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A Theory for Spontaneous Mach‐Stem Formation in Reacting Shock Fronts. II. Steady‐Wave Bifurcations and the Evidence for Breakdown
Author(s) -
Majda Andrew,
Rosales Rodolfo
Publication year - 1984
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1984712117
Subject(s) - mach number , detonation , shock wave , mach wave , conservation law , mechanics , shock (circulatory) , work (physics) , argument (complex analysis) , physics , scalar (mathematics) , bifurcation , classical mechanics , mathematical analysis , mathematics , thermodynamics , geometry , chemistry , quantum mechanics , nonlinear system , medicine , biochemistry , organic chemistry , explosive material
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.