Analysis of weakly nonlinear three-dimensional Rayleigh–Taylor instability growth

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Abstract
Understanding the Rayleigh–Taylor instability, which develops at an interface where a low density fluid pushes and accelerates a higher density fluid, is important to the design, analysis, and ultimate performance of inertial confinement fusion targets. Existing experimental results measuring the growth of two‐dimensional (2‐D) perturbations (perturbations translationally invariant in one transverse direction) are adequately modeled using the 2‐D hydrodynamic code LASNEX [G. B. Zimmerman and W. L. Kruer, Comments Plasma Phys. Controlled Fusion 11, 51 (1975)]. However, of ultimate interest is the growth of three‐dimensional (3‐D) perturbations such as those initiated by surface imperfections or illumination nonuniformities. Direct simulation of such 3‐D experiments with all the significant physical processes included and with sufficient resolution is very difficult. This paper addresses how such experiments might be modeled. A model is considered that couples 2‐D linear regime hydrodynamic code results with an analytic model to allow modeling of 3‐D Rayleigh–Taylor growth through the linear regime and into the weakly nonlinear regime. The model is evaluated in 2‐D by comparison with LASNEX results. Finally the model is applied to estimate the dynamics of a hypothetical 3‐D foil.