Problems in the Theory of Viscous Compressible Fluids

The present study was suggested by several problems and difficulties that had appeared in previous experimental and theoretical investigations of viscosity effects in compressible fluids. The outstanding problem was the extension of the classical (Prandtl) boundary-layer theory to high-speed flow, especially supersonic flow. In the boundary-layer theory the equations of motion are simplified by assuming that viscous effects are confined to a narrow region close by the wall through which changes are rapid compared to those in the direction of the wall. Then the resulting non-linear equations are studied with the aim of obtaining the flow field in this narrow region or boundary layer. The pressure is usually obtained from the potential or no-viscous flow about the body. Several authors have studied a boundary-layer theory which has the same basic assumptions but which allows for compressibility and heat conduction. However, in supersonic flow several phenomena are known which show that the basic assumptions of boundary-layer theory do not apply, at least in certain regions