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

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rsc16_rev_source_veps.pdf (455.6Kb)
Date
03/2017
Author
Reinaud, Jean Noel
Sokolovskiy, Mikhail
Carton, Xavier
Keywords
Stationery states
Two-layer quasi-geostrophic flows
Triton
Tripole
Round-about
QA Mathematics
QC Physics
NDAS
BDC
Metadata
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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.
Citation
Reinaud , J N , Sokolovskiy , M & Carton , X 2017 , ' Geostrophic tripolar vortices in a two-layer fluid : linear stability and nonlinear evolution of equilibria ' , Physics of Fluids , vol. 29 , no. 3 , 036601 . https://doi.org/10.1063/1.4978806
Publication
Physics of Fluids
Status
Peer reviewed
DOI
https://doi.org/10.1063/1.4978806
ISSN
1070-6631
Type
Journal article
Rights
Copyright © 2017, the Author(s). This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1063/1.4978806
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/10411

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