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1999, Journal of Marine Research
We consider the dispersion of particles in potential vorticity (PV)-conserving ows. Because particle drift is preferentially along the mean PV contours, Lagrangian dispersion is strongly anisotropic. If the mean PV eld moreover is spatially variable, as when there is topography, the anisotropy is more clearly visible in the dispersion of displacements along and across the mean PV eld itself. We examine several numerical examples of unforced barotropic ows; in all cases, this ''projected'' dispersion is more anisotropicthan that in cartesian (x, y) coordinates.What differs is the rate at which spreading occurs, both along and across contours. The method is applicable to real data, as is illustrated with oat data from the deep North Atlantic. The results suggest a preferential spreading along contours of (barotropic) f/H.
2009
We consider the dispersion of particles in potential vorticity (PV)-conserving ows. Because particle drift is preferentially along the mean PV contours, Lagrangian dispersion is strongly anisotropic. If the mean PV eld moreover is spatially variable, as when there is topography, the anisotropy is more clearly visible in the dispersion of displacements along and across the mean PV eld itself. We examine several numerical examples of unforced barotropic ows; in all cases, this ‘‘projected’’ dispersionis more anisotropicthan that in cartesian (x, y) coordinates.What differs is the rate at which spreadingoccurs, both along and across contours.The method is applicable to real data, as is illustrated with oat data from the deep North Atlantic. The results suggest a preferential spreading along contours of (barotropic) f/H.
Journal of Atmospheric and Oceanic Technology, 2003
The statistical properties of Lagrangian velocities in a high-resolution numerical simulation of the North Atlantic Ocean are analyzed and discussed in the framework of particle dispersion parameterizations. Consistent with previous analyses of float trajectories, the modeled velocity distribution is shown to be non-Gaussian, both at the surface and at 1500 m. These results can have significant implications on oceanographic research, as they suggest that current parameterizations of particle dispersion by linear stochastic processes or eddy-diffusivity approaches may be incorrect, since they assume Gaussian velocity distributions. The results also indicate the need for empirical parameterizations of particle dispersion based on nonlinear stochastic processes. It is shown that, even for a truly non-Gaussian dataset, a Gaussian probability distribution function can be spuriously recovered when the sampling density is too low. The best compromise between data sampling and space averaging when a limited amount of data are available, as is the case in most field observations, is then identified.
Physical review letters, 2004
The dynamics of passive Lagrangian tracers in three-dimensional quasigeostrophic turbulence is studied numerically and compared with the behavior of two-dimensional barotropic turbulence. Despite the different Eulerian properties of the two flows, the Lagrangian dynamics of passively advected tracers in three-dimensional quasigeostrophic turbulence is very similar to that of barotropic turbulence. In both systems, coherent vortices play a major role in determining the mixing and dispersion properties. This work indicates that recent results on particle dynamics in barotropic, two-dimensional turbulence carry over to more realistic baroclinic flows, such as those encountered in the large-scale dynamics of the atmosphere and ocean.
Journal of Physical Oceanography, 1999
The dynamics of Lagrangian particles and tracers in the vicinity of a baroclinically unstable zonal jet are investigated in a simple two-layer model with an initially quiescent lower layer. The presence of a growing wave induces a particle drift dominated by Stokes drift rather then the contribution of the wave to the mean Eulerian velocity. Stable and unstable waves have zonal Stokes drift with similar meridional structure while only unstable waves possess meridional drift, which is in the direction of increasing meridional wave displacement. Particle dispersion in the upper layer is maximum at critical lines, where the jet and phase speeds are equal. In the lower layer, dispersion is maximum where the wave amplitude is maximum. Zonal mean tracer evolution is formulated as an advection-diffusion equation with an order Rossby number advection and an orderone eddy diffusion. The latter is proportional to two-particle dispersion.
Lecture Notes in Physics, 2008
We review statistical analyses made with Lagrangian data from the atmosphere and ocean. The focus is on the types of measures used and on how the results reflect the underlying dynamics. First we discuss how the most common measures come about and how they are related to one another. The measures can be subdivided into those concerning single particles and those pertaining to groups of particles. Single particle analysis is more typical with oceanic data. The most widely-used such analysis involves binning velocities geographically to estimate characteristics of the Eulerian flow, such as the mean velocities and the diffusivities. Single particle statistics have also been used to study Rossby wave propagation, the sensitivity to bottom topography and eddy heat fluxes. The dispersion of particle pairs has been studied more in the atmosphere, although examples in the oceanic literature have also appeared recently. Pair dispersion at sub-deformation scales is similar in the two systems, with particle separations growing exponentially in time. The larger scale behavior varies, possibly reflecting details of the large scale shear flow. Analyses involving three or more particles are fairly rare but have been used to measure divergence and vorticity, as well as turbulent dispersion.
2016
Lagrangian data can provide relevant information on the advection and diffusion properties of geophysical flows at different scales of motion. In this study, the dispersion properties of an ensemble of trajectories transported by a surface ocean flow are analyzed. The data come from a set of Lagrangian drifters released in the South Brazilian Bight, during several oceanographic campaigns. Adopting a dynamical systems approach, the attention is primarily focused on scale-dependent indicators, like the finite-scale Lyapunov exponent. The relevance of mechanisms like two-dimensional turbulence for the dispersion process is addressed. Some deviations from the classical turbulent dispersion scenario in two-dimensions are found, likely to be ascribed to the nonstationary and nonhomogeneous characteristics of the flow. Relatively small-scale features (of order 1-10 km) are also considered to play a role in determining the properties of relative dispersion as well as the shape of the kineti...
Journal of Marine Systems, 2001
A study of the mesoscale eddy field in the presence of coherent vortices, by means of Lagrangian trajectories released in a high-resolution ocean model, is presented in this paper. The investigation confirms previous results drawn from real float data statistics that the eddy field characteristics are due to the superposition of two distinct regimes associated with strong coherent vortices and with a typically more quiescent background eddy flow. The former gives rise to looping trajectories characterized by subdiffusivity properties due to the trapping effect of the vortices, while the latter produces nonlooping floats characterized by simple diffusivity features. Moreover, the present work completes the study by in regard to the nature of the spin parameter ⍀, which was used in the Lagrangian stochastic model that best described the observed eddy statistics.
As two fluid particles separate in time, the entire spectrum of eddy motions is being sampled from the smallest to the largest scales. In large-scale geophysical systems for which the Earth rotation is important, it has been conjectured that the relative diffusivity should vary respectively as D^2 and D^4/3 for distances respectively smaller and larger than a well-defined forcing scale of the order of the internal Rossby radius (with D the r.m.s. separation distance). Particle paths data from a mid-latitude float experiment in the central part of the North Atlantic appear to support these statements partly: two particles initially separated by a few km within two distinct clusters west and east of the mid-Atlantic ridge, statistically dispersed following a Richardson regime (D^2 ∼ t^3 asymptotically) for r.m.s. separation distances between 40 and 300 km, in agreement with a D^4/3 law. At early times, and for smaller separation distances, an exponential growth, in agreement with a D^2 law, was briefly observed but only for the eastern cluster (with an e-folding time around 6 days). After a few months or separation distances greater than 300 km, the relative dispersion slowed down naturally to the Taylor absolute dispersion regime.
Journal of Physical Oceanography, 2011
Large-scale vortices, that is, eddies whose characteristic length scale is larger than the local Rossby radius of deformation Rd, are ubiquitous in the oceans, with anticyclonic vortices more prevalent than cyclonic ones. Stability or robustness properties of already formed shallow-water vortices have been investigated to explain this cyclone–anticyclone asymmetry. Here the focus is on possible asymmetries during the generation of vortices through barotropic instability of a parallel flow. The initial stage and the nonlinear stage of the instability are studied by means of linear stability analysis and direct numerical simulations of the one-layer rotating shallow-water equations, respectively. A wide variety of parallel flows are studied: isolated shears, the Bickley jet, and a family of wakes obtained by combining two shears of opposite signs. The results show that, when the flow is characterized by finite relative isopycnal deviation, the barotropic instability favors the formati...
Deep-sea Research Part I-oceanographic Research Papers, 2000
Recent works have shown that parameterizing eddy fluxes as a downgradient diffusion of potential vorticity (PV) generates circulation over topography. This result is examined in the context of a simple barotropic quasi-geostrophic model. It is shown that, unless a constraint on the eddy diffusivity is maintained, the PV mixing parameterization creates a fictitious torque which generates angular momentum. These considerations indicate that momentum conservation is not maintained in recent models that purport to show generation of net alongslope flow associated with PV mixing over topography.
Journal of Physical Oceanography, 2012
This study investigates the anisotropic properties of the eddy-induced material transport in the near-surface North Atlantic from two independent datasets, one simulated from the sea surface height altimetry and one derived from real-ocean surface drifters, and systematically examines the interactions between the mean-and eddy-induced material transport in the region. The Lagrangian particle dispersion, which is widely used to characterize the eddy-induced tracer fluxes, is quantified by constructing the ''spreading ellipses.'' The analysis consistently demonstrates that this dispersion is spatially inhomogeneous and strongly anisotropic. The spreading is larger and more anisotropic in the subtropical than in the subpolar gyre, and the largest ellipses occur in the Gulf Stream vicinity. Even at times longer than half a year, the spreading exhibits significant nondiffusive behavior in some parts of the domain. The eddies in this study are defined as deviations from the long-term time-mean. The contributions from the climatological annual cycle, interannual, and subannual (shorter than one year) variability are investigated, and the latter is shown to have the strongest effect on the anisotropy of particle spreading. The influence of the mean advection on the eddy-induced particle spreading is investigated using the ''eddy-following-full-trajectories'' technique and is found to be significant. The role of the Ekman advection is, however, secondary. The pronounced anisotropy of particle dispersion is expected to have important implications for distributing oceanic tracers, and for parameterizing eddy-induced tracer transfer in non-eddy-resolving models.
… Analysis and Prediction …
As more high-resolution observations become available, our view of ocean mesoscale turbulence more closely becomes that of a "sea of eddies." The presence of the coherent vortices significantly affects the dynamics and the statistical properties of mesoscale flows, with important consequences on tracer dispersion and ocean stirring and mixing processes. Here we review some of the properties of particle transport in vortex-dominated flows, concentrating on the statistical properties induced by the presence of an ensemble of vortices. We discuss a possible parameterization of particle dispersion in vortex-dominated flows, adopting the view that ocean mesoscale turbulence is a two-component fluid which includes intense, localized vortical structures with non-local effects immersed in a Kolmogorovian, low-energy turbulent background which has mostly local effects. Finally, we report on some recent results regarding the role of coherent mesoscale eddies in marine ecosystem functioning, which is related to the effects that vortices have on nutrient supply. frequency mesoscale variability (i.e. the medium-size fluctuations in the general circulation), for the mesoscale and sub-mesoscale coherent vortices (vortical motions at scales smaller than the internal Rossby radius of deformation, McWilliams 1985), or for a generic complicated motion in the presence of turbulence.
Journal of Physical Oceanography, 2004
Results of a variety of numerical simulations are presented and the accuracy of quasigeostrophic (QG) and semigeostrophic (SG) vertical velocity estimates of the total vertical velocity is analyzed. The authors examine the dependence of the results on the potential vorticity (PV) anomaly of the flow, its time evolution, and the amount of numerical diffusion. The SG equation is solved in a novel way in the original physical coordinates rather than in geostrophic coordinates. A three-dimensional numerical model is used that explicitly conserves the PV on isopycnal surfaces through a contour-advective semi-Lagrangian (CASL) algorithm. The numerical simulations consist initially of one or two horizontal cylinders of anomalous PV: a shear zone that induces two or three counterflowing jets. These jets destabilize and break into cyclones or anticyclones. This is accompanied by enhanced vertical motion, which exhibits a dominantly balanced quadrupole pattern in horizontal cross sections, depending on the ellipticity of the gyres, together with weak second-order inertia-gravity waves. For flows containing only negative PV anomalies the magnitude of both the QG and SG vertical velocities are smaller than the magnitude of the total vertical velocity, while the opposite occurs for flows containing only positive PV anomalies. The reason for this behavior is that the QG equation misses a term proportional to the Laplacian of the horizontal velocity. A new, more accurate, equation is proposed to recover the vertical velocity when both experimental density and horizontal velocity data are available. The SG solution is nearly always more accurate than the QG solution, particularly for the largest vertical velocity values and when the flow has single-signed PV anomalies. For flows containing both positive and negative PV anomalies, for example, mushroomlike eddies, the QG vertical velocity is a better approximation to the total vertical velocity than the SG solution. The reason for this anomalous behavior lies in one additional assumption concerning the conservation of volume that is usually adopted to derive the SG equation.
Journal of Physical Oceanography, 2011
In the framework of Monitoring by Ocean Drifters (MONDO) project, a set of Lagrangian drifters were released in proximity of the Brazil Current, the western branch of the subtropical gyre in the South Atlantic Ocean. The experimental strategy of deploying part of the buoys in clusters offers the opportunity to examine relative dispersion on a wide range of scales. Adopting a dynamical systems approach, the authors focus their attention on scale-dependent indicators, like the finite-scale Lyapunov exponent (FSLE) and the finite-scale (mean square) relative velocity (FSRV) between two drifters as a function of their separation and compare them with classic time-dependent statistical quantities like the mean-square relative displacement between two drifters and the effective diffusivity as functions of the time lag from the release. The authors find that, dependently on the given observable, the quasigeostrophic turbulence scenario is overall compatible with their data analysis, with d...
Fluid Dynamics Research, 1988
Journal of Oceanography, 1983
The Lagrangian diffusion equation appropriate for the dispersion of current followers (e. g., floats, drogues, drifters) is proposed. The analytical solution to the equation is obtained for a uniform deformation field, characterized by Lagrangian deformations and anisotropic eddy diffusivities both varying with time. Expressions are derived for the patch area and its elongation and rotation. For small values of elapsed time after the initial release the patch area can be accounted for by the exponential of the cumulative value of the horizontal divergence; the relative rate of change of the patch area can be accounted for by the horizontal divergence.
Journal of Marine Research, 2005
Coherent vortices are known to play an important role in transport processes of ideal flows such as two-dimensional and quasi-geostrophic turbulent flows. In this paper, their effect on eddy dispersion and diffusivity is studied in a realistic oceanic flow, using synthetic Lagrangian data simulated within a high-resolution ocean general circulation model in the Gulf Stream recirculation region. The possibility of using a Lagrangian Stochastic Model (LSM) with nonzero mean spin statistic, ⍀, to parameterize the observed characteristics is considered. The probability distribution of the ⍀ parameter (which is representative of the looping behavior of trajectories embedded inside the coherent vortices) is also studied.
Fluids, 2019
The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted to eastward mean flows, but a wide range of flow regimes with different bottom friction strengths, layer thickness ratios, and background potential vorticity (PV) gradients were otherwise considered. It was found that coherent eddies become more prevalent and longer-lasting as the strength of bottom drag increases and the stratification becomes more surface-intensified. The number of coherent eddies is minimal when the shear-induced PV gradient is 10–20 times the planetary PV gradient and increases for both larger and smaller values of the planetary PV gradient. These coherent eddies, with an average core radius close to the deformation radius, propagate meridionall...
Oceanic internal tides and other inertia-gravity waves propagate in an energetic turbulent flow whose length scales are similar to the wavelengths. Advection and refraction by this flow cause the scattering of the waves, redistributing their energy in wavevector space. As a result, initially plane waves radiated from a source such as a topographic ridge become spatially incoherent away from the source. To examine this process, we derive a kinetic equation which describes the statistics of the scattering under the assumptions that the flow is quasigeostrophic, barotropic and well represented by a stationary homogeneous random field. Energy transfers are quantified by computing a scattering cross-section and shown to be restricted to waves with the same frequency and identical vertical structure, hence the same horizontal wavelength. For isotropic flows, scattering leads to an isotropic wave field. We estimate the characteristic time and length scales of this isotropisation, and study their dependence on parameters including the energy spectrum of the flow. Simulations of internal tides generated by a planar wavemaker carried out for the linearised shallow-water model confirm the pertinence of these scales. A comparison with the numerical solution of the kinetic equation demonstrates the validity of the latter and illustrates how the interplay between wave scattering and transport shapes the wave statistics.
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