Simple model for the turbulent mixing width at an ablating surface

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 gamma of the perturbations in the presence of stabilizing mechanisms: h/h(class) = (gamma/gamma(class))(1/2), where h(class) = 0.07 Ag tau(2) and gamma(class) = root Agk (where A is the Atwood number, g is the acceleration, tau is the time, and k = 2 pi/lambda = 2 pi/(omega h(class)), omega being a dimensionless constant in the model). The method is illustrated with several examples for h(ablation), each based on a different gamma(ablation). 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. (C) 1996 American Institute of Physics.