On Some Singular Solutions of the Tricomi Equation relating to Transonic Flow

Abstract

Among many investigations hitherto made by making use of the Tricomi equation of mixed type, a series of investigations by Guderley and his collaborators on the flow at Mach number one have given the most reliable informations.
In the present paper are presented two singular solutions of the Tricomi equation relating to transonic flow, both of which have a singularity corresponding to a uniform flow at infinity upstream—either subsonic or supersonic— and tend to Guderley’s solution when the Mach number at infinity approaches unity.
First, the solutions are given formally in integral forms, and then their analytic continuations, which are valid within various portions in the hodograph plane, are studied. Special references are also made to the behaviour of the solution in the vicinity of their singular point.