Abstract:We use the classical normal mode approach of hydrodynamics stability theory to define stability determinants (Evans functions) for multidimensional strong detonations in three commonly studied models of combustion: the full reactive Navier-Stokes (RNS) model, and the simpler Zeldovich-von Neumann-Döring (ZND) and Chapmand-Jougeuet (CJ) models. The determinants are functions of frequencies (λ,η), where λ is a complex variable dual to the time variable, and η ∈ R^{d-1}is dual to the transverse spatial variables. The zeros of these determinants in ℜλ>0 correspond to perturbations that grow exponentially with time.The CJ determinant Δ

_{CJ}(λ,η), turns out to be explicitly computable. The RNS and ZND determinants are impossible to compute explicitly, but we are able to compute their first-order low frequency expansions with an error term that is uniformly small with respect to all possible (λ,η) directions. Somewhat surprisingly, this computation yields an Equivalence Theorem: the leading coefficient in the expansions of both the RNS and ZND determinants is a constant multiple of Δ_{CJ}! In this sense the low frequency stability coditions for strong detonations in all three models are equivalent. By computing Δ_{CJ}we are able to give low frequency stability criteria valid for all three models in terms of the physical quantities: Mach number, Gruneisen coefficient, compression ratio, and heat release. The Equivalence Theorem and its surrounding analysis is a step toward the rigorous theoretical justification of the CJ and ZND models as approximations to the full RNS model.

**Paper:**- Available as PDF (408 Kbytes).
**Author(s):**- Helge Kristian Jenssen, <hkjensse@unity.ncsu.edu>
- Gregory Lyng, <glyng@umich.edu>
- Mark Williams
**Publishing information:****Comments:****Submitted by:**- <hkjensse@unity.ncsu.edu> September 6 2004.

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