Mode coupling theory in ablative Rayleigh–Taylor instability

Abstract

The weakly nonlinear stage of the ablative Rayleigh–Taylor instability has been investigated by expanding the one-fluid and one-temperature equations to second order. Mode coupling of linear growing perturbations with wave numbers kA and kB and corresponding growth rates γA and γB excite a long-wavelength perturbation with wave number k0=kA−kB. Time evolution of the excited perturbation has been studied for two cases, the first having no initial perturbation with the wave number k0 and the second having a finite perturbation. In both cases, parts of the excited perturbation are initially convected out from an ablation surface toward the first and second sonic points. In the latter case, the perturbation grows initially with a linear growth rate and later with the growth rate γA+γB. Mass flows across an ablation surface, which determine deformation of the surface, are investigated in detail. Calculated mass flows to first and second order are found to be quite different.