AI 中文总结
该研究采用条件非线性最优扰动（CNOP）方法，识别出二维可压缩瑞利-泰勒不稳定性中动能增长最大的最危险初始速度扰动，揭示了其对空间分辨率和优化时间的依赖规律。
AI 中文摘要
天体物理流体中的长期不稳定性本质上是非线性的，即使是小振幅扰动也能触发剧烈的不稳定性。然而，由于非正规模式之间的复杂相互作用，导致最大增长的扰动结构仍鲜为人知。本文采用称为条件非线性最优扰动（CNOP）的非线性优化方法，识别天体物理流体力学中二维可压缩瑞利-泰勒不稳定性下的最危险初始速度扰动，即动能增长最大的扰动。与随机扰动相比，最优扰动形成了局域在密度界面附近的相干波包结构。通过两组数值实验，研究了其对空间分辨率和优化时间范围的依赖关系：在固定优化时间下，提高空间分辨率会产生更尖锐局域的波包；在固定空间分辨率下，增加优化时间会使波包逐渐扩散。此外，使用快速傅里叶变换（FFT）在傅里叶空间分析最优扰动，可更清晰地表征其谱分布：高分辨率模拟将大部分扰动能量集中在少数主导模式中，而更长的优化时间则使能量分布在更宽的模式范围内。这些结果表明，短优化时间范围涉及相对较弱的模式相互作用，更接近线性机制；而更长的优化时间会增强非线性模式相互作用，拓宽谱分布，并降低线性稳定性理论的预测能力。
英文摘要
Long-term instabilities in astrophysical fluids are inherently nonlinear, where even small-amplitude perturbations can trigger dramatic instability. However, owing to the complex interactions among non-normal modes, the perturbation structures responsible for the greatest growth remain poorly understood. In this paper, we employ the nonlinear optimization method known as the conditional nonlinear optimal perturbation (CNOP) to identify the most dangerous initial velocity perturbation, i.e., the perturbation that maximizes the kinetic energy growth in the two-dimensional compressible Rayleigh-Taylor instability in astrophysical hydrodynamics. Compared with random perturbations, the optimal perturbation forms a coherent wave-packet structure localized around the density interface. We investigate its dependence on spatial resolution and optimization time horizon through two sets of numerical experiments. For a fixed optimization time, increasing the spatial resolution produces a more sharply localized wave packet, whereas for a fixed spatial resolution, increasing the optimization time causes the wave packet to become progressively more dispersed. Furthermore, we analyze the optimal perturbations in Fourier space using the fast Fourier transform (FFT), which provides a clearer characterization of the spectral distribution. Higher-resolution simulations concentrate most of the perturbation energy into only a few dominant modes, while longer optimization times distribute the energy over a broader range of modes. These results indicate that short optimization time horizons involve relatively weak modal interactions and remain closer to the linear regime, whereas longer optimization times enhance nonlinear modal interactions, broaden the spectral distribution, and reduce the predictive capability of linear stability theory.
Comments15 pages, 7 figures, submitted to ApJ
