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

[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.


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


Zbl 0544.76135
Full Text: DOI


[1] Fickett, Detonation (1979)
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[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)
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