arXiv subjects

F. J. Beron-Vera

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

47 records · Page 3Linked to original sources

arXiv2006

Persistent Transport Barrier on the West Florida Shelf

Analysis of drifter trajectories in the Gulf of Mexico has revealed the existence of a region on the southern portion of the West Florida Shelf (WFS) that is not visited by drifters that are released outside of the region. This so-called ``forbidden zone'' (FZ) suggests the existence of a persistent cross-shelf transport barrier on the southern portion of the WFS. In this letter a year-long record of surface currents produced by a Hybrid-Coordinate Ocean Model simulation of the WFS is used to identify Lagrangian coherent structures (LCSs), which reveal the presence of a robust and persistent cross-shelf transport barrier in approximately the same location as the boundary of the FZ. The location of the cross-shelf transport barrier undergoes a seasonal oscillation, being closer to the coast in the summer than in the winter. A month-long record of surface currents inferred from high-frequency (HF) radar measurements in a roughly 60 km $\times$ 80 km region on the WFS off Tampa Bay is also used to identify LCSs, which reveal the presence of robust transient transport barriers. While the HF-radar-derived transport barriers cannot be unambiguously linked to the boundary of the FZ, this analysis does demonstrate the feasibility of monitoring transport barriers on the WFS using a HF-radar-based measurement system. The implications of a persistent cross-shelf transport barrier on the WFS for the development of harmful algal blooms on the shoreward side of the barrier are considered.

physics.ao-ph↗

arXiv2006

The Effects of Lagrangian vs. Population Dynamics on Plankton Patchiness Generation

The relative importance of Lagrangian and population dynamics on spatial pattern formation in the distribution of plankton near the ocean's surface is investigated. Phytoplankton and zooplankton are treated as biologically interacting tracers that are passively advected by a divergence-free two-dimensional nonsteady velocity field. The time-dependence of this field is assumed to be quasiperiodic, which extends the analysis presented beyond standard chaotic advection. Various forms of predator--prey interactions, including complex interactions, are considered. Numerical simulations illustrate how Lagrangian dynamics, which is characterized by a mixed phase space with coexisting regular and chaotic motion regions, influences plankton patchiness generation depending on the nature of the biological interactions.

nlin.CD↗

arXiv2006

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 travelling Rossby waves are superimposed. The associated Lagrangian motion is studied with the aid of KAM (Kolmogorov--Arnold--Moser) 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 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.

physics.ao-ph↗

arXiv2005

Phase space structure of nonautonomous one-degree-of-freedom Hamiltonian systems with nontrivial time dependence

It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a superposition of time-periodic functions with incommensurate frequencies. Furthermore, such systems are constrained by one fewer integral of motion than is required to render the system completely integrable. As a consequence, the phase space in systems of this type is expected to be partitioned into nonintersecting regular and chaotic regions. In this note we provide numerical evidence of the existence of such a characteristic mixed phase space structure. This is done by considering the problem of acoustic ray dynamics in deep ocean environments, which is naturally described as a nonautonomous one-degree-of-freedom Hamiltonian system with a multiply periodic Hamiltonian in the independent (time-like) variable. Also, we discuss the implications of a mixed phase space for the dynamics of that geophysical system and another one which describes Lagrangian motion in the ocean. The latter is also naturally described as a nonautonomous one-degree-of-freedom Hamiltonian system with a multiply time-periodic Hamiltonian.

nlin.CD↗

arXiv2004

Linear waves and baroclinic instability in an inhomogeneous-density layered primitive-equation ocean model

We consider a multilayer generalization of Ripa's inhomogeneous-density single-layer primitive-equation model. In addition to vary arbitrarily in horizontal position and time, the horizontal velocity and buoyancy fields are allowed to vary linearly with depth within each layer of the model. Preliminary results on linear waves and baroclinic instability suggest that a configuration involving a few layers may set the basis for a quite accurate and numerically efficient ocean model.

physics.ao-ph↗

arXiv2004

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 of both types of environment, 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.

nlin.CD↗

arXiv2004

A Didactic Approach to Linear Waves in the Ocean

The general equations of motion for ocean dynamics are presented and the waves supported by the (inviscid, unforced) linearized system with respect to a state of rest are derived. The linearized dynamics sustains one zero frequency mode (called buoyancy mode) in which salinity and temperature rearrange in such a way that seawater density does not change. Five nonzero frequency modes (two acoustic modes, two inertia--gravity or Poincaré modes, and one planetary or Rossby mode) are also sustained by the linearized dynamics, which satisfy an asymptotic general dispersion relation. The most usual approximations made in physical oceanography (namely incompressibility, Boussinesq, hydrostatic, and quasigeostrophic) are also consider, and their implications in the reduction of degrees of freedom (number of independent dynamical fields or prognostic equations) of, and compatible waves with, the linearized governing equations are particularly discussed and emphasized.

physics.ed-ph↗

arXiv2003

Constrained-Hamiltonian Shallow-Water Dynamics on the Sphere

Salmon's nearly geostrophic model for rotating shallow-water flow is derived in full spherical geometry. The model, which results upon constraining the velocity field to the height field in Hamilton's principle for rotating shallow-water dynamics, constitutes an important prototype of Hamiltonian balanced models. Instead of Salmon's original approach, which consists in taking variations of particle paths at fixed Lagrangian labels and time, Holm's approach is considered here, namely variations are taken on Lagrangian particle labels at fixed Eulerian positions and time. Unlike the classical quasigeostrophic model, Salmon's is found to be sensitive to the differences between geographic and geodesic coordinates. One consequence of this result is that the $β$ plane approximation, which is included in Salmon's original derivation, is not consistent for this class of model.

physics.ao-ph↗

arXiv2003

Deep ocean influence on upper ocean baroclinic instability saturation

In this paper we extend earlier results regarding the effects of the lower layer of the ocean (below the thermocline) on the baroclinic instability within the upper layer (above the thermocline). We confront quasigeostrophic baroclinic instability properties of a 2.5-layer model with those of a 3-layer model with a very thick deep layer, which has been shown to predict spectral instability for basic state parameters for which the 2.5-layer model predicts nonlinear stability. We compute and compare maximum normal-mode perturbation growth rates, as well as rigorous upper bounds on the nonlinear growth of perturbations to unstable basic states, paying particular attention to the region of basic state parameters where the stability properties of the 2.5- and 3-layer model differ substantially. We found that normal-mode perturbation growth rates in the 3-layer model tend to maximize in this region. We also found that the size of state space available for eddy-amplitude growth tends to minimize in this same region. Moreover, we found that for a large spread of parameter values in this region the latter size reduces to only a small fraction of the total enstrophy of the system, thereby allowing us to make assessments of the significance of the instabilities.

physics.ao-ph↗

arXiv2003

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 are considered. Both general theoretical arguments and analytical estimates of time spreads suggest that travel time stability is largely controlled by a property $ω^{\prime}$ 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 $ω^{\prime}$.

nlin.CD↗

arXiv2003

Ray stability in weakly range-dependent sound channels

Ray stability is investigated in environments consisting of a range-independent background sound-speed profile on which a range-dependent perturbation, such as that produced by internal waves in deep ocean environments, is superimposed. Numerical results show that ray stability is strongly influenced by the background sound speed profile. Ray instability is shown to increase with increasing magnitude of alpha := I omega^{prime} / omega, where 2 pi / omega(I) is the range of a ray double loop and I is the ray action variable. The mechanism, shear-induced instability enhancement, by which alpha controls ray instability is described.

nlin.CD↗