A framework for the study of surface ocean inertial particle motion is built from the Maxey-Riley set. A new set is obtained by vertically averaging each term of the original set, adapted to account for Earth's rotation effects, across the extent of a sufficiently small spherical particle that floats at an assumed unperturbed airsea interface with unsteady nonuniform winds and ocean currents above and below, respectively. The inertial particle velocity is shown to exponentially decay in time to a velocity that lies close to an average of seawater and air velocities, weighted by a function of the seawater-to-particle density ratio. Such a weighted average velocity turns out to fortuitously be of the type commonly discussed in the search-and-rescue literature, which alone cannot explain the observed role of anticyclonic mesoscale eddies as traps for marine debris or the formation of great garbage patches in the subtropical gyres, phenomena dominated by finite-size effects. A heuristic extension of the theory is proposed to describe the motion of nonspherical particles by means of a simple shape factor correction, and recommendations are made for incorporating wave-induced Stokes drift, and allowing for inhomogeneities of the carrying fluid density. The new Maxey-Riley set outperforms an ocean adaptation that ignored wind drag effects and the first reported adaption that attempted to incorporate them.

We construct a Markov-chain representation of the surface-ocean Lagrangian dynamics in a region occupied by the Gulf of Mexico (GoM) and adjacent portions of the Caribbean Sea and North Atlantic using satellite-tracked drifter trajectory data, the largest collection so far considered. From the analysis of the eigenvectors of the transition matrix associated with the chain, we identify almost-invariant attracting sets and their basins of attraction. With this information we decompose the GoM’s geography into weakly dynamically interacting provinces, which constrain the connectivity between distant locations within the GoM. Offshore oil exploration, oil spill contingency planning, and fish larval connectivity assessment are among the many activities that can benefit from the dynamical information carried in the geography constructed here.

We present results from an experiment designed to better understand the mechanism by which ocean currents and winds control flotsam drift. The experiment consisted in deploying in the Florida Current and subsequently satellite tracking specially designed drifting buoys of varied sizes, buoyancies, and shapes. We explain the differences in the trajectories described by the special drifters as a result of their inertia, primarily buoyancy, which constrains the ability of the drifters to adapt their velocities to instantaneous changes in the ocean current and wind that define the carrying flow field. Our explanation of the observed behavior follows from the application of a recently proposed Maxey-Riley theory for the motion of finite-size particles floating at the surface ocean. The nature of the carrying flow and the domain of validity of the theory are clarified, and a closure proposal is made to fully determine its parameters in terms of the carrying fluid system properties and inertial particle characteristics.

Using trajectories from acoustically tracked (RAFOS) floats in the Gulf of Mexico, we construct a geography of its Lagrangian circulation within the 1500–2500-m layer. This is done by building a Markov-chain representation of the Lagrangian dynamics. The geography is composed of weakly interacting provinces that constrain the connectivity at depth. The main geography includes two provinces of near-equal areas separated by a roughly meridional boundary. The residence time is about 4.5 (3.5) years in the western (eastern) province. The exchange between these provinces is effected through a slow cyclonic circulation, which is well constrained in the western basin by preservation of f/H, where f is the Coriolis parameter and H is depth. Secondary provinces of varied shapes covering smaller areas are identified with residence times ranging from about 0.4 to 1.2 years or so. Except for the main provinces, the deep Lagrangian geography does not resemble the surface Lagrangian geography recently inferred from satellite-tracked drifter trajectories. This implies disparate connectivity characteristics with potential implications for pollutant (e.g., oil) dispersal at the surface and at depth. Support for our results is provided by a Markov-chain analysis of satellite-tracked profiling (Argo) floats, which, while forming a smaller dataset and having seemingly different water-following characteristics than the RAFOS floats, replicate the main aspects of the Lagrangian geography. Our results find further validation in independent results from a chemical tracer release experiment.

We used transition path theory (TPT) to infer “reactive” pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the National Oceanic and Atmospheric Administration's Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific garbage patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds.

Markov-chain models are constructed for the probabilistic description of the drift of marine debris from Malaysian Airlines flight MH370. En route from Kuala Lumpur to Beijing, the MH370 mysteriously disappeared in the southeastern Indian Ocean on 8 March 2014, somewhere along the arc of the 7th ping ring around the Inmarsat-3F1 satellite position when the airplane lost contact. The models are obtained by discretizing the motion of undrogued satellite-tracked surface drifting buoys from the global historical data bank. A spectral analysis, Bayesian estimation, and the computation of most probable paths between the Inmarsat arc and confirmed airplane debris beaching sites are shown to constrain the crash site, near 25 • S on the Inmarsat arc.PACS numbers: 02.50.Ga; 47.27.De; 92.10.Fj Application of tools from ergodic theory on historical Lagrangian ocean data is shown to constrain the crash site of Malaysian Airlines flight MH370 given airplane debris beaching site information. The disappearance of flight MH370 constitutes one of the most enigmatic episodes in the history of commercial aviation. The tools employed have far-reaching applicability as they are particularly well suited in inverse modeling, critical for instance in revealing contamination sources in the ocean and the atmosphere. The only requirement for their success is sufficient spatiotemporal Lagrangian sampling.

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