Mode selection in weakly unstable two-dimensional detonations

A formulation of the reactive Euler equations in the shock-attached frame is used to study the two-dimensional instability of weakly unstable detonation through direct numerical simulation. The results are shown to agree with the predictions of linear stability analysis. Comparisons are made with linear perturbation growth rates and oscillation frequencies as a function of transverse disturbance wavelength. The perturbation eigenfunctions predicted by linear stability analysis are directly validated through numerical simulation. Three regimes of unstable behavior – linear, weakly nonlinear, and fully nonlinear – are explored and characterized in terms of the power spectrum of the normal shock velocity for a Chapman–Jouguet detonation with weak heat release.