Spectral Analysis of Unstable Detonation

We present a spectral analysis of a turbulent over-driven unstable detonation wave that exhibits highly irregular cellular structures to better understand scale interactions in detonations. Numerical soot foils and suitable Quantities of Interest (QoIs) for a stoichiometric methane-air (\ce{CH4}+2\ce{O2}) mixture using GRI-Mech 3.0 mechanism were obtained and analyzed in the Fourier space using a partially-periodized Fourier transform for non-periodic 2-D signals. We find key flow features of the unstable detonation front to come out naturally as coherent structures after due filtering is done in the Fourier space. The triple point vortex collisions, that are points of peak vorticity and pressure, are shown to be the primary drivers of detonation-generated turbulence. The population of these scales is further shown by evaluating the inter-scale and inter-spectral term between pressure and TKE spectra.