We use the classical normal mode approach of hydrodynamic stability
theory to define stability determinants (Evans functions) for multi-d
strong detonations in three commonly studied combustion models:
Reactive Navier-Stokes, Zeldovich-von Neumann-Doering, and
Chapman-Jouguet. We compute first-order low-frequency expansions of
the RNS and ZND determinants and show that the leading coefficient in
each of the expansions is a constant multiple of the explicitly
computable CJ determinant. By computing the CJ determinant, we are
then able to compute low-frequency stability criteria in terms of
physical quantities (Mach number, compression ratio, Gruneisen
coefficient, heat release) that are valid for all three models of
combustion. This is joint work with H.K. Jenssen (NC State) and M.
Williams (UNC-Chapel Hill).
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