Chapman-Jouguet detonations three-dimensional structures

The experimental prevalence of multiheaded spin has prompted categorical statements to the effect that all self-sustaining detonations exhibit significant three-dimensional structure [25]. The belief that no Chapman-Jouguet detonations are planar rests on the conclusion that all such planar waves are unstable to certain nonplanar disturbances. This conclusion is difficult to substantiate in general because of the complexity of the needed... 

We thus see that the motion of a real detonation front is far from the steady and one-dimensional motion given by the ZND model. Instead, it proceeds in a cyclic manner in which the shock velocity fluctuates within a cell about the equilibrium Chapman-Jouguet value. Chemical reactions are essentially complete within a cycle or a cell length. However, the gas dynamic flow structure is highly three-dimensional and full equilibration of the transverse shocks, so that the flow becomes essentially one-dimensional, will probably take an additional distance of the order of a few more cell lengths. 

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