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Instabilities and nonlinear patterns of overdriven detonations in gases. (English) Zbl 1271.76102
Berestycki, Henri (ed.) et al., Nonlinear PDEs in condensed matter and reactive flows. Proceedings of the NATO Advanced Study Institute on PDE’s in models of superfluidity, superconductivity and reactive flows, Cargèse, France, 21 June – 3 July 1999. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0972-0/hbk). NATO ASI Ser., Ser. C, Math. Phys. Sci. 569, 49-97 (2002).
Summary: Linear and weakly nonlinear analyses in the neighborhood of the multidimensional instability threshold of overdriven detonations propagating in gases are presented. An asymptotic solution to the reactive Euler equations is obtained in a “Newtonian limit” yielding a nonlinear integral-differential equation for the dynamics of the cellular front. The solution is valid for a general irreversible kinetics of the chemical heat release but is limited to strongly overdriven regimes. Mach-stems formation is described by a Burgers type equation. “Diamond” patterns similar to those observed in experiments are solutions to this equation. A nonlinear selection mechanism of the pattern is described, participating to the explanation of a mean cell size much larger than the unperturbed detonation thickness. An unusual self-sustained mean streaming motion is also exhibited in the nonlinear analysis. A particular attention is paid to the physical insights into this difficult hyperbolic and nonlinear problem whose asymptotic solution has been obtained very recently.
For the entire collection see [Zbl 1028.00035].

MSC:
76E99 Hydrodynamic stability
76V05 Reaction effects in flows
76E30 Nonlinear effects in hydrodynamic stability
80A32 Chemically reacting flows
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