A Theory for Spontaneous Mach Stem Formation in Reacting Shock Fronts, I. The Basic Perturbation Analysis

Abstract

A theory to explain the experimentally observed spontaneous formation of Mach stems in reacting shock fronts is developed. A linearized mechanism of instability through radiating boundary waves is analyzed. Then through weakly nonlinear asymptotics, an integro-differential scalar conservation law is derived. The asymptotic expansion relates the breakdown of solutions for this scalar equation with the spontaneous formation of the complete triple-shock, slip-line Mach stem configuration.