Nonhydrostatic, multiscale processes are an important part of our understanding of ocean dynamics. However, resolving these dynamics with traditional computational techniques can often be prohibitively expensive. We apply the hybridizable discontinuous Galerkin (HDG) finite element methodology to perform computationally efficient, high-order, nonhydrostatic ocean modeling by solving the Navier-Stokes equations with the Boussinesq approximation. In this work, we introduce a distributed implementation of our HDG projection method algorithm. We provide numerical experiments to verify our methodology using the method of manufactured solutions and provide preliminary benchmarking for our distributed implementation that highlight the advantages of the HDG methodology in the context of distributed computing. Lastly, we present simulations in which we capture nonhydrostatic internal waves that form as a result of tidal interactions with ocean topography. First, we consider the case of tidally-driven oscillatory flow over an abrupt, shallow seamount, and next, the case of strongly-stratified, oscillatory flow over a tall seamount. We analyze and compare our simulations to other results in literature.

The present paper demonstrates the use of exact equations to predict time-optimal mission plans for a marine vehicle that visits a number of locations in a given dynamic ocean current field. This problem bears close resemblance to that of the classic “traveling salesman”, albeit with the added complexity that the vehicle experiences a dynamic flow field while traversing the paths. The paths, or “legs”, between all goal waypoints are generated by numerically solving the exact time-optimal path planning level-set differential equations. Overall, the planning proceeds in four steps. First, current forecasts for the planning horizon is obtained utilizing our data-driven 4-D primitive equation ocean modeling system (Multidisciplinary Simulation Estimation and Assimilation System; MSEAS), forced by high-resolution tidal and real-time atmopsheric forcing fields. Second, all tour permutations are enumerated and the minimum number of times the time-optimal PDEs are to be solved is established. Third, due to the spatial and temporal dynamics, a varying start time results in different paths and durations for each leg and requires all permutations of travel to be calculated. To do so, the minimum required time-optimal PDEs are solved and the optimal travel time is computed for each leg of all enumerated tours. Finally, the tour permutation for which travel time is minimized is identified and the corresponding time-optimal paths are computed by solving the backtracking equation. Even though the method is very efficient and the optimal path can be computed serially in real-time for common naval operations, for additional computational speed, a high-performance computing cluster was used to solve the level set calculations in parallel. Our equation and software is applied to simulations of realistic naval applications in the complex Philippines Archipelago region. Our method calculates the global optimum and can serve two purposes: (a) it can be used in its present form to plan multiwaypoint missions offline in conjunction with a predictive ocean current modeling system, or (b) it can be used as a litmus test for approximate future solutions to the traveling salesman problem in dynamic flow fields.

The interest in hydrokinetic conversion systems has significantly grown over the last decade with a special focus on cross-flow systems, generally known as Vertical Axis Water Turbines (VAWTs). However, analyzing of regions of interest for tidal energy extraction and outlining optimal rotor geometry is currently very computationally expensive via conventional 3D Computational Fluid Dynamics (CFD) methods. In this work, a VAWT load prediction routine developed at University of Pisa based upon the Blade Element-Momentum (BEM) theory is presented and validated against high-resolution 2D CFD simulations. Our model is able to work in two configurations, i.e. Double-Multiple Streamtube (DMST) mode, using 1D flow simplifications for quick analyses, and Hybrid mode, coupled to a CFD software for more accurate results. As a practical application, our routine is employed for a site assessment analysis of the Cape Cod area to quickly highlight oceanic regions with high hydrokinetic potential, where further higher-order and more computationally expensive CFD analyses can be performed. Ocean data are obtained from data-assimilative ocean simulations predicted by the 4D regional ocean modeling system of the Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) group of the Massachusetts Institute of Technology.

Recent advances in probabilistic forecasting of regional ocean dynamics, and stochastic optimal path planning with massive ensembles motivate principled analysis of their large datasets. Specifically, stochastic time-optimal path planning in strong, dynamic and uncertain ocean flows produces a massive dataset of the stochastic distribution of exact timeoptimal trajectories. To synthesize such big data and draw insights, we apply machine learning and data mining algorithms. Particularly, clustering of the time-optimal trajectories is important to describe their PDFs, identify representative paths, and compute and optimize risk of following these paths. In the present paper, we explore the use of hierarchical clustering algorithms along with a dissimilarity matrix computed from the pairwise discrete Frechet distance between all the optimal trajectories. We apply the algorithms to two datasets of massive ensembles of vehicle trajectories in a stochastic flow past a circular island and stochastic wind driven double gyre flow. These paths are computed by solving our dynamically orthogonal level set equations. Hierarchical clustering is applied to the two datasets, and results are qualitatively and quantitatively analyzed.