SUMMARY

In this paper the work of Lighthill (1) for one-diniensional unsteady motion is extended to the problem of steady, supersonic flow past a two-dimensional slender body. Goldsworthy (2) and others have shown that, in the limit when the Mach number, M, of the undisturbed flow tends to infinity, the two motions become identical. As in (1), an accuracy hypothesis is formulated concerning the degree of accuracy of the Friedrichs theory (3) for nearly plane, two-dimensional, steady shocks. A comprehensive check of this theory on the lines of the accuracy hypothesis is made for a fluid with general thermodynamic properties: in the process of justifying this hypothesis the picture of the flow as a whole is improved. A relationship is found between the increased total energy flux across a plane transverse to the flow in the residual wave, and the entropy flux across the region of the shock upstream from this plane. The relationship is checked by comparing the value of the pressure fluctuations in the residual wave (due to entropy change at the shock) as determined from a consideration of conditions in the residual wave, with the value obtained from an investigation of the local reflection of the simple wave in the shock. The work is extended to the problem of the actual flow past a two-dimensional aero-foil when there are two shocks forming an N-wave, and in this case, conditions very far downstream are investigated. 1