Laminar flow over unsteady humps: the formation of waves

Abstract

Both the incompressible and supersonic laminar flow over a small, unsteady hump are considered. The Reynolds number is assumed large, and the analysis is based upon triple-deck theory. In the incompressible case disturbances tend to grow downstream, as a result of triggering the Tollmien–Schlichting mode of instability. For the supersonic case the flow disturbances tend to decay downstream across the entire frequency spectrum. However, for sufficiently large humps a seemingly catastrophic failure of the governing equations may occur, our results suggesting that this is caused by an inviscid, short-scale, Rayleigh type of instability.