Local temperature perturbations in the boundary layer in regime of free   viscous-inviscid interaction
  We analyze the disturbed flow in the supersonic laminar boundary layer when local heated elements are placed on the surface. It is exhibited that these flows are described in terms of free interaction theory for specific sizes of thermal sources. We construct the numerical solution for flat supersonic problem in the viscous asymptotic layer in which the flow is described by nonlinear equations for vorticity, temperature with the interaction condition which provides influence of perturbations to the pressure in the main order. 
M.V. Koroteev and I.I. Lipatov
physics.flu-dyn