Three dimensional shock wave propagation in an ideal gas

Abstract

A systematic study is made of an unsteady three dimensional motion of a shock wave of arbitrary strength propagating through an ideal gas. The dynamical coupling between the shock front and the rearward flow is investigated by considering an infinite system of transport equations for the variation of jumps in pressure and its space derivatives across the shock. This infinite system is then truncated to get a closed system of coupled differential equations, which efficiently describes the shock motion. Disturbances propagating on the shock and the onset of shock-shocks are briefly discussed. In the limit of vanishing shock strength, the first order truncation approximation leads to an exact description of acceleration waves. Asymptotic decay laws for the weak shocks and rearward precursor disturbances are exactly recovered. In the strong shock limit, the first order approximation leads to a propagation law for imploding shocks, which is in agreement with the Guderley's exact similarity solution. Attention is drawn to the connection between the transport equations along shock rays obtained here and the corresponding results obtained from an alternative method, using the theory of generalized functions.