Dimensionality dependence of the Rayleigh-Taylor and Richtmyer-Meshkov instability late-time scaling laws

The late-time nonlinear evolution of the three-dimensional (3D) Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated. Using full 3D numerical simulations, a statistical mechanics bubble-competition model, and a Layzer-type drag-buoyancy model, it is shown that the RT scaling parameters, α_B and α_S, are similar in two and three dimensions, but the RM exponents, θ_B and θ_S are lower by a factor of 2 in three dimensions. The similarity parameter h_B/〈λ〉 is higher by a factor of 3 in the 3D case compared to the 2D case, in very good agreement with recent Linear Electric Motor (LEM) experiments. A simple drag-buoyancy model, similar to that proposed by Youngs [see J. C. V. Hanson et al., Laser Part. Beams 8, 51 (1990)], but using the coefficients from the A = 1 Layzer model, rather than phenomenological ones, is introduced.