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This study uses a simplified detonation model to investigate the behaviour ofdetonations with galloping-like pulsations. The reactive Burgers equation isused for the hydrodynamic equation, coupled to a pulsed source whereby all theshocked reactants are simultaneously consumed at fixed time intervals. Themodel mimics the short periodic amplifications of the shock front followed byrelatively lengthy decays seen in galloping detonations. Numerical simulationsreveal a saw tooth evolution of the front velocity with a period-averageddetonation speed equal to the Chapman-Jouguet velocity. The detonation velocityexhibits two distinct groups of decay time scales, punctuated by reactionpulses. At each pulse, a rarefaction wave is created at the reaction front'slast position. A characteristic investigation reveals that characteristicsoriginating from the head of this rarefaction take 1.57 periods to reach andattenuate the detonation front, while characteristics at the tail take anadditional period. The leading characteristics are amplified twice, by passingthrough the reaction fronts of subsequent pulses, before arriving at the shockfront, whilst the trailing characteristics are amplified three times. Thisleads to the two distinct groups of time scales seen in the detonation frontspeed.

On the two separate decay time scales of a detonation wave modelled by the Burgers equation and their relation to its chaotic dynamics