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MSEAS research featured on MIT front page

Recent results from the MSEAS group on the multiscale interactions of internal tides in the Middle Atlantic Bight and Shelfbreak front regions were featured on MIT front page on Sept 28, 2016. The article is entitled “Researchers find explanation for interacting giant, hidden ocean waves” and can be accessed here. The relevant papers “Internal-tide Interactions with the Gulf Stream and Middle Atlantic Bight Shelfbreak Front” published in JGR Oceans can be accessed here and the paper “A Coupled-mode Shallow Water model for tidal analysis: Internal-tide reflection and refraction by the Gulf Stream” published in JPO can be accessed here.

Time-Optimal Path Planning in Dynamic Flows using Level Set Equations: Realistic Applications

Lolla, T., P.J. Haley, Jr. and P.F.J. Lermusiaux, 2014. Time-Optimal Path Planning in Dynamic Flows using Level Set Equations: Realistic Applications. Ocean Dynamics, 64, 10:1399–1417. DOI: 10.1007/s10236-014-0760-3.

The level set methodology for time-optimal path planning is employed to predict collision-free and fastest time trajectories for swarms of underwater vehicles deployed in the Philippine Archipelago region. To simulate the multiscale ocean flows in this complex region, a data-assimilative primitive-equation ocean modeling system is employed with telescoping domains that are interconnected by implicit two-way nesting. These data-driven multiresolution simulations provide a realistic flow environment, including variable large-scale currents, strong jets, eddies, wind-driven currents and tides. The properties and capabilities of the rigorous level set methodology are illustrated and assessed quantitatively for several vehicle types and mission scenarios. Feasibility studies of all-to-all broadcast missions, leading to minimal time transmission between source and receiver locations, are performed using a large number of vehicles. The results with gliders and faster propelled vehicles are compared. Reachability studies, i.e.~determining the boundaries of regions that can be reached by vehicles for exploratory missions, are then exemplified and analyzed. Finally, the methodology is used to determine the optimal strategies for fastest time pick-up of deployed gliders by means of underway surface vessels or stationary platforms. The results highlight the complex effects of multiscale flows on the optimal paths, the need to utilize the ocean environment for more efficient autonomous missions and the benefits of including ocean forecasts in the planning of time-optimal paths.

Time-Optimal Path Planning in Dynamic Flows using Level Set Equations: Theory and Schemes

Lolla, T., P.F.J. Lermusiaux, M.P. Ueckermann and P.J. Haley, Jr., 2014. Time-Optimal Path Planning in Dynamic Flows using Level Set Equations: Theory and Schemes. Ocean Dynamics, 64, 10:1373–1397. DOI: 10.1007/s10236-014-0757-y.

We develop an accurate partial differential equation based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow-fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned, even in the presence of complex flows in domains with obstacles. Finally, we present, and support through illustrations, several remarks that describe specific features of our methodology.

Global Analysis of Navier-Stokes and Boussinesq Stochastic Flows using Dynamical Orthogonality

Sapsis, T.P., M.P. Ueckermann and P.F.J. Lermusiaux, 2013. Global Analysis of Navier-Stokes and Boussinesq Stochastic Flows using Dynamical Orthogonality, J. Fluid Mech., 734, 83-113. doi:10.1017/jfm.2013.458

We provide a new framework for the study of fl‡uid ‡flows presenting complex uncertain behavior. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal field equations. By numerically solving these equations we evolve in a fully coupled way the mean fl‡ow and the statistical and spatial characteristics of the stochastic fl‡uctuations. This set of equations is formulated for the general case of stochastic boundary conditions and allows for the application of projection methods that reduce considerably the computational cost. We analyze the transformation of energy from stochastic modes to mean dynamics, and vice-versa, by deriving exact expressions that quantify the interaction among different components of the fl‡ow. The developed framework is illustrated through specifi…c fl‡ows in unstable regimes. In particular, we consider the ‡flow behind a disk and the Rayleigh–-Bénard convection, for which we construct bifurcation diagrams that describe the variation of the response as well as the energy transfers for different parameters associated with the considered ‡flows. We reveal the low-dimensionality of the underlying stochastic attractor.