On the One-dimensional Stability of Viscous Strong Detonation Waves

Abstract

Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following the work of Alexander, Gardner & Jones and Gardner & Zumbrun, is the calculation of a stability index whose sign determines a necessary condition for spectral stability. We show that for an ideal gas this index can be evaluated in the ZND limit of vanishing dissipative effects. Moreover, when the heat of reaction is sufficiently small, we prove that strong detonations are spectrally stable provided the underlying shock is stable. Finally, for completeness, the stability index calculations for the nonreacting Navier-Stokes equations are included

66 pages, 7 figures

References in corpus (2)

• A stability index for detonation waves in Majda's model for reacting flow
• Stability of viscous shock profiles for dissipative symmetric hyperbolic-parabolic systems

Cited by in corpus (13)

• Viscous hyperstabilization of detonation waves in one space dimension
• Efficient numerical stability analysis of detonation waves in ZND
• Stability of viscous detonations for Majda's model
• A numerical stability investigation of strong ZND detonations for Majda's model
• Galloping instability of viscous shock waves
• Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions
• Stability of detonations in the ZND limit
• Pointwise Green function bounds and stability of combustion waves
• Evans Functions, Jost Functions, and Fredholm Determinants
• Stability of ZND detonations for Majda's model
• Majda and ZND models for detonation: nonlinear stability vs. formation of singularities
• Ion-acoustic shock in a collisional plasma
• Hopf bifurcation of viscous shock wave solutions of compressible Navier-Stokes equations and MHD