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-Ta ylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial pertu rbations is investigated. Using full 3D numerical simulations, a statistica l mechanics bubble-competition model, and a Layzer-type drag-buoyancy model , it is shown that the RT scaling parameters, alpha (B) and alpha (S), are similar in two and three dimensions, but the RM exponents, theta (B) and th eta (S) are lower by a factor of 2 in three dimensions. The similarity para meter h(B)/< lambda > 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 Yo ungs [see J. C. V. Hanson , Laser Part. Beams 8, 51 (1990)], but using the coefficients from the A=1 Layzer model, rather than phenomenological ones, is introduced. (C) 2001 American Institute of Physics.