Normal shock wave-turbulent boundary layer interactions in transonic flow near separation

The problem of a normal shock wave impinging on a flat plate, turbulent boundary layer is considered for the case where the external flow is transonic. Asymptotic methods are employed. It is shown that there are two outer regions, including the outer part of the boundary layer and the external flow, in which inviscid flow governing equations hold, and two regions near the wall, in which Reynolds and/or viscous stresses need be taken into account. The solutions in the outer regions lead to the pressure distribution on the wall, for which an analytical expression is presented, valid under those conditions when separation is imminent but has not yet occurred. The solutions valid in the inner regions lead to a separation criterion.