Influence of two-dimensional smooth humps on linear and non-linear instability of a supersonic boundary layer

Stability of a supersonic boundary layer over two-dimensional smooth humps with their heights considerably smaller than the local boundary layer thickness is studied by using parabolized stability equations (PSEs). Influence of humps on linear and non-linear evolution of first mode oblique wave in Mach 1.6 boundary layers is investigated. Overall destabilization influence of the hump is confirmed for both linear and non-linear cases. For the case of linear stability, an overall effect of the hump on destabilization is found to be similar to the case of subsonic boundary layer. However, in contrast to the subsonic case, considerable increase of growth rates realized in the fore part of the hump is found to contribute significantly to the overall destabilization in supersonic boundary layer. Oblique breakdown is investigated for the case of non-linear stability study. When compared to the case of flat plate, all the characteristic stages of the oblique breakdown are found to appear at a far more upstream position due to the hump. Results of parametric studies to examine the effect of hump height, location, etc. on stability characteristics are also given. Influence of dip instead of hump is also found to be very significant.