Theory of weakly nonlinear self-sustained detonations

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

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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
Pages (from-to)163-198
Number of pages36
JournalJournal of Fluid Mechanics
Publication statusPublished - 3 Nov 2015
Externally publishedYes


  • chaos
  • detonation waves
  • nonlinear instability


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