F. J. Beron-Vera

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.

Objective Detection of Oceanic Eddies and the Agulhas Leakage

Mesoscale oceanic eddies are routinely detected from instantaneous velocities derived from satellite altimetry data. While simple to implement, this approach often gives spurious results and hides true material transport. Here it is shown how geodesic transport theory, a recently developed technique from nonlinear dynamical systems, uncovers eddies objectively. Applying this theory to altimetry-derived velocities in the South Atlantic reveals, for the first time, Agulhas rings that preserve their material coherence for several months, while ring candidates yielded by other approaches tend to disperse or leak within weeks. These findings suggest that available velocity-based estimates for the Agulhas leakage, as well as for its impact on ocean circulation and climate, need revision.

Ray dynamics in a long-range acoustic propagation experiment.

A ray-based wave-field description is employed in the interpretation of broadband basin-scale acoustic propagation measurements obtained during the Acoustic Thermometry of Ocean Climate programs 1994 Acoustic Engineering Test. Acoustic observables of interest are wavefront time spread, probability density function (PDF) of intensity, vertical extension of acoustic energy in the reception finale, and the transition region between temporally resolved and unresolved wavefronts. Ray-based numerical simulation results that include both mesoscale and internal-wave-induced sound-speed perturbations are shown to be consistent with measurements of all the aforementioned observables, even though the underlying ray trajectories are predominantly chaotic, that is, exponentially sensitive to initial and environmental conditions. Much of the analysis exploits results that relate to the subject of ray chaos; these results follow from the Hamiltonian structure of the ray equations. Further, it is shown that the collection of the many eigenrays that form one of the resolved arrivals is nonlocal, both spatially and as a function of launch angle, which places severe restrictions on theories that are based on a perturbation expansion about a background ray.

On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex

The Lagrangian dynamics of zonal jets in the atmosphere are considered, with particular attention paid to explaining why, under commonly encountered conditions, zonal jets serve as barriers to meridional transport. The velocity field is assumed to be two-dimensional and incompressible, and composed of a steady zonal flow with an isolated maximum (a zonal jet) on which two or more traveling Rossby waves are superimposed. The associated Lagrangian motion is studied with the aid of the Kolmogorov–Arnold–Moser (KAM) theory, including nontrivial extensions of well-known results. These extensions include applicability of the theory when the usual statements of nondegeneracy are violated, and applicability of the theory to multiply periodic systems, including the absence of Arnold diffusion in such systems. These results, together with numerical simulations based on a model system, provide an explanation of the mechanism by which zonal jets serve as barriers to the meridional transport of passive tracers under commonly encountered conditions. Causes for the breakdown of such a barrier are discussed. It is argued that a barrier of this type accounts for the sharp boundary of the Antarctic ozone hole at the perimeter of the stratospheric polar vortex in the austral spring.

Tracing the Early Development of Harmful Algal Blooms on the West Florida Shelf 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 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 Lagrangian coherent structures (LCSs) to trace potential early locations of the development of a HAB in late 2004 before it was transported to a region where it could be detected by satellite imagery. The LCSs, which are extracted from surface ocean currents produced by a data-assimilative HYCOM (HYbrid-Coordinate Ocean Model) simulation, constitute material fluid barriers that demarcate potential pathways for HAB evolution. Using a simplified population dynamics model we infer the factors that could possibly lead to the development of the HAB in question. The population dynamics model determines nitrogen in two components, nutrients and phytoplankton, which are assumed to be passively advected by surface ocean currents produced by the above HYCOM simulation. Two nutrient sources are inferred for the HAB whose evolution is found to be strongly tied to the simulated LCSs. These nutrient sources are found to be located nearshore and possibly due to land runoff.

Rip?current pulses tied to Lagrangian coherent structures

The trapping and ejection of surfzone floating material is examined by unveiling Lagrangian Coherent Structures (LCSs) hidden in the pulsating rip?current surface velocity field produced by a three?dimensional numerical model resolving wave?group induced Very Low Frequency motions (VLFs). LCSs explain the typically observed patchiness of flotsam within the surf zone and the streaky distribution outside of the surf zone. The ejection of surfzone material occurs when filament?like LCSs separate form the main rip?current circulation corresponding to a situation where eddies temporarily extend the rip current beyond the surf zone and subsequently detach. The LCSs support the idea that VLFs form the dominant exchange mechanism of surfzone floating material with the inner shelf.

Zonal Jets as Transport Barriers in Planetary Atmospheres

Abstract 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 Jupi...

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.

Travel time stability in weakly range-dependent sound channels

Travel time stability is investigated in environments consisting of a range-independent background sound-speed profile on which a highly structured range-dependent perturbation is superimposed. The stability of both unconstrained and constrained (eigenray) travel times is considered. Both general theoretical arguments and analytical estimates of time spreads suggest that travel time stability is largely controlled by a property ω′ of the background sound-speed profile. Here, 2π/ω(I) is the range of a ray double loop and I is the ray action variable. Numerical results for both volume scattering by internal waves in deep-ocean environments and rough surface scattering in upward-refracting environments are shown to confirm the expectation that travel time stability is largely controlled by ω′.Travel time stability is investigated in environments consisting of a range-independent background sound-speed profile on which a highly structured range-dependent perturbation is superimposed. The stability of both unconstrained and constrained (eigenray) travel times is considered. Both general theoretical arguments and analytical estimates of time spreads suggest that travel time stability is largely controlled by a property ω′ of the background sound-speed profile. Here, 2π/ω(I) is the range of a ray double loop and I is the ray action variable. Numerical results for both volume scattering by internal waves in deep-ocean environments and rough surface scattering in upward-refracting environments are shown to confirm the expectation that travel time stability is largely controlled by ω′.

Rays, modes, wavefield structure, and wavefield stability

Sound propagation is considered in range-independent environments and environments consisting of a range-independent background on which a weak range-dependent perturbation is superimposed. Recent work on propagation in both types of environments, involving both ray- and mode-based wavefield descriptions, have focused on the importance of α, a ray-based “stability parameter,” and β, a mode-based “waveguide invariant.” It is shown that, when β is evaluated using asymptotic mode theory, β=α. Using both ray and mode concepts, known results relating to the manner by which α (or β) controls both the unperturbed wavefield structure and the stability of the perturbed wavefield are briefly reviewed.