A theory for spontaneous Mach stem formation in reacting shock fronts. I. The basic perturbation analysis. (English) Zbl 0544.76135

Summary: 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.


76V05 Reaction effects in flows
76L05 Shock waves and blast waves in fluid mechanics
80A32 Chemically reacting flows
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