Multidimensional linear stability of a detonation wave at high activation energy

The one- and two-dimensional linear stability of a plane detonation wave characterized by a one-step Arrhenius chemical reaction is studied for large activation energies using a normal mode analysis based on the approach of Lee and Stewart [J. Fluid Mech., 216 (1990), p. 103]. It is shown that for one-dimensional disturbances, a low-frequency oscillatory mode present for moderate activation energies bifurcates into a slowly evolving nonoscillatory mode and a faster-evolving nonoscillatory mode as the activation energy is increased. It is also shown that for large activation energies, the stability spectrum consists of a large number of unstable one-dimensional modes, as predicted by the asymptotic analysis of Buckmaster and Neves [Phys. Fluids, 31 (1988), P. 3571], possessing a maximum growth rate at very high frequencies. For nonplanar disturbances, it is found that as the wavenumber increases, the two nonoscillatory modes present for zero wavenumber collapse into a single oscillatory unstable mode before stabilizing at a short wavelength.