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.