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The purpose of this note is to present an enhancement to a Maxey–Riley theory proposed in recent years for the dynamics of inertial particles on the ocean surface [Beron-Vera et al., “Building a Maxey–Riley framework for surface ocean inertial particle dynamics,” Phys. Fluids 31, 096602 (2019)]. This updated model removes constraints on the reserve buoyancy, defined as the fraction of the particle volume above the ocean surface. The refinement results in an equation that correctly describes both the neutrally buoyant and fully buoyant particle scenarios. 

This study addresses the horizontal and vertical dispersion of passive tracers in idealized wind-driven subtropical gyres. Synthetic particles within a closed basin are numerically advected to analyze their dispersion under different theoretical velocity fields. Horizontal dispersion simulations incorporate the classic wind-driven Stommel circulation along with (i) surface Ekman drift associated with the Stommel wind field and (ii) inertial effects due to particle size and buoyancy. Results reveal that the Ekman drift inhibits particle dispersion across the entire domain leading to tracer concentration in a quasi-stable distribution skewed toward the western side of the basin. Similar behavior is observed with inertial particles. The equilibrium state is quantified for different diffusivity values, particle sizes, and buoyancies. For vertical dispersion, simulations incorporate the three-dimensional Ekman velocity, which includes a negative vertical component, while ignoring inertial effects. Initially, surface particles accumulate around the gyre center while slowly sinking, but they disperse across the basin once they surpass the Ekman layer and are free from surface effects. Tracers sink more on the western side of the basin, regardless of horizontal diffusivity. On average, ignoring inertial effects, particles sink less with higher diffusivity and more with lower diffusivity, suggesting a potential for high horizontal distribution of sunken tracers in the ocean. 

Ulam’s method is a popular discretization scheme for stochastic operators that involves the construction of a transition probability matrix controlling a Markov chain on a set of cells covering some domain. We consider an application to satellite-tracked undrogued surface-ocean drifting buoy trajectories obtained from the National Oceanic and Atmospheric Administration Global Drifter Program dataset. Motivated by the motion of Sargassum in the tropical Atlantic, we apply Transition Path Theory (TPT) to drifters originating off the west coast of Africa to the Gulf of Mexico. We find that the most common case of a regular covering by equal longitude–latitude side cells can lead to a large instability in the computed transition times as a function of the number of cells used. We propose a different covering based on a clustering of the trajectory data that is stable against the number of cells in the covering. We also propose a generalization of the standard transition time statistic of TPT that can be used to construct a partition of the domain of interest into weakly dynamically connected regions. 

A recent Maxey–Riley theory for Sargassum raft motion, which models a raft as a network of elastically interacting finite size, buoyant particles, predicts the carrying flow velocity to be given by the weighted sum of the water and air velocities (1−α)v+αw. The theory provides a closed formula for parameter α, referred to as windage, depending on the water-to-particle-density ratio or buoyancy (δ). From a series of laboratory experiments in an air–water stream flume facility under controlled conditions, we estimate α ranging from 0.02% to 0.96%. On average, our windage estimates can be up to nine times smaller than that considered in conventional Sargassum raft transport modeling, wherein it is customary to add a fraction of w to v chosen in an ad hoc piecemeal manner. Using the formula provided by the Maxey–Riley theory, we estimate δ ranging from 1.00 to 1.49. This is consistent with direct δ measurements, ranging from 0.9 to 1.25, which provide support for our α estimation. 

Abstract In this note, we apply transition path theory (TPT) from Markov chains to shed light on the problem of Iceland–Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded revision of the traditional abyssal circulation theory, which postulates that ISOW should steadily flow along a deep boundary current (DBC) around the subpolar North Atlantic prior to exiting it. The TPT analyses carried out here allow attention to be focused on the portions of flow from the origin of ISOW to the region where ISOW exits the subpolar North Atlantic and suggest that insufficient sampling may be biasing the aforementioned demand. The analyses, appropriately adapted to represent a continuous input of ISOW, are carried out on three time-homogeneous Markov chains modeling the ISOW flow. One is constructed using a high number of simulated trajectories homogeneously covering the flow domain. The other two use much fewer trajectories which heterogeneously cover the domain. The trajectories in the latter two chains are observed trajectories or simulated trajectories subsampled at the observed frequency. While the densely sampled chain supports a well-defined DBC, whether this is a peculiarity of the simulation considered or not, the more heterogeneously sampled chains do not, irrespective of the nature of the trajectories used, i.e., observed or simulated. Studying the sampling sensitivity of the Markov chains, we can give recommendations for enlarging the existing float dataset to improve the significance of conclusions about long-time-asymptotic aspects of the ISOW circulation. 

Abstract Recently introduced in oceanography to interpret the near surface circulation, Transition Path Theory ( TPT ) is a methodology that rigorously characterizes ensembles of trajectory pieces flowing out from a source last and into a target next, i.e., those that most productively contribute to transport. Here we use TPT to frame, in a statistically more robust fashion than earlier analysis, equatorward routes of North Atlantic Deep Water (NADW) in the subpolar North Atlantic. TPT is applied on all available RAFOS and Argo floats in the area by means of a discretization of the Lagrangian dynamics described by their trajectories. By considering floats at different depths, we investigate transition paths of NADW in its upper (UNADW) and lower (LNADW) layers. We find that the majority of UNADW transition paths sourced in the Labrador and southwestern Irminger Seas reach the western side of a target arranged zonally along the southern edge of the subpolar North Atlantic domain visited by the floats. This is accomplished in the form of a well-organized deep boundary current (DBC). LNADW transition paths sourced west of the Reykjanes Ridge reveal a similar pattern, while those sourced east of the ridge are found to hit the western side of the target via a DBC and also several other places along it in a less organized fashion, indicating southward flow along the eastern and western flanks of the Mid-Atlantic Ridge. Naked-eye inspection of trajectories suggest generally much more diffusive equatorward NADW routes. A source-independent dynamical decomposition of the flow domain into analogous backward-time basins of attraction, beyond the reach of direct inspection of trajectories, reveals a much wider influence of the western side of the target for UNADW than for LNADW. For UNADW, the average expected duration of the pathways from the Labrador and Irminger Seas was found to be of 2 to 3 years. For LNADW, the duration was found to be influenced by the Reykjanes Ridge, being as long as 8 years from the western side of the ridge and of about 3 years on average from its eastern side.