MULTIDIMENSIONAL LINEAR-STABILITY OF A DETONATION-WAVE AT HIGH ACTIVATION-ENERGY

The one- and two-dimensional linear stability of a plane detonation wa ve characterized by a one-step Arrhenius chemical reaction is studied for large activation energies using a normal mode analysis based on th e approach of Lee and Stewart [J. Fluid Mech., 216 (1990), p. 103]. It is shown that for one-dimensional disturbances, a low-frequency oscil latory mode present for moderate activation energies bifurcates into a slowly evolving nonoscillatory mode and a faster-evolving nonoscillat ory mode as the activation energy is increased. It is also shown that for large activation energies, the stability spectrum consists of a la rge number of unstable one-dimensional modes, as predicted by the asym ptotic analysis of Buckmaster and Neves [Phys. Fluids, 31 (1988), P. 3 571], possessing a maximum growth rate at very high frequencies. For n onplanar disturbances, it is found that as the wavenumber increases, t he two nonoscillatory modes present for zero wavenumber collapse into a single oscillatory unstable mode before stabilizing at a short wavel ength.