Starting from Head's semi-empirical method for incompressible flow, two approaches to the prediction of turbulent boundary-layer development in compressible flow are explored. The first uses Head's incompressible method in conjunction with a compressibility transformation similar to Stewartson's transformation for laminar flow; the second carries over Head's physical arguments to treat the compressible flow directly. Measurements in supersonic flow, both on flat plates and downstream of an abrupt pressure rise, show broad agreement with the predictions of the second method but do not support the compressibility transformation. In particular, measurements on flat plates reveal that as Mach number increases the entrainment rate decreases to a lesser extent than the skin-friction coefficient. Whilst this result is consistent with the second treatment in this paper, it is difficult to reconcile with any of the compressibility transformations discussed, and the validity of these transformations in turbulent flow is therefore questioned.

Measurements are presented of the reflected wave field produced by a plane oblique shock wave impinging on a turbulent boundary layer at an initial Mach number of 2·5. The outgoing waves are either a single shock, with the same deflexion as the incident shock, or a shock of approximately 10° deflexion followed by a region of compression in which is embedded an expansion fan having the same turning as the incident shock. The transition between these two types of wave field was not studied, but it is fairly abrupt and appears to be closely linked to the onset of boundary-layer separation. The observed wave systems broadly agree with the suggestions of a number of previous workers, but not with a recent theoretical treatment. Surface-pressure measurements and oil flow photographs are used to determine the onset of separation, and from these it is found that the overall pressure rise associated with incipient separation is rather smaller than previous work would suggest.