Diamond patterns in the cellular front of an overdriven detonation

A nonlinear integral-differential equation describing the cellular front of an overdriven detonation is obtained by an analysis carried out in the neighborhood of the instability threshold. The analysis reveals both an unusual mean streaming motion, resulting from the rotational part of the oscillatory flow, and pressure bursts generated by the crossover of cusps representative of Mach stems propagating on the detonation front. A numerical study of the nonlinear equation exhibits the "diamond" patterns observed in experiments. An overall physical understanding is provided.