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The critical conditions for the initiation of a strong Zeldovich--von Neumann--Doring (ZND) detonation in a nonuniformly perturbed reactive fluid are derived using a high activation-energy asymptotic analysis. The initial disturbances are taken to have amplitudes of the order of the small inverse activation energy, with a characteristic wavelength of the order of an acoustic scale, and consist of initial temperature, concentration, pressure, velocity, or density perturbations. The detonation initiation mechanism is based on the work of Dold and Kapila, which describes how ignition of a reactive fluid leads to the generation of a supersonic, shockless, weak detonation. A transition from the weak detonation to a ZND detonation occurs if the initial disturbance is sufficiently strong to induce a gradient of thermal ignition times that cause the weak detonation to slow to the Chapman--Jouguet detonation velocity. Underpinning the whole process is the ability to calculate the path of the weak detonation. In Do...

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 befor...

The evolution to thermal runaway in a shock-compressed material driven by a contact surface is studied using high-activation energy asymptotics. It is demonstrated that an unsteady induction evolution terminates in thermal runaway away from the contact surface. This is in contrast to that of thermal runaway in an evolving piston-shock structure. Also, by obtaining high-resolution numerical solutions of thermal runaway at a piston face, it has been possible to verify the asymptotic spatial structure of thermal runaway provided by Jackson, Kapila, and Stewart (SIAM J. Appl. Math., 49 (1989), pp. 432-458).