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

Type Article
Date 2017-03
Language English
Author(s) Reinaud J. N.1, Sokolovskiy M. A.2, 3, Carton Xavier4
Affiliation(s) 1 : Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland.
2 : Russian Acad Sci, Inst Water Problems, 3 Gubkina St, Moscow 119333, Russia.
3 : Russian Acad Sci, PP Shirshov Inst Oceanol, 36 Nakhimovsky Prospect, Moscow 117997, Russia.
4 : UBO UBL, IUEM, Lab Oceanog Phys & Spatiale, Technopole Brest Iroise, F-29280 Plouzane, France.
Source Physics Of Fluids (1070-6631) (Amer Inst Physics), 2017-03 , Vol. 29 , N. 3 , P. 036601 (16p.)
DOI 10.1063/1.4978806
WOS© Times Cited 6
Abstract We investigate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed 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 the nonlinear evolution of a few selected cases of tripoles. Published by AIP Publishing.
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