## Abstract

The evolution of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for incompressible and immiscible fluids and their dependence on the initial perturbation spectrum is evaluated using a new mean field formulation of the Haan-Ofer-Shvarts mode coupling model. The height of the lighter fluid bubbles penetrating into the denser fluid is shown to reach asymptotic, universal, self-similar behavior when the initial spectrum is dominated by short wavelengths and at least 3-4 mode coupling generations have occurred. For RT, the model yields h = α_{RT} Agt^{2} for the bubble front penetration height, in good agreement with experimental data and 3D numerical simulations for various initial conditions. For RM, the lack of a natural length scale leads to a 2nd type self-similar solution h = α R M t θ and θ is rigorously determined from a detailed solution of the model equation, while α_{RM} retains knowledge of the initial spectrum. The value of θ_{RM} in two dimensions is θ_{2} _{D} = 2/5, consistent with the Alon-Shvarts bubble-merger model and numerical simulations, and in three dimensions, it is θ_{3} _{D} = 1/3. We find that the smaller value θ_{3} _{D} ∼ 0.25 ± 0.05 obtained in numerical simulations and experiments [Dimonte and Schneider, Phys. Fluids 12, 304 (2000)] results from the lack of enough mode coupling generations needed to reach the RM asymptotic self-similar stage. The feasibility of a true self-similar RM experiment on NIF is discussed.

Original language | English |
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Article number | 062126 |

Journal | Physics of Plasmas |

Volume | 25 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jun 2018 |

## ASJC Scopus subject areas

- Condensed Matter Physics