Statistical approach of weakly nonlinear ablative Rayleigh–Taylor instability

In this paper a weakly nonlinear sWNLd theory is developed for the ablative RT instability. The first WNL analysis in a simplified framework was performed in Ref. 5. We aim at deriving closed-form expressions for the most important physical quantities. The simplest and most studied case is that of a single-mode perturbation. A third-order WNL analysis of the single-mode case was presented in Ref. 6 in the limit of a very large density ratio. We derive in Sec. III analytic formulas for the second and third harmonic generation efficiency and the nonlinear correction to the exponential growth of the fundamental modulation for arbitrary Atwood numbers. A suitable choice of the self-consistent Atwood number then gives accurate results relevant to ICF. In the multimode case we also give in Sec. IV the expression of the interface elevation taking into account the mode coupling. Recently a WNL theory was presented in the framework of a finite bandwidth 7 where the results can only be integrated numerically. We show that it is necessary to compute the third-order WNL corrections in the multimode case to capture the first statistical corrections. We get expressions for the saturation amplitudes which show that shortwavelength modes saturate at a significantly higher amplitude scompared to the wavelengthd than long-wavelength modes. We finally report in Sec. V the results of simulations performed with a two-dimensional s2Dd Lagrangian code which confirm the theoretical predictions.