Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part 1: Pressure distribution. Part 2: Wall shear stress. Part 3: Simplified formulas for the prediction of surface pressures and skin friction

An asymptotic description is derived for the interaction between a shock wave and a turbulent boundary layer in transonic flow, for a particular limiting case. The dimensionless difference between the external flow velocity and critical sound speed is taken to be much smaller than one, but large in comparison with the dimensionless friction velocity. The basic results are derived for a flat plate, and corrections for longitudinal wall curvature and for flow in a circular pipe are also shown. Solutions are given for the wall pressure distribution and the shape of the shock wave. Solutions for the wall shear stress are obtained, and a criterion for incipient separation is derived. Simplified solutions for both the wall pressure and skin friction distributions in the interaction region are given. These results are presented in a form suitable for use in computer programs.