The merger of vertically offset 
quasi-geostrophic vortices

Reinaud, Jean Noel; Dritschel, David G.

doi:10.1017/s0022112002001854

Cited by 56 publications

(119 citation statements)

References 17 publications

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“…In order to obtain numerically equilibrium state, we use a numerical technique, originated in two dimensions by Pierrehumbert (1980), further developed by Dritschel (1985) and adapted to three-dimensional flows for two rotating (Reinaud and Dritschel, 2002) or translating (Reinaud, 2015) vortices, adapted here to the three vortex problem. The method makes the PV jumps which bound the uniform PV vortices converge to streamlines in a frame rotating with the vortices.…”

Section: Resultsmentioning

confidence: 99%

“…This analysis quantifies wave growth along PV contours (see Appendix II). In practice, 10 wave numbers are used for every contour, details of the approach can be found in the Appendix of Reinaud and Dritschel (2002) or in Reinaud (2015). Figure 4 shows the non-dimensional growth rate of the most unstable mode, σ/|q|, along the first cross-section of parameters with d/h = 1 and various aspect ratios versus the non-dimensional gap δ/r.…”

Section: Finite Core Equilibriamentioning

confidence: 99%

“…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: Resultsmentioning

confidence: 99%

Section: Finite Core Equilibriamentioning

confidence: 99%

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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“…Given the explicit form of the Green's function, however, it is now possible to use the techniques described in Reinaud & Dritschel (2002) to search for equilibria of single vortices in the compressible system. Finding these would permit a more detailed and systematic analysis of the stability of ellipsoidal vortices in a wider range of parameter space.…”

Section: Discussionmentioning

confidence: 99%

Quasi-geostrophic vortices in compressible atmospheres

Scott

Dritschel

2005

J. Fluid Mech.

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This paper considers the effect of an exponential variation in the background density field (as exists in compressible atmospheres) on the structure and dynamics of the quasi-geostrophic system, and compares the results with the corresponding Boussinesq limit in which background density variations are assumed small. The behaviour of the compressible system is understood via a closed-form analytic expression for the Green's function of the inversion operator relating potential vorticity and streamfunction. This expression makes explicit the anisotropy of the Green's function, inherited from the density profile, which has a slow, algebraic decay directly above the source and an exponential decay in all other directions. An immediate consequence for finite-volume vortices is a differential rotation of upper and lower levels that results in counterintuitive behaviour during the nonlinear evolution of ellipsoidal vortices, in which vortex destruction is confined to the lower vortex and wave activity is seen to propagate downwards. This is in contrast to the Boussinesq limit, which exhibits symmetric destruction of the upper and lower vortex, and in contrast to naive expectations based on a consideration of the mass distribution alone, which would lead to greater destruction of the upper vortex. Finally, the presence of a horizontal lower boundary introduces a strong barotropic component that is absent in the unbounded case (the presence of an upper boundary has almost no effect). The lower boundary also alters the differential rotation in the lower vortex with important consequences for the nonlinear evolution: for very small separation between the lower boundary and the vortex, the differential rotation is reversed leading to strong deformations of the middle vortex; for a critical separation, the vortex is stabilized by the reduction of the differential rotation, and remains coherent over remarkably long times.

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“…When two like-signed vortices come in close contact, they can merge to form a vortex which is often larger. Vortex merger has been studied in two-dimensional or quasi-geostrophic models, relevant to the mesoscale dynamics in the ocean interior (Overman and Zabusky, 1982;Dritschel, 1985Dritschel, , 1986Griffiths and Hopfinger, 1987: Melander et al, 1987, 1988Pavia and Cushman-Roisin, 1990;Carnevale et al 1991;Carton, 1992;Bertrand and Carton, 1993;Valcke and Verron, 1993;Verron and Valcke, 1994;Yasuda, 1995;Yasuda and Flierl, 1995;Verron, 1996, 1997;Yasuda and Flierl, 1997;von Hardenberg et al, 2000;Dritschel, 2002;Reinaud and Dritschel, 2002;Meunier et al, 2002;Bambrey et al 2007;Ozugurlu et al, 2008). Depending on the initial conditions, the merging process can finally form one large vortex or two asymmetric vortices.…”

Section: Introductionmentioning

confidence: 99%

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 merger of vertically offset quasi-geostrophic vortices

Cited by 56 publications

References 17 publications

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

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

Quasi-geostrophic vortices in compressible atmospheres

Vortex merger in surface quasi-geostrophy

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