ON AN ASYMPTOTIC MODEL FOR MACH STEM FORMATION IN PLANAR DETONATIONS

Abstract

A striking instability occurs in nearly planar detonation waves in a reactive gas. In contrast to shocks in inert gases, small two-dimensional perturbations in the primary shock curve are excited in certain regimes. This ultimately leads to the formation of Mach stems that propagate in a direction transverse to that of the primary front. The main evidence for this has for the most part been the experimental observation of a striated rather than uniform ash trail in the wake of the primary planar front. Recently, an elegant asymptotic theory originating with the Euler equations of compressible reactive flow was devised in an effort to explain how spontaneous Mach Stem formation can be supported by such equation. The Mach stem formation propagates in a direction transverse to that of the primary front. This chapter describes the construction of an asymptotic model for Mach stem formation in planar detonations devised by Majda and Rosales. The following are the main physical assumptions of the model: (1) the gas is inviscid and non-heat conducting, (2) the reaction occurs instantaneously across an infinitely thin zone, and (3) disturbances produced in the surrounding medium by the evolving shock front, which are called radiating boundary waves, propagate only into the burned region behind the shock front. This is clearly plausible on physical grounds; it plays the crucial role of an entropy condition in the construction of the approximation scheme.