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

• DOI: 10.1063/1.1362529
• Publication Date: 2002-07-26T14:17:48Z
• Authors: D. Oron; L. Arazi; D. Kartoon; A. Rikanati; U. Alon; D. Shvarts
• Keywords: 0103 physical sciences; 01 natural sciences

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, αB and αS, are similar in two and three dimensions, but the RM exponents, θB and θS are lower by a factor of 2 in three dimensions. The similarity parameter hB/〈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.