The Strait of Gibraltar is a region characterized by intricate oceanic submesoscale 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 Massachusetts Institute of Technology (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, and 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.

Buffet is a self-sustaining oscillation that can endanger an aircraft in transonic flight. Early automatic detection of the onset of buffet from simulation data is a necessary step in optimization algorithms used to design new aircraft geometries. We use the Dynamic Mode Decomposition (DMD) eigenvalues to detect the onset of buffet from transient simulations of the OAT15A airfoil across a range of angles of attack. During transients, different eigenvalues may be expressed at different times, and we process shorter segments of the data (sliding windows) in order to obtain robust, time-varying estimates of frequency of oscillation and decay/growth rates. We demonstrate that the onset of oscillation can be identified by analyzing DMD eigenvalues, and that physically different mechanisms of oscillation can additionally be identified from spatial profiles associated with DMD modes. The dominant buffeting modes can be detected through DMD before they become apparent in the physically relevant quantities, such as the coefficient of lift. We expect that such early detection of the onset of buffet could reduce the computational burden of aircraft design and expand the feasible design space.

Transonic buffet, characterized by shock-induced oscillations, presents a significant challenge to aircraft stability and performance. This study developed a sensor based on Dynamic Mode Decomposition (DMD) to predict buffet onset by analyzing the aerodynamic characteristics of the OAT15A airfoil under varying flow conditions, including different Mach numbers, Reynolds numbers, and angles of attack. The sensor was developed using data from a simulation at a Reynolds number of $3 \times 10^6$, a Mach number of 0.73, and an angle of attack of 3.35. The sliding-window DMD approach was employed to accurately identify the Strouhal number associated with buffeting and the transitions in flow stability, leading to the determination of the buffet onset boundary for different flow conditions. This boundary was subsequently used to validate the sensor, resulting in the development of a robust buffet detection tool. The sensor can be integrated into the design cycle to monitor and dynamically adjust parameters, thereby preempting buffet conditions.