Existence of energy minimizing vortices attached to a flat-top seamount |
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| Affiliation: | 1. Department of Mathematics, Tarbiat Modares University, Tehran, Iran;2. Department of Meteorology, Stockholm University, 106 91 Stockholm, Sweden;1. Misum, Stockholm School of Economics and Department of Economics, Södertörn University, Stockholm, Sweden;2. Department of Statistics, Virginia Tech, USA;1. Stockholm International Peace Research Institute (SIPRI), Sweden;2. University of Massachusetts, Boston, Untied States;1. Radboud University Medical Centre, Donders Institute for Brain, Cognition and Behaviour, Department of Cognitive Neuroscience, Nijmegen, the Netherlands;2. Karakter Child and Adolescent Psychiatry University Centre, Nijmegen, the Netherlands;3. Ghent University, Department of Experimental-Clinical and Health Psychology, Belgium;4. Radboud University Medical Centre, Department of Psychiatry, Nijmegen, the Netherlands;5. Centre for Brain and Cognitive Development, Birkbeck College, University of London, United Kingdom;6. Center of Neurodevelopmental Disorders at Karolinska Institutet (KIND), Neuropsychiatry Unit, Department of Women''s and Children''s Health, Karolinska Institutet, Stockholm, Sweden;7. Child and Adolescent Psychiatry, Center for Psychiatry Research, Stockholm County Council, Stockholm, Sweden;8. University of Warsaw, Faculty of Psychology, Department of Health and Rehabilitation Psychology, Poland;9. Uppsala University, Department of Psychology, Sweden;10. Helmholtz Institute, Department of Experimental Psychology, Utrecht, the Netherlands;11. Utrecht University, Department of Developmental Psychology, Utrecht, the Netherlands;12. Psychology Department, University of Cambridge, United Kingdom;13. King’s College London, Psychology Department, Institute of Psychiatry, Psychology & Neuroscience, London, United Kingdom;14. South London and Maudsley NHS Foundation Trust, London, United Kingdom;1. KTH Royal Institute of Technology, FLOW, 10044, Stockholm, Sweden;2. ISAE-SUPAERO, Université de Toulouse, 31400, Toulouse, France |
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| Abstract: | ![]()
The existence of an energy minimizer relative to a class of rearrangements of a given function is proved. The minimizers are stationary and stable solutions of the two-dimensional barotropic vorticity equation, governing the evolution of geophysical flow over a surface of variable height. The theorem proved implies the existence of a family of stable anticyclonic vortices with cyclonic potential vorticity over a seamount, and a corresponding family of cyclonic vortices with anticyclonic potential vorticity over a localized depression. The seamount is described by a characteristic function (corresponding to a flat top) with arbitrary shape. |
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