Oceanic three-dimensional Lagrangian Coherent Structures: A study of a mesoscale eddy in the Benguela ocean region

We study three dimensional oceanic Lagrangian Coherent Structures (LCSs) in the Benguela region, as obtained from an output of the ROMS model. To do that we first compute Finite-Size Lyapunov exponent (FSLE) fields in the region volume, characterizing mesoscale stirring and mixing. Average FSLE values show a general decreasing trend with depth, but there is a local maximum at about 100 m depth. LCSs are extracted as ridges of the calculated FSLE fields. They present a "curtain-like" geometry in which the strongest attracting and repelling structures appear as quasivertical surfaces. LCSs around a particular cyclonic eddy, pinched off from the upwelling front are also calculated. The LCSs are confirmed to provide pathways and barriers to transport in and out of the eddy

Motion of Three Vortices near Collapse

A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, vortex triangle remains similar to the original one, while its area decreases (grows) at a constant rate. A contracting configuration brings three vortices to a single point in a finite time; this phenomenon known as vortex collapse is of principal importance for many-vortex systems. Dynamics of close-to-collapse vortex configurations depends on the way the collapse conditions are violated. Using an effective potential representation, a detailed quantitative analysis of all the different types of near-collapse dynamics is performed when two of the vortices are identical. We discuss time and length scales, emerging in the problem, and their behavior as the initial vortex triangle is approaching to an exact collapse configuration. Different types of critical behaviors, such as logarithmic or power-law divergences are exhibited, which emphasizes the importance of the way the collapse is approached. Period asymptotics for all singular cases are presented as functions of the initial vortices configurations. Special features of passive particle mixing by a near-collapse flows are illustrated numerically.Comment: 45 pages, 22 figures Last version of the paper with all update

Horizontal advection, diffusion, and plankton spectra at the sea surface

Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 114 (2009): C02001, doi:10.1029/2007JC004671.Plankton patchiness is ubiquitous in the oceans, and various physical and biological processes have been proposed as its generating mechanisms. However, a coherent statement on the problem is missing, because of both a small number of suitable observations and an incomplete understanding of the properties of reactive tracers in turbulent media. It has been suggested that horizontal advection may be the dominant process behind the observed distributions of phytoplankton and zooplankton, acting to mix tracers with longer reaction times (Rt) down to smaller scales. Conversely, the relative distributions of sea surface temperature and phytoplankton has been attributed to small-scale upwelling, where tracers with longer Rt are able to homogenize more than those with shorter reaction times. Neither of the above mechanisms can explain simultaneously the (relative) spectral slopes of temperature, phytoplankton, and zooplankton. Here, with a simple advection model and a large suite of numerical experiments, we concentrate on some of the physical processes influencing the relative distributions of tracers at the ocean surface, and we investigate (1) the impact of the spatial scale of tracer supply, (2) the role played by coherent eddies on the distribution of tracers with different Rt, and (3) the role of diffusion (so far neglected). We show that diffusion determines the distribution of temperature, regardless of the nature of the forcing. We also find that coherent structures together with differential diffusion of tracers with different Rt impact the tracer distributions. This may help in understanding the highly variable nature of observed plankton spectra.This work was initiated at WHOI during the summer of 2006, while S.C. was a summer student fellow, partially funded by the NSF. A.B. is funded by NSF–OCE 0751775 and NSF–OCE 0815280, and C.P. is funded by NSF–PHY 0551164

Jets, Stickiness and Anomalous Transport

Dynamical and statistical properties of the vortex and passive particle advection in chaotic flows generated by four and sixteen point vortices are investigated. General transport properties of these flows are found anomalous and exhibit a superdiffusive behavior with typical second moment exponent (\mu \sim 1.75). The origin of this anomaly is traced back to the presence of coherent structures within the flow, the vortex cores and the region far from where vortices are located. In the vicinity of these regions stickiness is observed and the motion of tracers is quasi-ballistic. The chaotic nature of the underlying flow dictates the choice for thorough analysis of transport properties. Passive tracer motion is analyzed by measuring the mutual relative evolution of two nearby tracers. Some tracers travel in each other vicinity for relatively large times. This is related to an hidden order for the tracers which we call jets. Jets are localized and found in sticky regions. Their structure is analyzed and found to be formed of a nested sets of jets within jets. The analysis of the jet trapping time statistics shows a quantitative agreement with the observed transport exponent.Comment: 17 pages, 17 figure