Time-dependent two-dimensional detonation: the interaction of edge rarefactions with finite-length reaction zones

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Abstract
A theory of time-dependent two-dimensional detonation is developed for an explosive with a finite-thickness reaction zone. A representative initial–boundary-value problem is treated that illustrates how the planar shock of an initially one-dimensional detonation becomes non-planar in response to the action of an edge rarefaction that is generated at the explosive's lateral surface. The solution of this time-dependent problem has a wave-hierarchy structure that at late times includes a weakly two-dimensional hyperbolic region and a fully two-dimensional parabolic region. The wave head of the rarefaction is carried by the hyperbolic region. We show that the shock locus is analytic at the wave head. The dynamics of the final approach to two-dimensional steady-state detonation is controlled by Burgers’ equation for the shock locus. We also present some results concerning the stability of the solutions to our problem.

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