Transverse structures for detonations

It is curious that the basis for the discovery of transverse structures in detonations existed more than 50 years ago. Peculiar detonations that appeared to propagate along helical paths in tubes with round cross sections... 

In Chapter 8.5, B. Veyssiere exposes the state of knowledge in detonations. Particular features of the complex multidimensional structure of detonations are presented in relation with the recent results obtained either by nonintrusive optical diagnostics or numerical simulations from high performance calculations. The role of transverse waves in detonation propagation, the existence of correlations between the characteristic dimension of the cellular structure and the critical conditions for detonation initiation and detonation transmission, and the influence of the nonmonotonous heat release process behind the front are examined. Recent developments in the study of spinning detonations are also discussed. 

It should be understood that since the stability predictions involve reaction-rate properties, planar Chapman-Jouguet detonations are stable for suitable rate functions. For example, if the rate of heat release decreases monotonically with an increasing extent of reaction behind the shock, then the mechanism for the instability is absent. The failure to find Chapman-Jouguet detonations without transverse structures reflects the inability to encounter real chemical systems with reaction-rate properties suitable for stability. 

For purposes of further analyses of detonation structure, the shock wave may be treated as a discontinuity. Both the viscous interaction between the shock and the reaction region and the molecular transport within the reaction region are small perturbations that do not appear to exert qualitatively significant influences on the wave structure. This conclusion appears to apply not only to steady, planar waves but also to unsteady, three-dimensional structures it affords one helpful simplification in the complicated analyses of transverse wave structures. It also alters the interpretation of a detonation as a deflagration-supported shock the support provided by the chemical reactions is of a nonplanar compressible gasdynamic character with negligible molecular transport. 

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