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

The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features arising from the interplay of topography, tidal forcing, hydrodynamic instabilities, and strongly nonlinear internal hydraulic processes, all governed by the nonlinear equations of fluid motion. In this study, we aim to uncover the underlying physics of these phenomena as represented in the 3D MIT general circulation model simulations, including simulated 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 numerical accuracy and the robustness of its eigenvalues. DMD analysis yields a comprehensive understanding of flow patterns, internal wave formation, and the dynamics and meandering behaviors within the Strait of Gibraltar, the formation of the secondary 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.