228 research outputs found
Multilayer primitive equations model with velocity shear and stratification
The purpose of this paper is to present a multilayer primitive equations
model for ocean dynamics in which the velocity and buoyancy fields within each
layer are not only allowed to vary arbitrarily with horizontal position and
time, but also with depth--linearly at most. The model is a generalization of
Ripa's inhomogeneous one-layer model to an arbitrary number of layers. Unlike
models with homogeneous layers, the present model is able to represent
thermodynamics processes. Unlike models with slab layers, i.e. those in which
the layer velocity and buoyancy fields are depth-independent, the present model
can represent explicitly the thermal-wind balance within each layer which
dominates at low frequency. In the absence of external forcing and dissipation,
energy, volume, mass, and buoyancy variance constrain the dynamics;
conservation of total zonal momentum requires in addition the usual zonal
symmetry of the topography and horizontal domain. The model further possesses a
singular Hamiltonian structure. Unlike the single-layer counterpart, however,
no steady solution has been possible to prove formally (or Arnold) stable using
the above invariants. It is shown here that a model with only two layers
provides an excellent representation of the exact gravest baroclinic mode phase
speed. This suggests that configurations with only a small number of layers
will be needed to tackle a large variety of problems with enough realism
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.Comment: Revised 27 June 201
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.Comment: To appear in JFM Rapid
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.Comment: To be submitte
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.Comment: To appear \emph{in} O. U. Velasco-Fuentes et al. (eds.),
\textit{Nonlinear Processes in Geophysical Fluid Dynamics}, Kluwer Academi
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).Comment: Submitted to Geophys. Res. Letter
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.Comment: In pres
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 of the background sound speed profile. Here, is
the range of a ray double loop and 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
.Comment: Submitted to J. Acoust. Soc. Am., 30 June 200
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