Amplitude-dependent neutral modes in compressible boundary layer flows

The ideas of Benney and Bergeron (1969) and Davies (1969) on nonlinear critical layers are extended, and some new nonlinear neutral modes are computed for compressible boundary layer flow. A special case of the work is when the generalized inflexion point criterion holds. Neutral modes are found for a range of phase-speeds, dependent on the Mach number, and the properties of these are discussed. As in the linear case when the flow is relatively supersonic, multiple neutral modes exist. The behavior of the neutral amplitude in some limiting cases is also considered, and it is found that the results are significantly different from that in incompressible flow when the flow is locally supersonic.