Spectral Energy Cascade of Forced Shock Waves in the Presence of Species Inhomogeneity

We investigate the interaction of two-dimensional forced shock waves with species inhomogeneity of a circular geometry (bubble) using direct numerical simulations (DNS). We derive the spectral energy cascade, the spectral flux and spectral dissipation for such interactions. We use two forcing methods—stochastic forcing and rescaled forcing to generate shock waves and show that the forcing type influences mixing. The acoustic spectral energy scales as \({\upepsilon }^{2/3}{\text{l}}^{-1/3}{k}^{-2}\) , where \(\upepsilon\) is the energy dissipation, \(\text{l}\) is the integral length scale and k is the wavenumber. The spectral dissipation shows that dissipation occurs across all scales. The type of forcing influences the behaviour of spectral flux. We show that the spectral flux generated by stochastic forcing indicates the triggering of Ritchtmyer-Meshov instability, thereby showing improved mixing compared to rescaled forcing. We also analyse the effect of the density ratio on the spectral flux and the mixing width when random forcing is used.