REFLECTION AT A LAMINAR BOUNDARY LAYER OF A WEAK STEADY DISTURBANCE TO A SUPERSONIC STREAM, NEGLECTING VISCOSITY AND HEAT CONDUCTION

Abstract

A perfect gas, with constant specific heats and zero viscosity and thermal conductivity, is considered to flow in a steady two-dimensional pattern which is only slightly disturbed from a basic flow parallel to a solid plane wall. The Mach number of the basic flow varies continuously and monotonically from zero at the wall to a supersonic value at a distance δ from the wall, beyond which it takes this supersonic value uniformly. The disturbance is considered to be due to a weak stationary simple plane wave incident on the ‘boundary layer’ from outside. The streamline pattern and pressure coefficient distribution, resulting from a given incident wave, are found to depend only on the Mach number distribution in the basie flow (not on the individual velocity and temperature distributions). Any singularity in the incident wave is propagated along characteristics in the supersonic part of the layer (increasing in strength) and is reflected from the sonic line modified in character. Thus a discontinuous increase (in pressure or pressure gradient) is reflected as a positive logarithmic infinity of the quantity (which result of a linearized theory may correspond to a ridge in the real values). The upstream influence of the disturbance on the layer is shown (for all Mach number distributions) to be completely negligible at a distance of one layer thickness ahead of the point of incidence of the wave front on the outside of the layer. (It is explained in section 8 why this conclusion, in the limiting case of a discontinuous Mach number distribution considered by Tsien and Finston (1), is at variance with their results.) For this reason the theory must be completely inadequate as a theory of shock laminar boundary layer interaction, and the significance of this conclusion is discussed in section 1. Four radically different possible mechanisms for the interaction (of a more complicated nature) are suggested, none of which can be discarded in the light of the data known to the author.