标题： 直布罗陀海峡潮汐流的动态模态分解分析 显示英文标题

标题： Analysis of tidal flows through the Strait of Gibraltar using Dynamic Mode Decomposition

摘要： 直布罗陀海峡是一个以复杂的海洋次中尺度特征为特点的区域，受地形、潮汐力、不稳定性及非线性水力学过程的影响，所有这些都由流体运动的非线性方程控制。 在本研究中，我们的目标是揭示3D MIT通用环流模型模拟中的这些现象的基本物理机制，包括波浪、涡旋和环流。 为了实现这一目标，我们采用动态模态分解（DMD）将模拟快照分解为Koopman模态，这些模态具有不同的指数增长/衰减率和振荡频率。 我们的目标包括评估DMD在捕捉已知特征方面的有效性，揭示新元素，对模态进行排序，并探索降阶方法。 我们还引入了修改措施以提高DMD的鲁棒性、数值精度和特征值的鲁棒性。 DMD分析提供了对流动模式、内部波形成以及直布罗陀海峡的动力学、其蜿蜒行为以及次级环流——特别是西部阿尔博兰环流的形成，以及沿非洲海岸的开尔文波和沿岸被困波传播的全面理解。 通过这种方式，它显著提高了我们对复杂海洋现象的理解，并强调了DMD作为分析此类复杂数据集的工具的巨大实用性，表明DMD可以成为海洋学家工具箱中的宝贵补充。 显示英文摘要

摘要： The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features, influenced by topography, tidal forces, instabilities, and nonlinear hydraulic processes, all governed by the nonlinear equations of fluid motion. In this study, we aim to uncover the underlying physics of these phenomena within 3D MIT general circulation model simulations, including waves, eddies, and gyres. To achieve this, we employ Dynamic Mode Decomposition (DMD) to break down simulation snapshots into Koopman modes, with distinct exponential growth/decay rates and oscillation frequencies. Our objectives encompass evaluating DMD's efficacy in capturing known features, unveiling new elements, ranking modes, and exploring order reduction. We also introduce modifications to enhance DMD's robustness, numerical accuracy, and robustness of eigenvalues. DMD analysis yields a comprehensive understanding of flow patterns, internal wave formation, and the dynamics of the Strait of Gibraltar, its meandering behaviors, and the formation of a secondary gyre, notably the Western Alboran Gyre, as well as the propagation of Kelvin and coastal-trapped waves along the African coast. In doing so, it significantly advances our comprehension of intricate oceanographic phenomena and underscores the immense utility of DMD as an analytical tool for such complex datasets, suggesting that DMD could serve as a valuable addition to the toolkit of oceanographers.