Dimensionality dependence of late time evolution of Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Using a statistical mechanics bubble competition model, Alon et al. (1994,1995) have shown that the two-dimensional Rayleigh-Taylor (RT) mixing zone bubble and spike fronts evolves as h=α_B/S·A·g·t² with α_B∼0.05 and α_S∼α_S· (1+A). The Richtmyer-Meshkov (RM) mixing zone fronts have been found to evolve as h=a₀·t^θ with different θ's for bubble and spikes. The model predictions were θ_B∼0.4 and θ_S∼θ_B at low A's and rises to 1.0 for A close to 1. Full 2D numerical simulations confirmed these scaling laws. Recent experimental results (Dimonte, 1999,2000) have indicated similar scaling laws of the mixing zone evolution, but there were some discrepancies in the values of the scaling parameters, mainly in the value of θ_B and the similarity parameter, h/〈λ〉. It will be shown, based on full 3D numerical simulations, a Layzer type model and a 3D statistical-mechanics model that these discrepancies are mainly the effect of dimensionality. Accounting for the 3D nature of the problem results in scaling parameters that are very similar to the experimental values. The 3D single mode evolution, used in this model, was confirmed by shock tube experiments.