Theory of cellular detonations in gases. Part 1. Stability limits at strong overdrive

A stability analysis of detonation waves is carried out at strong overdrive and in the Newtonian limit (small difference between the specific heats at constant pressure and at constant volume). The instability threshold is determined. An analytical expression of the dispersion relation and a linear integral-differential equation for the evolution of the detonation front, both valid at onset of the instability, are obtained. The analysis is valid for an arbitrary chemistry compatible with stable or weakly unstable gaseous detonations.