▪ Abstract This article reviews the transport properties of coherent vortices in rotating barotropic flows. It is shown that vortices induce regular Lagrangian motion inside their cores and are highly impermeable to inward and outward particle fluxes. Passive tracers can be trapped inside vortex cores for long times and are transported by the vortex motion over large distances. Absolute dispersion in vortex-dominated flows is discussed by studying particle dynamics in 2D turbulence, point-vortex systems, and subsurface float trajectories in the ocean. Finally, it is shown that anticyclonic coherent vortices in cyclonically rotating reference frames can concentrate heavy impurities (e.g. dust grains) in their cores. This process may play an important role in the formation of planetesimals in the early solar nebula.

http://www.o3d.org/abracco/anto_review.pdf

Transport by coherent barotropic vortices

Mesoscale coherent vortices are numerous in the ocean.Though they possess various structures in temperature and salinity,they are all long-lived, fairly intense and mostly circular. Thephysical variable which best describes the rotation and the density anomaly associated with coherent vortices is potential vorticity. It is diagnostically related to velocity and pressure, when the vortex is stationary. Stationary vortices can be monopolar (circular or elliptical) or multipolar; their stability analysis shows thattransitions between the various stationary shapes are possible when they become unstable. But stable vortices can also undergo unsteady evolutions when perturbed by environmental effects, likelarge-scale shear or strain fields, β-effect or topography. Changes in vortex shapes can also result from vortex interactions. such as the pairing, merger or vertical alignment of two vortices, which depend on their relative polarities and depths. Such interactions transfer energy and enstrophy between scales, and are essential in two-dimensional and in geostrophic turbulence. Finally, in relation with the observations, we describe a few mechanisms of vortex generation.

Hydrodynamical Modeling Of Oceanic Vortices

In Sect. 1.1 of this chapter we explain the subject of Geophysical Fluid Dynamics, and give the description of main vortex structures that have become objects of the present book: (a) Heton – a two-layer vortex with opposite rotations in different layers, and (b) Intrathermocline lens, which is studied in this work as a vortex patch in the intermediate layer of a three-layer ocean model. In this section, we propose also a short review of works in the related topics. Section 1.2 is a mathematical introduction. It contains all main formulae which are used further in Chaps. 2 and 3.

The Introductory Chapter

The vertical alignment of an initially tilted geostrophic vortex is shown here to be captured by linear vortex Rossby wave dynamics when the vortex cores at upper and lower levels overlap. The vortex beta Rossby number, defined as the ratio of nonlinear advection in the potential vorticity equation to linear radial advection, is less than unity in this case. A useful means of characterizing a tilted vortex flow in this parameter regime is through a wave‐mean flow decomposition. From this perspective the alignment mechanism is elucidated using a quasigeostrophic model in both its complete and linear equivalent barotropic forms. Attention is focused on basicstate vortices with continuous and monotonically decreasing potential vorticity profiles. For internal Rossby deformation radii larger than the horizontal scale of the tilted vortex an azimuthal wavenumber 1 quasi mode exists. The quasi mode is characterized by its steady cyclonic propagation, long lifetime, and resistance to differential rotation, behaving much like a discrete vortex Rossby wave. The quasi mode traps disturbance energy causing the vortex to precess, or corotate, and thus prevents alignment. For internal deformation radii smaller than the horizontal vortex scale, the quasi mode disappears into the continuous spectrum of vortex Rossby waves. Alignment then proceeds through the irreversible redistribution of potential vorticity by the sheared vortex Rossby waves. Further decreases in the internal deformation radius result in a decreased dependence of vortex evolution on initial tilt magnitude, consistent with a reduction of the vortex beta Rossby number. These results are believed to have relevance to the problem of tropical cyclone (TC) genesis. Cyclogenesis initiated through the merger and alignment of low-level convectively generated positive potential vorticity within a weak incipient vortex is captured by quasi-linear dynamics. A potential dynamical barrier to TC development in which the quasi mode frustrates vertical alignment can be identified using the linear alignment theory in this case.

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Three-Dimensional Alignment and Corotation of Weak, TC-like Vortices via Linear Vortex Rossby Waves

This article presents a new theory for the rate at which a quasigeostrophic vortex realigns, under conservative dynamics, after being tilted by an episode of external vertical shear. The initial tilt is viewed as the excitation of a three-dimensional ‘‘vortex Rossby mode.’’ This mode, that is, the tilt, decays exponentially with time during its early evolution. The decay rate g is proportional to the potential vorticity gradient at a critical radius, where the fluid rotation is resonant with the mode. The decay rate g also depends on the internal Rossby deformation radius lR, which is proportional to the stratification strength of the atmospheric or oceanic layer containing the vortex. The change of g with lR is sensitive to the form of the vortex. For the case of a ‘‘Rankine-with-skirt’’ vortex, the magnitude of g increases (initially) with increasing lR. On the other hand, for the case of a ‘‘Gaussian’’ vortex, the magnitude of g decreases with increasing lR. The relevance of this theory to tropical cyclogenesis is discussed.

/pdf/a-theory-for-the-vertical-alignment-of-a-quasigeostrophic-5ccq5n4979.pdf

A Theory for the Vertical Alignment of a Quasigeostrophic Vortex

We investigate the evolution of nearby like-sign vortices whose centres are at dierent vertical levels in a stably stratied rotating fluid. We employ two dierently singularized representations of the potential vorticity distribution in the quasi-geostrophic equations (QG), in order to elucidate the pair-interaction behaviour previously seen in non-singular QG numerical solutions. The rst is an analytically tractable conservative (Hamiltonian) elliptical-moment model (EM) for thin-core vortices, which exhibits a regime of very strong horizontal elongation of a vortex in response to the strain induced by its partner. We interpret this as an early evolutionary stage towards the irreversible dissipative merger and alignment interactions. This interpretation is strengthened by weakly dissipative numerical solutions of a thin-core contourdynamics model (CD), which exhibit even further progress towards the completion of these vortex interactions in the same regime. In the EM model we classify the co-rotating stationary states which exist always for vertically oset thin-core vortices. However, the mutual strain eld among the vortices cannot be balanced by co-rotation in a weakly elongated stationary state for a certain class of neighbouring, but substantially non-aligned, vortex congurations, and our interpretive assumption is that such congurations will rapidly evolve in non-singular QG solutions towards a more aligned conguration through signicantly non-conservative reorganizations of the potential vorticity eld. Both the EM and CD models show qualitatively similar regime boundaries between evolutions with weakly and strongly deformed vortices. In particular, there is a fairly close correspondence between the occurrence of strong vortex elongation in the EM solutions and signicant lamentation and splitting in the CD solutions.

Co-rotating stationary states and vertical alignment of geostrophic vortices with thin cores

This paper deals with the self-induced translation of intense vortices on the β-plane in the framework of the multi-layer quasi-geostrophic approximation. An analytical theory is presented and compared to numerical experiments. To predict the vortex trajectories, we consider initially monopolar vortices, with a core of piecewise-constant potential vorticity, and calculate the evolution of the dipolar circulation which advects the vortex core. This multi-layer model yields analytical solutions for a period while the Rossby wave radiation is small. The development of the dipolar circulation and corresponding vortex translation are described as the results of three effects. The first and second are similar to what was found in earlier studies with a one-layer model: advection of the planetary vorticity by the symmetric vortex circulation, and horizonal deformations of the vortex core. In addition, when stratification is taken into account, the vertical tilting of the vortex core also plays a role. This third effect is here represented by the relative displacement of potential vorticity contours in different layers. Examples are given for one-, two- and three-layer models and compared with numerical simulations. It is found that the analytical predictions are good for several Rossby wave periods.

Georgi G. Sutyrin

Papers

Co-rotating stationary states and vertical alignment of geostrophic vortices with thin cores

Intense vortex motion in a stratified fluid on the beta-plane: an analytical theory and its validation