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

Majda, Andrew; Rosales, Rodolfo

SIAM J. Appl. Math. 43, 1310-1334 (1983).

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.

MSC:

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

Keywords:

spontaneous formation of Mach stems; reacting shock fronts; linearized mechanism of instability; radiating boundary waves; weakly nonlinear asymptotics; integro-differential scalar conservation law; asymptotic expansion; triple-shock; slip-line Mach stem configuration