Ocean convergence and the dispersion of flotsam.

Floating oil, plastics, and marine organisms are continually redistributed by ocean surface currents. Prediction of their resulting distribution on the surface is a fundamental, long-standing, and practically important problem. The dominant paradigm is dispersion within the dynamical context of a nondivergent flow: objects initially close together will on average spread apart but the area of surface patches of material does not change.

Ergodicity and spectral cascades in point vortex flows on the sphere.

We present results for the equilibrium statistics and dynamic evolution of moderately large [n=O(10(2)-10(3))] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensemble-averaged wave-number spectra of the nonsingular velocity field induced by the vortices exhibit the expected k(-1) behavior at small scales for all energies.

Submesoscale dispersion in the vicinity of the Deepwater Horizon spill.

Reliable forecasts for the dispersion of oceanic contamination are important for coastal ecosystems, society, and the economy as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010 and the Fukushima nuclear plant incident in the Pacific Ocean in 2011. Accurate prediction of pollutant pathways and concentrations at the ocean surface requires understanding ocean dynamics over a broad range of spatial scales. Fundamental questions concerning the structure of the velocity field at the submesoscales (100 m to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales.

Persistent patterns and multifractality in fluid mixing.

Persistent patterns in periodically driven dynamics have been reported in a wide variety of contexts ranging from table-top and ocean-scale fluid mixing systems to the weak quantum-classical transition in open Hamiltonian systems. We illustrate a common framework for the emergence of these patterns by considering a simple measure of structure maintenance provided by the average radius of the scalar distribution in transform space. Within this framework, scaling laws related to both the formation and persistence of patterns in phase space are presented.

Acoustical dead zones and the spatial aggregation of whale strandings.

Cetacean strandings display a marked geographical clustering. We propose a simple, two-dimensional ray-dynamics model of cetacean echolocation to examine the role played by coastline topography in influencing the location and clustering of stranding sites. We find that a number of coastlines known to attract cetacean strandings produce acoustical "Dead Zones" where echolocation signals are severely distorted by purely geometric effects.