The Shock Strength in a Two-Dimensional Nonsteady Flow

ASSUME THAT A SMALL DISTURBANCE starts at origin (r = 0); when t = 0, the linearized theory will give a good approximation to the flow in and outside the Mach cone, r — C0(sonic velocity of the undisturbed fluid)t, with apex at f = 0, / = 0. In order to obtain an approximate solution uniformly valid on the Mach cone, Lighthill's technique ' 2 is applied. Expanding both the independent variable r — Cot, and the velocity potential <p into power series of a small parameter e,