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages, the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.