arXiv subjects

F. J. Beron-Vera

Publications and source records attributed to F. J. Beron-Vera.

At least 37 records · Page 2Linked to original sources

arXiv2020

Nonlinear dynamics of inertial particles in the ocean: From drifters and floats to marine debris and Sargassum

Buoyant, finite-size or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey-Riley equation. Derived from first principles - a result of over a century of research since the pioneering work by Sir George Stokes - the Maxey-Riley equation is a Newton-type-law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper we present an overview of recent efforts to port the Maxey-Riley framework to oceanography. These involved: 1) including the Coriolis force, which was found to explain behavior of submerged floats near mesoscale eddies; 2) accounting for the combined effects of ocean current and wind drag on inertial particles floating at the air-sea interface, which helped understand the formation of great garbage patches and the role of anticyclonic eddies as plastic debris traps; and 3) incorporating elastic forces, which are needed to simulate the drift of pelagic Sargassum. Insight on the nonlinear dynamics of inertial particles in every case was possible to be achieved by investigating long-time asymptotic behavior in the various Maxey-Riley equation forms, which represent singular perturbation problems involving slow and fast variables.

physics.ao-ph↗

arXiv2020

Transition paths of marine debris and the stability of the garbage patches

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 NOAA 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.

physics.ao-ph↗

arXiv2020

Genesis, evolution, and apocalypse of Loop Current rings

We carry out assessments of the life cycle of Loop Current vortices, so-called rings, in the Gulf of Mexico by applying three objective (i.e., observer-independent) coherent Lagrangian vortex detection methods on velocities derived from satellite altimetry measurements of sea-surface height (SSH). The methods reveal material vortices with boundaries that withstand stretching or diffusion, or whose fluid elements rotate evenly. This involved a technology advance that enables framing vortex genesis and apocalypse robustly and with precision. We find that the stretching- and diffusion-withstanding assessments produce consistent results, which show large discrepancies with Eulerian assessments that identify vortices with regions instantaneously filled with streamlines of the SSH field. The even-rotation assessment, which is vorticity-based, is found to be quite unstable, suggesting life expectancies much shorter than those produced by all other assessments.

physics.ao-ph↗

arXiv2020

Clustering of marine-debris- and \emph{Sargassum}-like drifters explained by inertial particle dynamics}

Drifters designed to mimic floating marine debris and small patches of pelagic \emph{Sargassum} were satellite tracked in four regions across the North Atlantic. Though subjected to the same initial conditions at each site, the tracks of different drifters quickly diverged after deployment. We explain the clustering of drifter types using a recent Maxey-Riley theory for surface ocean inertial particle dynamics applied on multidata-based mesoscale ocean currents and winds from reanalysis. Simulated trajectories of objects at the air-sea interface are significantly improved when represented as inertial (accounting for buoyancy and size), rather than as perfectly Lagrangian (fluid following) particles. Separation distances between simulated and observed trajectories were substantially smaller for debris-like drifters than for \emph{Sargassum}-like drifters, suggesting that additional consideration of its physical properties relative to fluid velocities may be useful. Our findings can be applied to model variability in movements and distribution of diverse objects floating at the ocean surface.

physics.ao-ph↗

arXiv2019

Observation and quantification of inertial effects on the drift of floating objects at the ocean surface

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.

physics.ao-ph↗

arXiv2019

Building a Maxey--Riley framework for surface ocean inertial particle dynamics

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 air--sea 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.

physics.ao-ph↗

arXiv2019

Markov-chain-inspired search for MH370

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$^{\circ}$S on the Inmarsat arc.

stat.AP↗

arXiv2018

Enduring Lagrangian coherence of a Loop Current ring assessed using independent observations

Ocean flows are routinely inferred from low-resolution satellite altimetry measurements of sea surface height assuming a geostrophic balance. Recent nonlinear dynamical systems techniques have revealed that surface currents derived from altimetry can support mesoscale eddies with material boundaries that do not filament for many months, thereby representing effective transport mechanisms. However, the long-range Lagrangian coherence assessed for mesoscale eddy boundaries detected from altimetry is constrained by the impossibility of current altimeters to resolve ageostrophic submesoscale motions. These may act to prevent Lagrangian coherence from manifesting in the rigorous form described by the nonlinear dynamical systems theories. Here we use a combination of satellite ocean color and surface drifter trajectory data, rarely available simultaneously over an extended period of time, to provide observational evidence for the enduring Lagrangian coherence of a Loop Current ring detected from altimetry. We also seek indications of this behavior in the flow produced by a data-assimilative system which demonstrated ability to reproduce observed relative dispersion statistics down into the marginally submesoscale range. However, the simulated flow, total surface and subsurface or subsampled emulating altimetry, is not found to support the long-lasting Lagrangian coherence that characterizes the observed ring. This highlights the importance of the Lagrangian metrics produced by the nonlinear dynamical systems tools employed here in assessing model performance.

physics.ao-ph↗

arXiv2017

Persistent Lagrangian transport patterns in the northwestern Gulf of Mexico

Persistent Lagrangian transport patterns at the ocean surface are revealed from Lagrangian Coherent Structures (LCSs) computed from daily climatological surface current velocities in the northwestern Gulf of Mexico (NWGoM). The velocities are produced by a submesoscale permitting regional ocean model of the Gulf of Mexico. The significance of the climatological LCSs (cLCSs) is supported with ensemble-mean drifter density evolutions from simulated and historical satellite-tracked drifter trajectories. A persistent attracting barrier between the NWGoM shelf and the deep ocean is effectively identified by a hook-like pattern associated with groups of overall strongly attracting cLCSs that extend along the shelf break. Localized reductions in the attraction rate along these overall strongly attracting cLCSs proximal to cross-shore oriented cLCSs identify a pathway for potential transport across the shelf break. Groups of overall weakly-attracting cLCSs are not seen to strongly constrain material transport. Tracers originating over the shelf tend to be trapped there by the hook-like pattern as they spread cyclonically. Tracers originating beyond the shelf tend to be initially attracted to the hook-like pattern as they spread anti-cyclonically and eventually over the deep ocean. The findings have important implications for the mitigation of contaminant accidents such as oil spills.

physics.ao-ph↗

arXiv2017

Lagrangian dynamical geography of the Gulf of Mexico

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.

physics.ao-ph↗

arXiv2016

Statistics of simulated and observed pair separations in the Gulf of Mexico

Pair-separation statistics of in-situ and synthetic surface drifters deployed near the \emph{Deepwater Horizon} site in the Gulf of Mexico are investigated. The synthetic trajectories derive from a 1-km-resolution data-assimilative Navy Coastal Ocean Model (NCOM) simulation. The in-situ drifters were launched in the Grand LAgrangian Deployment (GLAD). Diverse measures of the dispersion are calculated and compared to theoretical predictions. For the NCOM pairs, the measures indicate nonlocal pair dispersion at the smallest sampled scales. At separations exceeding 100 km, pair motion is uncorrelated, indicating absolute rather than relative dispersion. With the GLAD drifters however the statistics suggest local dispersion (in which pair separations exhibit power law growth), in line with previous findings. The disagreement stems in part from inertial oscillations, which affect the energy levels at small scales without greatly altering the net particle displacements. They were significant in GLAD but much weaker in the NCOM simulations. In addition the GLAD drifters were launched close together, producing few independent realizations and hence weaker statistical significance. Restricting the NCOM set to those launched at the same locations yields very similar statistics.

physics.ao-ph↗

arXiv2016

The life cycle of a coherent Lagrangian Agulhas ring

We document the long-term evolution of an Agulhas ring detected from satellite altimetry using a technique from nonlinear dynamical systems that enables objective (i.e., observer-independent) eddy framing. Such objectively detected eddies have Lagrangian (material) boundaries that remain coherent (unfilamented) over the detection period. The ring preserves a quite compact material entity for a period of about 2 years even after most initial coherence is lost within 5 months after detection. We attribute this to the successive development of short-term coherent material boundaries around the ring. These boundaries provide effective short-term shielding for the ring, which prevents a large fraction of the ring's interior from being mixed with the ambient turbulent flow. We show that such coherence regain events cannot be inferred from Eulerian analysis. This process is terminated by a ring-splitting event which marks the ring demise, near the South American coast. The genesis of the ring is characterized by a ring-merging event away from the Agulhas retroflection, followed by a 4-month-long partial coherence stage, scenario that is quite different than a simple current occlusion and subsequent eddy pinch off.

physics.ao-ph↗

arXiv2015

Coherent water transport across the South Atlantic

The role of mesoscale eddies in transporting Agulhas leakage is investigated using a recent technique from nonlinear dynamical systems theory applied on geostrophic currents inferred from the over two-decade-long satellite altimetry record. Eddies are found to acquire material coherence away from the Agulhas retroflection, near the Walvis Ridge in the South Atlantic. Yearly, 1 to 4 coherent material eddies are detected with diameters ranging from 40 to 280 km. A total of 23 eddy cores of about 50 km in diameter and with at least 30\pct of their contents traceable into the Indian Ocean were found to travel across the subtropical gyre with minor filamentation. Only 1 eddy core was found to pour its contents on the North Brazil Current. While ability of eddies to carry Agulhas leakage northwestward across the South Atlantic is supported by our analysis, this is more restricted than suggested by earlier ring transport assessments.

physics.ao-ph↗

arXiv2015

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived \emph{Sargassum} distributions.

physics.ao-ph↗

arXiv2014

Addendum to "Coherent Lagrangian vortices: The black holes of turbulence"

In Haller and Beron-Vera (2013) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null-geodesics of the Lorentzian metric associated with a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here we give an improved discussion on this analogy.

physics.ao-ph↗

arXiv2013

Coherent Lagrangian vortices: The black holes of turbulence

We introduce a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. Solutions to this problem turn out to be mathematically equivalent to photon spheres around black holes in cosmology. The fluidic photon spheres satisfy explicit differential equations whose outermost limit cycles are optimal Lagrangian vortex boundaries. As an application, we uncover super-coherent material eddies in the South Atlantic, which yield specific Lagrangian transport estimates for Agulhas rings.

physics.ao-ph↗

arXiv2008

Zonal Jets as Transport Barriers in Planetary Atmospheres

The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV-staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV-steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV-staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter's midlatitude weather layer and in the Earth's summer hemisphere subtropical stratosphere.

physics.ao-ph↗

arXiv2007

Tracing the early development of harmful algal blooms with the aid of Lagrangian coherent structures

Several theories have been proposed to explain the development of harmful algal blooms (HABs) produced by the toxic dinoflagellate \emph{Karenia brevis} on the West Florida Shelf. However, because the early stages of HAB development are usually not detected, these theories have been so far very difficult to verify. In this paper we employ simulated \emph{Lagrangian coherent structures} (LCSs) to trace the early location of a HAB in late 2004 before it was transported to an area where it could be detected by satellite imagery, and then we make use of a population dynamics model to infer the factors that may have led to its development. The LCSs, which are computed based on a surface flow description provided by an ocean circulation model, delineate past and future histories of boundaries of passively advected fluid domains. The population dynamics model determines nitrogen in two components, nutrients and phytoplankton, which are assumed to be passively advected by the simulated surface currents. Two nearshore nutrient sources are identified for the HAB whose evolution is found to be strongly tied to the simulated LCSs. While one nutrient source can be associated with a coastal upwelling event, the other is seen to be produced by river runoff, which provides support to a theory of HAB development that considers nutrient loading into coastal waters produced by human activities as a critical element. Our results show that the use of simulated LCSs and a population dynamics model can greatly enhance our understanding of the early stages of the development of HABs.

physics.ao-ph↗