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

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  • D. Oron
    Department of Physics, Nuclear Research Center Negev 84190, Israel
  • L. Arazi
    School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel
  • D. Kartoon
    Department of Physics, Nuclear Research Center Negev 84190, Israel
  • A. Rikanati
    Department of Physics, Nuclear Research Center Negev 84190, Israel
  • U. Alon
    Faculty of Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
  • D. Shvarts
    Department of Physics, Nuclear Research Center Negev 84190, Israel

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<jats:p>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.</jats:p>

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