| Summary: | Multiscale ocean dynamics and multi-resolution numerical modeling of canyons and shelfbreaks are outlined. The dynamics focus is on fronts, currents, tides, and internal tides/waves that occur in these regions. Due to the topographic gradients and strong internal field gradients, nonlinear terms and non-hydrostatic dynamics can be significant. Computationally, a challenge is to achieve accurate simulations that resolve strong gradients over dynamically significant space- and time-scales. To do so, one component are high-order schemes that are more accurate for the same efficiency than lower-order schemes. A second is multi-resolution grids that allow optimized refinements, such as reducing errors near steep topography. A third are methods that allow to solve for multiple dynamics, e.g., hydrostatic and non-hydrostatic, seamlessly. To address these components, new hybridizable discontinuous Galerkin (HDG) finite-element schemes for (non)-hydrostatic physics including a nonlinear free-surface are introduced. The results of data-assimilative multi-resolution simulations are then discussed, using the primitive-equation MSEAS system and telescoping implicitly two-way nested domains. They correspond to collaborative experiments: (i) Shallow Water 06 (SW06) and the Integrated Ocean Dynamics and Acoustics (IODA) research in the Middle Atlantic Bight region; (ii) Quantifying, Predicting and Exploiting Uncertainty (QPE) in the Taiwan-Kuroshio region; and (iii) Philippines Straits Dynamics Experiment (PhilEx).
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