Stabilisation of first-mode disturbances in compressible boundary-layer flows

The growth of inviscid, subsonic disturbances in an external, compressible boundary-layer flow is linked with the existence of generalised points of inflection in the base flow. An inviscid neutral mode can propagate at a wavespeed equal to the streamwise boundary-layer velocity at the generalised point of inflection, and this neutral mode is adjacent to unstable modes in wavenumber space. This is an extension of the classical Rayleigh inflection point theorem in the incompressible theory. A compressible, flat-plate boundary layer contains a single generalised point of inflection and hence is unstable in the inviscid limit. Under the influence of a favourable pressure gradient and a heated surface, the boundary-layer flow develops a velocity overshoot; the streamwise velocity exhibits a local maximum. This development also modifies the number and location of generalised points of inflection, and hence, the behaviour of inviscid disturbances. In this paper we summarise the linear stability properties of boundary layers with a velocity overshoot and focus on the case where the first-mode disturbance is neutralised.