Interface Width Effect on the Weakly Nonlinear Rayleigh–Taylor Instability in Spherical Geometry

Interface width effect on the spherical Rayleigh–Taylor instability in the weakly nonlinear regime is studied by numerical simulations. For Legendre perturbation mode P_n with wave number k_n and interface half-width L, the commonly adopted empirical linear growth rate formula \gamma_n^\rm em(L)=\gamma_n/\sqrt1+k_nL is found to be sufficient in spherical geometry. At the weakly nonlinear stage, the interface width affects the mode coupling processes. The development of the mode P_2n is substantially influenced by the interface width. Moreover, the nonlinear saturation amplitude increases with the interface width.