Crossover of boundary currents in the Red Sea is seen in mean circulation schemes from several models. This work studies buoyancy-forced circulation in an idealized Red Sea. The mechanism that controls the crossover of boundary currents is explored by using an eddy-resolving numerical model and an analytical estimate on a β-plane. The observational support is also reviewed. The surface buoyancy loss increases northward in the idealized model. The resolved mean circulation consists of an anticyclonic gyre in the south and a cyclonic gyre in the north. In mid-basin, the northward surface flow crosses from the western boundary to the eastern boundary. Numerical experiments with different parameters indicate that the crossover latitude of the boundary currents changes with f₀, β and the meridional gradient of surface buoyancy forcing. An ad hoc analytical model is developed based on PV dynamics and successfully predicts the crossover latitude of boundary currents. In the analytical estimate, the sign of PV advection determines the location of the northward boundary currents. It is the competition between the advection of planetary PV and the buoyancy-loss related term that determines the crossover latitude.

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.

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.