arXiv subjects

Francisco J. Beron-Vera

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

14 recordsLinked to original sources

arXiv2026

Geodesic vortex detection on curved surfaces: Analyzing the 2002 austral stratospheric polar vortex warming event

Geodesic vortex detection is a tool in nonlinear dynamical systems to objectively identify transient vortices with flow-invariant boundaries that defy the typical deformation found in 2-d turbulence. Initially formulated for flows on the Euclidean plane with Cartesian coordinates, we have extended this technique to flows on 2-d Riemannian manifolds with arbitrary coordinates. This extension required the further formulation of the concept of objectivity on manifolds. Moreover, a recently proposed birth-and-death vortex framing algorithm, based on geodesic detection, has been adapted to address the limited temporal validity of 2-d motion in otherwise 3-d flows, like those found in the Earth's stratosphere. With these adaptations, we focused on the Lagrangian, i.e., kinematic, aspects of the austral stratospheric polar vortex during the exceptional sudden warming event of 2002, which resulted in the vortex splitting. This study involved applying geodesic vortex detection to isentropic winds from reanalysis data. We provide a detailed analysis of the vortex's life cycle, covering its birth, the splitting process, and its eventual death. In addition, we offer new kinematic insights into ozone depletion within the vortex.

nlin.CD↗

arXiv2026

Predictability of El Niño from Delayed Observations

Using monthly Niño-3.4 anomalies through July 2026, we investigate how much predictive information is contained in delayed observations of the index. Ridge regression identifies informative delays, while multilayer perceptron and sparse identification of nonlinear dynamics (SINDy) models test whether nonlinear complexity provides additional direct forecast skill; gated recurrent unit (GRU) and long short-term memory (LSTM) networks provide a complementary test in which the temporal representation is learned internally. Delayed observations substantially improve forecasts over persistence and climatology at leads of up to six months, but increasing model complexity provides no systematic improvement. Historical recursive experiments favor a simple explicit SINDy recurrence and select shallow recurrent architectures, with no appreciable gain from learning the temporal representation internally. These results support a compact predictive representation of Niño-3.4 evolution in which the representation of past information is more consequential than model complexity. As a prospective application, the selected models are used to forecast the developing 2026 event beyond the last available observation and to compare its predicted evolution with completed historical El Niño events.

physics.ao-ph↗

arXiv2026

A new formulation of metriplectic dynamics with an application to quasigeostrophic ocean modeling with advected quantities

A general formulation of metriplectic dynamics is presented, where the metriplectic four-bracket is constructed by multiplying two skew-symmetric brackets. The new formulation is then used to introduce irreversibility in a generalized two-dimensional (2D) quasigeostrophic (QG) upper-ocean model involving advected quantities, with the thermal QG model as a special case. By construction, the resulting dynamics ensure the conservation of internal energy and the generation of entropy, in accordance with the first and second laws of thermodynamics. Our metriplectic dynamics formulation allows for a flexible specification of irreversibility, ranging from a type that results in nearly material conservation of potential vorticity to the representation of realistic forcing and dissipation in 2D QG ocean modeling with advected quantities.

math-ph↗

arXiv2026

Quasi-material finite-time rotationally coherent sets in photospheric supergranulation

Supergranular flows organize transport in the solar photosphere over spatial and temporal scales much larger than granulation. While coherent vortical motions have been identified using objective Lagrangian diagnostics such as the Lagrangian-averaged vorticity deviation (LAVD), rotational coherence captures only one aspect of coherent flow organization. Here we introduce finite-time rotationally coherent sets (FTRCS) by combining the inflated dynamic Laplacian (IDL), which identifies finite-time quasi-material coherent regions, with LAVD-based rotational diagnostics. The IDL extracts coherent structures with finite lifetimes, while LAVD identifies those exhibiting enhanced intrinsic rotation. Application to photospheric velocity fields shows that instantaneous vortical features do not necessarily correspond to finite-time rotationally coherent structures. The analysis also illustrates the effect of compressibility: coherent sets may form through persistent contraction associated with convergent transport, rather than through the persistence of rotating material regions. The combined IDL--LAVD approach separates finite-time transport coherence from intrinsic rotational organization in time-dependent flows.

physics.flu-dyn↗

arXiv2026

Loop Current Extension as an Effective Delayed Dynamical System

The Loop Current is the dominant circulation feature of the Gulf of Mexico and exhibits pronounced variability associated with northward extension, retraction, and eddy shedding. Despite decades of study, the extent to which this variability admits a reduced dynamical description remains unclear. We investigate this question using delayed-coordinate representations constructed from satellite-altimetry observations of Loop Current extension. Ridge regression, multilayer perceptron forecasting, and Sparse Identification of Nonlinear Dynamics (SINDy) are applied to learn delayed evolution maps from the extension time series. Forecast skill consistently exceeds persistence at lead times of 30--90 days while requiring only a small number of delayed coordinates. Ridge regression reveals saturation with delayed-state dimension, indicating that much of the predictive information is contained within a compact representation. Neural-network forecasts provide modest additional improvements, while delayed SINDy identifies sparse evolution maps involving intraseasonal memory scales, from approximately two weeks to a few months, that remain stable under recursive iteration. Physical diagnostics associated with Yucatan Channel inflow, Florida Straits outflow, gateway geometry, and northern Caribbean vorticity contain predictive information but do not provide additional independent state information once the delayed Loop Current state is included. These results support the interpretation of Loop Current extension as an observable evolving on an effective low-dimensional delayed dynamical system. A substantial fraction of the predictable variability can be reconstructed from a small number of delayed observations and represented through compact delayed evolution maps.

nlin.CD↗

arXiv2026

Tracing the origin of tropical North Atlantic Sargassum blooms to West Africa

We simulate the dynamics of pelagic \emph{Sargassum} rafts as systems of finite-size floating particles, governed by a Maxey--Riley law with nonlinear elastic interactions. Using surface ocean currents and wind data from reanalysis systems for clump transport, we computed trajectories within a domain covering the tropical and subtropical north Atlantic. The subsequent motion is reduced using Ulam's discretization method into a time-inhomogeneous Markov chain that simulates a background \emph{Sargassum} concentration. Bayesian inversion, combined with nonautonomous transition path theory, was used to infer the origin of the first significant recorded bloom in the tropical North Atlantic, which unfolded in April 2011. Both methodologies independently identified the bloom's origin as near the West African coast, up to two years before it was detectable via satellite imagery on the basin's western side. This finding supports anecdotal evidence of \emph{Sargassum} strandings on the Ghanaian coast in 2009. Moreover, it correlates with unusual environmental conditions -- such as increased nutrient loads from significant upwelling linked to a pronounced Dakar Niña and Saharan dust deposition -- that promote bloom proliferation. Additionally, it aligns with the observation that the species of \emph{Sargassum} in the 2011 bloom differ from those in the Sargasso Sea, which might otherwise be considered a natural origin.

physics.ao-ph↗

arXiv2025

Discovering the dynamics of \emph{Sargassum} rafts' centers of mass

Since 2011, rafts of floating \emph{Sargassum} seaweed have frequently obstructed the coasts of the Intra-Americas Seas. The motion of the rafts is represented by a high-dimensional nonlinear dynamical system. Referred to as the eBOMB model, this builds on the Maxey--Riley equation by incorporating interactions between clumps of \emph{Sargassum} forming a raft and the effects of Earth's rotation. The absence of a predictive law for the rafts' centers of mass suggests a need for machine learning. In this paper, we evaluate and contrast Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs) and Sparse Identification of Nonlinear Dynamics (SINDy). In both cases, a physics-inspired closure modeling approach is taken rooted in eBOMB. Specifically, the LSTM model learns a mapping from a collection of eBOMB variables to the difference between raft center-of-mass and ocean velocities. The SINDy model's library of candidate functions is suggested by eBOMB variables and includes windowed velocity terms incorporating far-field effects of the carrying flow. Both LSTM and SINDy models perform most effectively in conditions with tightly bonded clumps, despite declining precision with rising complexity, such as with wind effects and when assessing loosely connected clumps. The LSTM model delivered the best results when designs were straightforward, with fewer neurons and hidden layers. While LSTM model serves as an opaque black-box model lacking interpretability, the SINDy model brings transparency by discerning explicit functional relationships through the function libraries. Integration of the windowed velocity terms enabled effective modeling of nonlocal interactions, particularly in datasets featuring sparsely connected rafts.

nlin.CD↗

arXiv2024

Dual Euler--Poincaré/Lie--Poisson formulation of subinertial stratified thermal ocean flow with identification of Casimirs as Noether quantities

This paper investigates the geometric structure of a quasigeostrophic approximation to a recently introduced reduced-gravity thermal rotating shallow-water model that accounts for stratification. Specifically, it considers a low-frequency approximation of a model for flow above the ocean thermocline, governed by primitive equations with buoyancy variations in both horizontal and vertical directions. Like the thermal model, the stratified variant generates circulation patterns reminiscent of submesoscale instabilities visible in satellite images. An improvement is its ability to model mixed-layer restratification due to baroclinic instability. The primary contribution of this paper is to demonstrate that the model is derived from an Euler--Poincaré variational principle, culminating in a Kelvin--Noether theorem, previously established solely for the primitive-equation parent model. The model's Lie--Poisson Hamiltonian structure, earlier obtained through direct calculation, is shown to result from a Legendre transform with the associated geometry elucidated by identifying the relevant momentum map. Another significant contribution of this paper is the identification of the Casimirs of the Lie--Poisson system, including a newly found weaker Casimir family forming the kernel of the Lie--Poisson bracket, which results in potential vorticity evolution independent of buoyancy details as it advects under the flow. These conservation laws related to particle relabeling symmetry are explicitly linked to Noether quantities from the Euler--Poincaré principle when variations are not constrained to vanish at integration endpoints. The dual Euler--Poincaré/Lie--Poisson formalism provides a unified framework for describing quasigeostrophic reduced-gravity stratified thermal flow, mirroring the approach used in the primitive-equation setting.

physics.flu-dyn↗

arXiv2023

Coherent spore dispersion via drop-leaf interactions

The dispersion of plant pathogens, such as rust spores, is responsible for more than 20% of global yield loss annually, and poses a significant threat to human health. However, the release mechanics of pathogens from flexible plant surfaces into the canopy is not well understood. In this study, we investigated the interplay between leaf elasticity and raindrop momentum, revealing how it induces flow coherence and enhances spore transport with 2-10 times greater energy compared to impacts on stationary surfaces. We observed that a flexible leaf generates vortex dipoles, leading to a super-diffusive stream flow. We then developed a theoretical model that accurately predicted the average air flux from leaf edges and the vortex strength to be proportional the vibration speed of the leaves. With Lagrangian diagnostics, we further revealed the presence of hyperbolic and elliptical coherent structures around fluttering leaves, providing the dynamical description of spore transport. Our model demonstrated that a leaf aspect ratio (length/width) negatively correlates with dispersion, indicating that shorter and wider leaves promote greater pathogen spread. Additionally, we found that leaf rigidity positively correlates with dispersion due to damping effects. These mechanistic insights would help the construction of physically informed analytical models for improve local crop disease management.

physics.flu-dyn↗

arXiv2017

Extracting quasi-steady Lagrangian transport patterns from the ocean circulation: An application to the Gulf of Mexico

We construct a climatology of Lagrangian coherent structures (LCSs), the concealed skeleton that shapes transport, with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy-Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent Lagrangian circulation patterns. cLCSs strongly constrain the ensemble-mean Lagrangian circulation of the instantaneous model velocity, thus we show that a climatological velocity may preserve meaningful transport information. Also, the climatological transport patterns we report agree well with GoM kinematics and dynamics, as described in several previous observational and numerical studies. For example, cLCSs identify regions of persistent isolation, and suggest that coastal regions previously identified as high-risk for pollution impact, are regions of maximal attraction. Also, we show examples where cLCSs are remarkably similar to transport patterns observed during the Deepwater Horizon and Ixtoc oil spills, and during the Grand LAgrangian Deployment (GLAD) experiment. Thus, it is shown that cLCSs are an efficient way of synthesizing vast amounts of Lagrangian information. The cLCS method confirms previous GoM studies, and contributes to our understanding by revealing the persistent nature of the dynamics and kinematics treated therein.

physics.ao-ph↗

arXiv2016

Inertia-induced accumulation of flotsam in the subtropical gyres

Recent surveys of marine plastic debris density have revealed high levels in the center of the subtropical gyres. Earlier studies have argued that the formation of great garbage patches is due to Ekman convergence in such regions. In this work we report a tendency so far overlooked of drogued and undrogued drifters to accumulate distinctly over the subtropical gyres, with undrogued drifters accumulating in the same areas where plastic debris accumulate. We show that the observed accumulation is too fast for Ekman convergence to explain it. We demonstrate that the accumulation is controlled by finite-size and buoyancy (i.e., inertial) effects on undrogued drifter motion subjected to ocean current and wind drags. We infer that the motion of flotsam in general is constrained by similar effects. This is done by using a newly proposed Maxey--Riley equation which models the submerged (surfaced) drifter portion as a sphere of the fractional volume that is submerged (surfaced).

physics.ao-ph↗

arXiv2014

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 meters to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales. \textcolor{black} {Using high-frequency position data provided by the near-simultaneous release of hundreds of accurately tracked surface drifters, we study the structure of submesoscale surface velocity fluctuations in the Northern Gulf Mexico. Observed two-point statistics confirm the accuracy of classic turbulence scaling laws at 200m$-$50km scales and clearly indicate that dispersion at the submesoscales is \textit{local}, driven predominantly by energetic submesoscale fluctuations.} The results demonstrate the feasibility and utility of deploying large clusters of drifting instruments to provide synoptic observations of spatial variability of the ocean surface velocity field. Our findings allow quantification of the submesoscale-driven dispersion missing in current operational circulation models and satellite altimeter-derived velocity fields.

physics.ao-ph↗

arXiv2003

Passive tracer patchiness and particle trajectory stability in incompressible two-dimensional flows

Particle motion is considered in incompressible two-dimensional flows consisting of a steady background gyre on which an unsteady wave-like perturbation is superimposed. A dynamical systems point of view that exploits the action--angle formalism is adopted. It is argued and demonstrated numerically that for a large class of problems one expects to observe a mixed phase space, i.e., the occurrence of ``regular islands'' in an otherwise ``chaotic sea.'' This leads to patchiness in the evolution of passive tracer distributions. Also, it is argued and demonstrated numerically that particle trajectory stability is largely controlled by the background flow: trajectory instability, quantified by various measures of the ``degree of chaos,'' increases on average with increasing $|\mathrm{d}ω/\mathrm{d}I|$, where $ω(I)$ is the angular frequency of the trajectory in the background flow and $I$ is the action.

physics.flu-dyn↗

arXiv2003

Ray dynamics in a long-range acoustic propagation experiment

A ray-based wavefield description is employed in the interpretation of measurements made during the November 1994 Acoustic Engineering Test (the AET experiment). In this experiment phase-coded pulse-like signals with 75 Hz center frequency and 37.5 Hz bandwidth were transmitted near the sound channel axis in the eastern North Pacific Ocean. The resulting acoustic signals were recorded on a moored vertical receiving array at a range of 3252 km. In our analysis both mesoscale and internal-wave-induced sound speed perturbations are taken into account. Much of this analysis exploits results that relate to the subject of ray chaos; these results follow from the Hamiltonian structure of the ray equations. We present evidence that all of the important features of the measured AET wavefields, including their stability, are consistent with a ray-based wavefield description in which ray trajectories are predominantly chaotic.

nlin.CD↗