Chaotic advection, mixing, and property exchange in three-dimensional ocean eddies and gyres

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2018This work investigates how a Lagrangian perspective applies to models of two oceanographic flows: an overturning submesoscale eddy and the Western Alboran Gyre. In the first case, I focus on the importance of diffusion as compared to chaotic advection for tracers in this system. Three methods are used to quantify the relative contributions: scaling arguments including a Lagrangian Batchelor scale, statistical analysis of ensembles of trajectories, and Nakamura effective diffusivity from numerical simulations of dye release. Through these complementary methods, I find that chaotic advection dominates over turbulent diffusion in the widest chaotic regions, which always occur near the center and outer rim of the cylinder and sometimes occur in interior regions for Ekman numbers near 0.01. In thin chaotic regions, diffusion is at least as important as chaotic advection. From this analysis, it is clear that identified Lagrangian coherent structures will be barriers to transport for long times if they are much larger than the Batchelor scale. The second case is a model of the Western Alboran Gyre with realistic forcing and bathymetry. I examine its transport properties from both an Eulerian and Lagrangian perspective. I find that advection is most often the dominant term in Eulerian budgets for volume, salt, and heat in the gyre, with diffusion and surface fluxes playing a smaller role. In the vorticity budget, advection is as large as the effects of wind and viscous diffusion, but not dominant. For the Lagrangian analysis, I construct a moving gyre boundary from segments of the stable and unstable manifolds emanating from two persistent hyperbolic trajectories on the coast at the eastern and western extent of the gyre. These manifolds are computed on several isopycnals and stacked vertically to construct a three-dimensional Lagrangian gyre boundary. The regions these manifolds cover is the stirring region, where there is a path for water to reach the gyre. On timescales of days to weeks, water from the Atlantic Jet and the northern coast can enter the outer parts of the gyre, but there is a core region in the interior that is separate. Using a gate, I calculate the continuous advective transport across the Lagrangian boundary in three dimensions for the first time. A Lagrangian volume budget is calculated, and challenges in its closure are described. Lagrangian and Eulerian advective transports are found to be of similar magnitudes.Funding for this work was provided by Woods Hole Oceanographic Institution and the Office of Naval Research. The ONR support was through the MURI on Dynamical Systems Theory and Lagrangian Data Assimilation in 4D and the CALYPSO project