Numerical turbulence simulations typically involve parameterizations such as Large Eddy Simulations (LES). Applications to geophysical flows, especially ocean flows, are further complicated by the presence of complex topography and interior landforms such as coastlines, islands, and capes. In this work, we extend pseudo-spectral quasi-geostrophic (QG) numerical schemes and GPU-based solvers to simulate flows with coastal boundaries using the Brinkman volume penalization approach. We incorporate sponging and a splitting scheme to handle inflow and aperiodic boundary conditions. We evaluate four analytical sub-grid-scale (SGS) closures based on the eddy viscosity hypothesis: the standard Smagorinsky and Leith closures, and their dynamic variants. We show applications to QG flows past circular islands and capes with the β-plane approximation. We perform both a priori analysis of the SGS closure terms as well as a posteriori assessment of the SGS terms and simulated vorticity fields. Our results showcase differences between the various closures, especially their approach to phase and feature reconstruction errors in the presence of coastal boundaries.

In this paper, we use our MIT Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) including Error Subspace Statistical Estimation (ESSE) large-ensemble forecasting to provide real-time probabilistic forecasts for the Gulf of Mexico during the collaborative GRand Adaptive Sampling Experiment (GRASE) from April to September 2025. These forecasts are used for optimal planning and adaptive sampling for multiple platforms deployed during the experiment. We highlight real-time forecasts for probabilistic glider reachability and optimal planning. We showcase mutual information forecasts for optimal adaptive sampling with gliders and floats, maximizing information about the Loop Current (LC) and its eddies (LCEs). We showcase reachability and flow map forecasts for floats, characterizing water mass transports and eddy filamentations. We present probabilistic LCE forecasts using clustering techniques. Finally, we guide two gliders to recovery points using reachability and heading forecasts.

In this paper, we illustrate the use of our partial differential equations for flow maps to quantify Lagrangian transports and non-advective dynamics in geophysical fluid flows. Our emphasis is on the use of spatiotemporal flow maps to help differentiate the advective transports from non-advective transformations of water masses and ocean features in four dimensions. Preliminary results are presented for real-time sea experiments with autonomous sensing platforms and advanced modeling systems in diverse ocean regions and dynamical regimes. They include the Nova Scotia Shelf-Slope and New England Seamount Chain regions, Gulf of Mexico, and Balearic and Alboran Seas in the western Mediterranean. Our differentiations directly highlight regions of higher shear and mixing, including the edges of meanders, eddies, filaments, and internal waves, and the regions undergoing strong vertical or spiral motions.