3-DIMENSIONAL SHOCK-WAVE PROPAGATION IN AN IDEAL-GAS

A systematic study is made of an unsteady three dimensional motion of a shock wave of arbitrary strength propagating through an ideal gas. T he 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 acro ss the shock. This infinite system is then truncated to get a closed s ystem of coupled differential equations, which efficiently describes t he shock motion. Disturbances propagating on the shock and the onset o f shock-shocks are briefly discussed. In the limit of vanishing shock strength, the first order truncation approximation leads to an exact d escription of acceleration waves. Asymptotic decay laws for the weak s hocks and rearward precursor disturbances are exactly recovered. In th e strong shock limit, the first order approximation leads to a propaga tion law for imploding shocks, which is in agreement with the Guderley 's exact similarity solution. Attention is drawn to the connection bet ween the transport equations along shock rays obtained here and the co rresponding results obtained from an alternative method, using the the ory of generalized functions.