Low Frequency Stability of Multi-dimensional Inviscid Planar Detonation Waves

We consider the problem of multi-dimensional linearized stability of planar, inviscid detonation waves. For an abstract, multi-step reaction model a normal mode analysis leads to a stability function similar to the Lopatinski determinant for gas dynamics. In the lowfrequency/long wave limit of the perturbation we obtain explicit criteria for uniform stability, weak stability, and strong instability in terms of a reduced stability function. An analytic extension allows us to give a necessary condition for stability in terms of this reduced stability function. When applied to the one-step reactive Euler equations (ZND-model) the analysis shows that the various stability regimes are determined by the Mach number, the Gruneisen coefficient (evaluated at the burnt state), and the compression ratios across the Neumann shock and across the reaction zone.