Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 163-198 |
| Number of pages | 36 |
| Journal | Journal of Fluid Mechanics |
| Volume | 784 |
| DOIs | |
| State | Published - Nov 3 2015 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: 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.