发表机构
Imperial College London; University of Cambridge; Barcelona Supercomputing Center; University of Bristol（帝国理工学院; 剑桥大学; 巴塞罗那超级计算中心; 布里斯托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用spDMD方法实验观测到内波波束中亚阈值三体共振信号，证明其为受限非传播振荡，并揭示次级波分支反馈机制，可推广至海洋环境。
AI 中文摘要
本研究通过稀疏促进动态模态分解（spDMD）对实验观测中的波结构进行诊断，考察了涡环诱导扰动下内重力波场的亚阈值三体响应。与通过截断奇异值谱来选择模态的标准动态模态分解（DMD）方法相比，本文展示的spDMD方法转而寻求最小化重构误差，在三体共振不稳定性（TRI）和亚阈值持续三体响应（STR）两种情形下，均能稳健地识别出先前无法区分的、频率较高的振荡信号。这些信号与由频率为$\omega_0$的初级内波和频率分别为$\omega_1$和$\omega_2$的次级TRI波组成的波-波相互作用产物一致，从而产生频率为$\omega_3 = \omega_0 + \omega_1$和$\omega_4 = \omega_0 + \omega_2$的信号。我们表明，这些信号满足共振条件，但不满足内波的频散关系，表明它们是受限的、非传播的振荡信号，而非自由传播的内波。对波-波相互作用的层次分析提供了证据，表明TRI次级波两个分支之间的反馈产生了这些信号。虽然我们预期我们的观测结果可推广到多类波-波相互作用，但我们不能排除在实验室中做出的特定观测可能源于自由表面对初级波的反射。然而，在海洋中强密度分层区域之下，我们预计这些相互作用路径会面临相同的几何构型，因此我们确信我们的发现将直接迁移到自然环境中。
英文摘要
This work examines sub-threshold triadic responses to a vortex-ring-induced perturbation of an internal gravity-wave field, using sparsity-promoting dynamic mode decomposition (spDMD) to diagnose wave structures from experimental observations. Compared with a standard approach to dynamic mode decomposition (DMD) that selects modes by truncation of the singular value spectrum, spDMD, an alternative approach that instead seeks to minimise reconstruction error, is shown here to robustly identify previously indistinguishable oscillatory signals of high frequency in cases of both triadic resonance instability (TRI) and sub-threshold sustained triadic response (STR). These signals are consistent with wave--wave interaction products composed of a primary internal wave with frequency $ω_0$, and secondary TRI waves with frequencies $ω_1$ and $ω_2$ respectively, leading to signals with frequencies $ω_3 = ω_0 + ω_1$ and $ω_4 = ω_0 + ω_2$. We show that these signals satisfy conditions for resonance, but fail to satisfy the dispersion relation for internal waves, indicating that they are confined, non-propagating oscillatory signals rather than freely propagating internal waves. A hierarchical analysis of wave--wave interactions provides evidence that feedback between both branches of the TRI secondary waves gives rise to these signals. Whilst we expect our observations to generalise to many classes of wave--wave interaction, we cannot exclude the possibility that the particular observations we make in the laboratory may arise due to reflections of the primary wave from a free surface. However, beneath strongly density-stratified regions of the ocean we would expect to find these interaction pathways faced with the same geometric configuration, so we are confident our findings will transfer directly to the natural environment.
Comments25 pages, 14 figures
