Theory of weakly nonlinear self-sustained detonations

Luiz Faria, Aslan R. Kasimov, Rodolfo R. Rosales

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.
Original languageEnglish (US)
Pages (from-to)163-198
Number of pages36
JournalJournal of Fluid Mechanics
StatePublished - Nov 3 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: L.M.F. and A.R.K. gratefully acknowledge research support by King Abdullah University of Science and Technology (KAUST). The research by R.R.R. was partially supported by NSF grants DMS-1007967, DMS-1115278, DMS-1318942, and by KAUST during his research visit to KAUST in November 2013. L.M.F. would like to thank S. Korneev and D. Ketcheson for their help with numerical computations.


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