Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions

Abstract

We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier--Stokes equations is generically associated with Hopf bifurcation to nearby time-periodic "galloping", or "pulsating", solutions, in agreement with physical and numerical observation. In the process, we determine readily numerically verifiable stability and bifurcation conditions in terms of an associated Evans function, and obtain the first complete nonlinear stability result for strong detonations of the reacting Navier--Stokes equations, in the limit as amplitude (hence also heat release) goes to zero. The analysis is by pointwise semigroup techniques introduced by the authors and collaborators in previous works.

Final version, 59pp, 5 figures

References in corpus (2)

• An efficient shooting algorithm for Evans function calculations in large systems
• Stability of strong ideal-gas shock layers

Cited by in corpus (4)

• Metastability of solitary roll wave solutions of the St. Venant equations with viscosity
• Existence and stability of viscoelastic shock profiles
• Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD
• The refined inviscid stability condition and cellular instability of viscous shock waves