  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.
