REACTIVE EULER MODEL FOR DETONATION PROPAGATION IN A NONUNIFORM MEDIUM

In recent work [1], the analog Burgers model of detonation [2] was used to explore how detonation wave propagates in a medium with a periodically varying reactivity. It was found that the upstream state variations influence both the stability of the steady-state traveling wave solutions and the character of the ensuing instabilities. Interactions with upstream-state periodicity lead to complex nonlinear oscillations of the solution that includes existence of nonlinear wavepackets, period-doubling bifurcations, frequency locking, and resonance. In this work, we generalize [1] to the case of reactive Euler equations. The nonuniformity is modeled by periodic variations of the mixture parameters in the upstream state. Existence of mode locking and resonance, in precise analogy with the reactive Burgers model, is found and explored for the more realistic model of detonations.