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

Carton

2016

J. Fluid Mech.

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We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the three-dimensional quasi-geostrophic, contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as same-depth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally the intermediate regime is for moderate offsets. This is the regime where the formation of a meta-stable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finite-core vortices.

Section: Introductionmentioning

confidence: 99%

The interaction between two oppositely travelling, horizontally offset, antisymmetric quasi-geostrophic hetons

Carton

2016

J. Fluid Mech.

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“…This limiting case corresponds to a near dipole (or 'pseudo-dipole') where Thus, we perform the linear stability analysis of the stationary states, by analysing the deformation modes of the vortices boundary. The method follows straightforwardly that used in three-dimensional quasi-geostrophy 49,55,74 , adapted here to the two-layer context.…”

Section: Resultsmentioning

confidence: 99%

“…It is reached by an iterative method. The method converges when the boundaries of the vortices match streamlines in the relative reference frame moving with the vortices 14,33,35,49,55,74 . For tritons (µ = −2) the reference frame is in uniform translation, while it is in uniform rotation in the general case µ = −2 (eccentric or ordinary roundabouts).…”

Section: Numerical Setupmentioning

confidence: 99%

Geostrophic tripolar vortices in a two-layer fluid: Linear stability and nonlinear evolution of equilibria

Sokolovskiy

Carton³

2017

Physics of Fluids

1Geostrophic tripolar vortices in a two-layer fluid We investgate equilibrium solutions for tripolar vortices in a two-layer quasigeostrophic flow. Two of the vortices are like-signed and lie in one layer. An oppositesigned vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii.The two branches of equilibria can co-exist and intersect for small deformation radii.Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate of the nonlinear evolution of a few selected cases of tripoles.

“…The later method has been used in three dimension in various contexts (see Reinaud and Dritschel 2002, Reinaud and Dritschel 2009, Carton and Reinaud 2009, Reinaud 2015, and Reinaud and Carton 2015. For each calculation, the core vortex is discretised by 55 layers.…”

Section: Formulationmentioning

confidence: 99%

Piecewise uniform potential vorticity pancake shielded vortices

Geophysical & Astrophysical Fluid Dynamics

2017

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Shielded vortices consist of a core of potential vorticity of a given sign surrounded (or shielded) by a layer of opposite-signed potential vorticity. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where potential vorticity is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated potential vorticity is zero. We restrict attention to vortices of piecewise uniform potential vorticity in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of potential vorticity between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed.