Stability and transitions of hetonic quartets and baroclinic modons

Kizner, Ziv

doi:10.1063/1.2196094

Cited by 33 publications

(20 citation statements)

References 38 publications

(54 reference statements)

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“…Interactions between hetons have also been investigated numerically in two layer models by Sokolovskiy and Carton (2010) and the head-on collision of hetons in continuously stratified fluid has been investigated in . It should be noted that the interaction between two singular hetons (referred to as hetonic quartets) has been studied in two-layers including on the β−plane by Kizner (2006). All these interactions may produce multipolar vortices as either the product of baroclinic instabilities and/or the merger of like-signed poles or destructive interaction between horizontally aligned dipoles.…”

Section: Introductionmentioning

confidence: 99%

Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

Reinaud

Carton

2015

J. Fluid Mech.

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Hetons are baroclinic vortices able to transport tracers or species, and which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasi-geostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. Firstly, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and of two lower (symmetric) satellites are studied analytically for point vortices and numerically for finite-area vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finite-volume stationary tripoles exist with marginal states having very elongated (figure-8) upper core. In the case of vertically distant upper and lower cores, these latter can nearly joint near the center of the plane. These steady states are compared with their two-layer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small, upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is short-lived and that hetons eventually emerge from the collision and drift away.

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Section: Introductionmentioning

confidence: 99%

Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

Reinaud

Carton

2015

J. Fluid Mech.

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“…and for a flat two-layer tripole, it is FðlÞ ¼ Hðl; l; 2lÞ ¼ 3 ln l À 4K 0 ðlÞ þ K 0 ð2lÞ À ln 2: (29) It is directly checked that the function F(l) given by each one of formulas (27) and (29) is monotonic. Thus, the above logic, without any change, is applicable to the equivalentbarotropic and flat two-layer tripoles, the conclusion being that such tripoles are stable.…”

Section: Equivalent-barotropic and Flat Two-layer Tripolesmentioning

confidence: 99%

“…(again to within a constant coefficient), and for an equivalent-barotropic tripole, it is FðlÞ ¼ Hðl; l; 2lÞ ¼ À4K 0 ðlÞ þ K 0 ð2lÞ; (27) where l is the tripole leg. The Hamiltonian of a flat two-layer quasigeostrophic troika is…”

Section: Equivalent-barotropic and Flat Two-layer Tripolesmentioning

confidence: 99%

“…20-30 and the references therein). In particular, it was extended from the f-plane to the b-plane approximation (where the Coriolis parameter is not constant, but rather has a constant northward gradient) [26][27][28][29][30] and also generalized so as to incorporate singular two-layer vortices embedded in regular flows. [28][29][30] Below, three-and five-vortex ensembles with zero total circulation will be considered with the emphasis put on the tripole and pentapole relative equilibria and their stabilityinstability.…”

Section: B Ensembles Of Point Vorticesmentioning

confidence: 99%

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Stability of point-vortex multipoles revisited

Kizner

2011

Physics of Fluids

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The point-vortex tripoles and pentapoles with zero total circulation are considered in the rigid-lid barotropic, equivalent-barotropic, and quasigeostrophic two-layer models. A tripole is assembled by three symmetrically arranged collinear vortices, while a pentapole by five vortices, of which one is located at the center of a square and four in the vertices of the square. The vortices on the sides, termed satellite vortices, are equal in strength and opposite in sign to the central vortex. To fulfill the zero-total-circulation condition, the central vortex is taken to be twice as strong as each of the satellite vortices in a tripole and four times as strong in a pentapole. In the two-layer model, two cases are distinguished, namely, the flat multipoles whose vortices are all located in the same layer and the carousel multipoles whose central vortex and satellite vortices reside in different layers. In all the models, the tripoles are shown to be nonlinearly stable and pentapoles, generally, unstable. Carousel pentapoles comparable in their size with the Rossby radius, and smaller, are exceptional in that they are stable to centrally symmetric perturbations (and, presumably, to arbitrary perturbations). The simple proof of the tripole stability is based on the fact that among the possible three-vortex configurations with zero total circulation characterized by the same (fixed) value of the Hamiltonian, there exists only one tripole, and, within the iso-Hamiltonian sheet, the squared linear momentum vanishes at this unique tripole only. This approach, being in essence universal for all models, works only with tripoles. For instance, a quadrupole cannot be treated in such a way, because there is a continuum of configurations of four vortices with zero total circulation on which the squared impulse vanishes. Dealing with pentapoles, we consider the perturbations that do not violate the central symmetry of the vortex configuration, fix the angular momentum, and examine the second derivatives of the Hamiltonian on the iso-momentum sheet.

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“…The notion of 'hetonic quartet' was introduced in the literature 16 for four discrete vortices lying in the same vertical plane, in a two-layer flow. Such a hetonic quartet moves at a constant translation velocity in a direction perpendicular to the plane containing the vortices.…”

Section: Introductionmentioning

confidence: 99%

Hetonic quartets in a two-layer quasi-geostrophic flow: V-states and stability

Reinaud

Sokolovskiy

Carton³

2018

Physics of Fluids

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We investigate families of finite core vortex quartets in mutual equilibrium in a twolayer quasi-geostrophic flow. The finite core solutions stem from known solutions for discrete (singular) vortex quartets. Two vortices lie in the top layer and two vortices lie in the bottom layer. Two vortices have a positive potential vorticity anomaly while the two others have negative potential vorticity anomaly. The vortex configurations are therefore related to the baroclinic dipoles known in the literature as hetons. Two main branches of solutions exist depending on the arrangement of the vortices: the translating zigzag-shaped hetonic quartets and the rotating zigzagshaped hetonic quartets. By addressing their linear stability, we show that while the rotating quartets can be unstable over a large range of the parameter space, most translating quartets are stable. This has implications on the longevity of such vortex equilibria in the oceans.

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Stability and transitions of hetonic quartets and baroclinic modons

Cited by 33 publications

References 38 publications

Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

Stability of point-vortex multipoles revisited

Hetonic quartets in a two-layer quasi-geostrophic flow: V-states and stability

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