The critical merger distance between two co-rotating quasi-geostrophic vortices

Reinaud, Jean Noel; Dritschel, David G.

doi:10.1017/s0022112004002022

Cited by 47 publications

(71 citation statements)

References 21 publications

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“…Finally, tall poles may be unstable to tilting instability. Such instabilities can be related to similar modes observed in tall columns in shear (Dritschel and de la Torre Juarez, 1996) and for two interacting tall vortices (see Reinaud and Dritschel, 2005)). The formation of baroclinic tripoles from the collision of two hetons can be seen as a mechanism (temporarily) halting the transport of tracers in the flow.…”

Section: Resultssupporting

confidence: 62%

“…For these equilibria, the most deformed poles are the lower satellites, which exhibit the same inner sharp edge as for two identical co-rotating vortices. Such equilibria have been extensively studied in Reinaud and Dritschel (2002), Reinaud and Dritschel (2005), Bambrey, Reinaud and Dritschel (2007) and Ozugurlu, Reinaud and Dritschel (2008).…”

Section: Appendix I : Point Vortex Stabilitymentioning

confidence: 99%

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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: Resultssupporting

confidence: 62%

Section: Appendix I : Point Vortex Stabilitymentioning

confidence: 99%

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

Reinaud

Carton

2015

J. Fluid Mech.

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“…It has mostly been investigated in two-dimensional incompressible fluids and in quasi-geostrophic models (Overman and Zabusky 1982;Dritschel 1985Dritschel , 1986Griffiths and Hopfinger 1987;Melander et al 1987Melander et al , 1988Pavia and Cushman-Roisin 1990;Carnevale et al 1991;Carton 1992;Bertrand and Carton 1993;Valcke and Verron 1993;Valcke 1994, Yasuda 1995;Yasuda and Flierl 1995;Verron 1996, 1997;Yasuda and Flierl 1997;von Hardenberg et al 2000;Sokolovskiy and Verron, 2000;Dritschel 2002;Reinaud and Dritschel 2002;Meunier et al 2002;Reinaud and Dritschel 2005;Bambrey et al 2007;Ozugurlu et al 2008;Sokolovskiy and Carton, 2010;Sokolovskiy and Verron, 2014). These studies were performed in an unbounded fluid domain, over flat bottom.…”

Section: Introductionmentioning

confidence: 99%

Vortex merger near a topographic slope in a homogeneous rotating fluid

et al. 2017

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The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass 1 into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This alongshelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclones and near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.

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“…But only 3D QG dynamics allows the vertical tilting of vortices, which can lead to their merger at certain depths, while a part of the initial vortices does not merge at other depths (see for instance Reinaud and Dritschel, 2005). This supplementary degree of freedom is important for the dynamics of deep oceanic vortices, such as meddies for instance, considering their complex potential vorticity distribution.…”

Section: Resultsmentioning

confidence: 99%

“…The nonlinear evolution of the vortices is described and analysed. We recall that in 2D (incompressible) dynamics, the critical distance below which the two eddies merge is about d = (3.25 ± 0.05) R. For 3D QG vortex merger (with vortices at the same depth), the critical merger distance is d = 2.55R (for complete merger; it is d = 2.6R for partial merger; see Reinaud and Dritschel, 2005, figure 24). …”

Section: Two-vortex Evolution In the Absence Of External Flowmentioning

confidence: 95%

Vortex merger in surface quasi-geostrophy

Carton

Ciani

Verron

et al. 2015

Geophysical & Astrophysical Fluid Dynamics

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The merger of two identical surface temperature vortices is studied in the surface quasigeostrophic model. The motivation for this study is the observation of the merger of submesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incompressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and symmetric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vortex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.2

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The critical merger distance between two co-rotating quasi-geostrophic vortices

Cited by 47 publications

References 21 publications

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

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

Vortex merger near a topographic slope in a homogeneous rotating fluid

Vortex merger in surface quasi-geostrophy

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