A theory for spontaneous Mach-stem formation in reacting shock fronts. II: Steady-wave bifurcations and the evidence for breakdown. (English) Zbl 0584.76075

Majda, Andrew; Rosales, Rodolfo

Stud. Appl. Math. 71, 117-148 (1984).

[For part I see the authors, SIAM J. Appl. Math. 43, 1310-1334 (1983; Zbl 0544.76135)]
This paper continues earlier work of the authors on a theory for spontaneous Mach-stem formation. Shock formation in smooth solutions of the scalar integrodifferential conservation law from paper I is demonstrated through detailed numerical experiments - this completes the basic argument from paper I. The steady-state bifurcation of planar detonation waves into ”shallow-angle” reactive Mach stem structures is analyzed. The conclusions of this analysis agree with those predicted through the time-dependent asymptotics in paper I and provide a completely independent confirmation of that theory.

MSC:

76L05	Shock waves and blast waves in fluid mechanics
80A99	Thermodynamics and heat transfer
76E99	Hydrodynamic stability
76M99	Basic methods in fluid mechanics

Keywords:

spontaneous Mach-stem formation; Shock formation; smooth solutions; scalar integrodifferential conservation law; steady-state bifurcation; planar detonation waves; shallow-angle” reactive Mach stem structures; time-dependent asymptotics

Citations:

Zbl 0544.76135

References:

[1]	Fickett, Detonation (1979)
[2]	Courant, Supersonic Flow and Shock Waves (1948)
[3]	Majda, A theory for spontaneous Mach stem formation in reacting shock fronts, I: The basic perturbation analysis, SIAM J. Appl. Math. 43 (6) pp 1310– (1983) · Zbl 0544.76135
[4]	Sattinger, Topics in Stability and Bifurcation Theory (1973)
[5]	Whitham, Linear and Nonlinear Waves (1974)
[7]	Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math. 7 pp 159– (1954) · Zbl 0055.19404