Spherically symmetric solutions of the equations of gas dynamics

Abstract

The method developed by the author is adapted to the case of spherically symmetric gas motions. The pressure, density and velocity of the gas are shown to involve one arbitrary function Ф; if Ф = f ( t ) w ( rt -α ), where f and w are arbitrary functions, explicit formulae for the pressure, density and velocity are worked out. Amongst motions of this kind, those in which the velocity is proportional to r , are selected for detailed investigation. Cases in which the gas motion is adiabatic are determined; in one type w is a known function of rt -α , while f is the solution of a certain differential equation; in a second type, f is known but w remains arbitrary. Boundary conditions are then applied, first, on the assumption that the boundary is approximately a contact surface and that the motion is of the first type; secondly, when the boundary is a true shock surface and the motion has a special character and is common to both types. Primakoff's solution is obtained in the second case. The author’s method is contrasted with the conventional ones.