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We propose a theory of weakly nonlinear multi-dimensional self sustaineddetonations based on asymptotic analysis of the reactive compressibleNavier-Stokes equations. We show that these equations can be reduced to a modelconsisting of a forced, unsteady, small disturbance, transonic equation and arate equation for the heat release. In one spatial dimension, the modelsimplifies to a forced Burgers equation. Through analysis, numericalcalculations and comparison with the reactive Euler equations, the model isdemonstrated to capture such essential dynamical characteristics of detonationsas the steady-state structure, the linear stability spectrum, theperiod-doubling sequence of bifurcations and chaos in one-dimensionaldetonations and cellular structures in multi- dimensional detonations.

Theory of weakly nonlinear self sustained detonations