Simulation of the Weakly Nonlinear Rayleigh–Taylor Instability in Spherical Geometry

The Rayleigh–Taylor instability at the weakly nonlinear (WN) stage in spherical geometry is studied by numerical simulation. The mode coupling processes are revealed. The results are consistent with the WN model based on parameter expansion, while higher order effects are found to be non-negligible. For Legendre mode perturbation P_n(\cos\theta), the nonlinear saturation amplitude (NSA) of the fundamental mode decreases with the mode number n. When n is large, the spherical NSA is lower than the corresponding planar one. However, for large n, the planar NSA can be recovered by applying Fourier transformation to the bubble/spike near the equator and calculating the NSA of the converted trigonometric harmonic.