On the structure of supersonic flow

Abstract

If viscosity and heat conduction be neglected, the supersonic motion of a perfect gas is a radiation process, that is, the equations representing the mechanism of motion are of the hyperbolic type. A feature of such equations is that proper boundary or initial conditions prescribed on surfaces of finite extent determine the solution only in a finite portion of space, beyond which it can be continued in an arbitrary manner. This seems to suggest that the study of the structure of supersonic flow is limited to the consideration of such restricted portions of space, much in contrast to the study of the structure of incompressible flow, for example. The limitation is not entirely necessary, however. It is the purpose of this note to unify some of the known facts regarding the structure in the large of steady, two-dimensional, shockfree supersonic flow and to present new results and points of view.Closely analogous results hold for the one-dimensional, unsteady motion of a perfect, inviscid gas, and the considerations outlined in the following ma x" also be extended to steady, axially symmetrical, supersonic flow and other hyperbolic problems in two independent variables. UniquenessThe differential equations governing the steady, two-dimensional, irrotational, homentropic, supersonic flow of a perfect gas possess two families of characteristics with the respective slopes .dy_ : tan (0 +/~) (' minus' Mach lines)