On the propagation of weak and moderately strong, curved shock waves

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Abstract
In this paper we concern ourselves with the theoretical description of curved converging shock waves, where nonlinear interaction effects, between the shock fronts and the flow behind them, and refraction effects are equally important. In a non-viscous, isoenergetic and isentropic flow the problem can be described by a nonlinear wave equation for the pressure field. This equation then admits an analytical solution with the help of the method of strained coordinates provided that the nonlinear terms contain only derivatives with respect to two independent variables. This restrictive condition is approximately fulfilled if the incoming wave is only slightly curved.Replacing in the solution the strained coordinates – which themselves depend on the solution – by physical coordinates, we get an accurate description of the transition from the shock pattern obtained by the geometric-acoustics approach (very weak shocks) to the pattern determined by Whitham's shock dynamics (strong shocks). Furthermore, the solution describes the complete flow field and agrees very favourably with experimental data by Sturtevant & Kulkarny.

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