Weakly nonlinear hydrodynamic instabilities in inertial fusion

For many cases of interest to inertial fusion, growth of Rayleigh--Taylor and other hydrodynamic instabilities is such that the perturbations remain linear or weakly nonlinear. The transition to nonlinearity is studied via a second-order solution for multimode classical Rayleigh--Taylor growth. The second-order solution shows how classical Rayleigh--Taylor systems forget initial amplitude information in the weakly nonlinear phase. Stabilized growth relevant to inertial fusion is qualitatively different, and initial amplitudes are not dominated by nonlinear effects. In all systems with a full spectrum of modes, nonlinear effects begin when mode amplitudes reach about 1/Lk2, for modes of wave number k and system size L