Simple model for the turbulent mixing width at an ablating surface

Abstract

A diffusion model is applied to calculate the turbulent mixing width at an ablating surface. It is proposed that the general model be tested first on well-determined and easily accessible stabilizing mechanisms such as surface tension, viscosity, density gradient, or finite thickness. In this model the turbulent mixing width h is directly correlated with the growth rate γ of the perturbations in the presence of stabilizing mechanisms: h/hclass=(γ/γclass)1/2, where hclass=0.07 Agτ2 and γclass=√Agk (where A is the Atwood number, g is the acceleration, τ is the time, and k =2π/λ =2π/(ωhclass), ω being a dimensionless constant in the model). The method is illustrated with several examples for hablation, each based on a different γablation. Direct numerical simulations are presented comparing h with and without density gradients. In addition to mixing due to the Rayleigh–Taylor instability, the diffusion model is applied to the Kelvin–Helmholtz and the Richtmyer–Meshkov mixing layers.