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 Pn (cosθ), 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.

中文翻译：

---

球面几何中弱非线性 Rayleigh-Taylor 不稳定性的模拟

通过数值模拟研究了球面几何中弱非线性 (WN) 阶段的 Rayleigh-Taylor 不稳定性。揭示了模式耦合过程。结果与基于参数扩展的 WN 模型一致，同时发现高阶效应不可忽略。对于勒让德模式扰动 Pn (cosθ)，基模的非线性饱和幅度 (NSA) 随模式数 n 的增加而减小。当 n 很大时，球形 NSA 低于相应的平面 NSA。然而，对于较大的 n，可以通过对赤道附近的气泡/尖峰应用傅立叶变换并计算转换后的三角谐波的 NSA 来恢复平面 NSA。