Theory is developed to predict the growth and structure of sibling'' waves developing through triadic resonant instability of a vertically confined mode-1 internalparent’’ wave in uniform stratification including the influence of background rotation. For a sufficiently hydrostatic parent wave, two branches for growth of sibling waves are dominant. The branch with largest growth rate corresponds to sibling waves having frequencies much larger than that of the parent; the other branch corresponds to sibling waves having frequencies close to half the frequency of the parent. Numerical simulations show that sibling waves corresponding to the subharmonic branch appear in practice. In the absence of rotation, the sibling waves corresponding to this branch are predicted to have near-constant growth rate as their horizontal wavenumber increases. With rotation, however, the growth rate peaks at moderate wavenumber. In all cases, as confirmed by numerical simulations, the e-folding time for the growth of the sibling waves can be thousands of buoyancy periods for parent waves having amplitudes typical of realistic oceanic internal modes. In non-uniform stratification, the parent wave self-interacts immediately to force superharmonics. Nonetheless, numerical simulations with symmetric top-hat stratification show that triadic resonant instability eventually emerges. Such emergence is not evident in simulations with stratification more representative of the ocean. The results suggest a reconsideration of the efficacy of parametric subharmonic instability in leading to the breakdown of low-mode internal tides in the ocean.

中文翻译：

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水平周期内部模态的三单元共振不稳定性

发展理论来预测鱼的生长和结构 sibling'' waves developing through triadic resonant instability of a vertically confined mode-1 internal均匀分层中的``母体''波，包括背景旋转的影响。对于足够静水的母波，用于同级波生长的两个分支占主导地位。增长率最高的分支对应于频率远高于父级频率的同级波。另一分支对应于频率接近母体频率一半的同胞波。数值模拟表明，在实践中出现了与次谐波分支相对应的同胞波。在没有旋转的情况下，与该分支相对应的同级波随着其水平波数的增加而具有接近恒定的增长率。但是，随着旋转，增长率在中等波数处达到峰值。在所有情况下，如数值模拟所证实的，兄弟波生长的电子折叠时间可以是具有实际海洋内部模式典型振幅的母波的数千个浮力周期。在非均匀分层中，母波立即自相互作用以强迫超谐波。尽管如此，具有对称礼帽分层的数值模拟表明，三重共振共振不稳定性最终出现。在分层更能代表海洋的模拟中，这种出现并不明显。结果表明，重新考虑了参数次谐波不稳定性导致海洋低模内部潮汐破裂的功效。母波立即自相互作用以产生超谐波。尽管如此，带有对称礼帽分层的数值模拟表明，三重共振共振不稳定性最终会出现。在分层更能代表海洋的模拟中，这种出现并不明显。结果表明，重新考虑了参数次谐波不稳定性导致海洋低模内部潮汐破裂的功效。母波立即自相互作用以产生超谐波。尽管如此，带有对称礼帽分层的数值模拟表明，三重共振共振不稳定性最终会出现。在分层更能代表海洋的模拟中，这种出现并不明显。结果表明，重新考虑了参数次谐波不稳定性导致海洋低模内部潮汐破裂的功效。