Two-dimensional turbulence above topography: condensation transition and selection of minimum enstrophy solutions
We consider two-dimensional flows above topography, revisiting the selective decay (or minimum enstrophy) hypothesis of Bretherton and Haidvogel. We derive a ‘condensed branch’ of solutions to the variational problem where a domain-scale condensate coexists with a flow at the (smaller) scale of the...
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| Published in: | Journal of fluid mechanics Vol. 988 |
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| Format: | Journal Article |
| Language: | English |
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Cambridge, UK
Cambridge University Press
31.05.2024
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| ISSN: | 0022-1120, 1469-7645 |
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| Abstract | We consider two-dimensional flows above topography, revisiting the selective decay (or minimum enstrophy) hypothesis of Bretherton and Haidvogel. We derive a ‘condensed branch’ of solutions to the variational problem where a domain-scale condensate coexists with a flow at the (smaller) scale of the topography. The condensate arises through a supercritical bifurcation as the conserved energy of the initial condition exceeds a threshold value, a prediction that we quantitatively validate using direct numerical simulations. We then consider the forced–dissipative case, showing how weak forcing and dissipation select a single dissipative state out of the continuum of solutions to the energy-conserving system predicted by selective decay. As the forcing strength increases, the condensate arises through a supercritical bifurcation for topographic-scale forcing and through a subcritical bifurcation for domain-scale forcing, both predictions being quantitatively validated by direct numerical simulations. This method provides a way of determining the equilibrated state of forced–dissipative flows based on variational approaches to the associated energy-conserving system, such as the statistical mechanics of two-dimensional flows or selective decay. |
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| AbstractList | We consider two-dimensional flows above topography, revisiting the selective decay (or minimum enstrophy) hypothesis of Bretherton and Haidvogel. We derive a ‘condensed branch’ of solutions to the variational problem where a domain-scale condensate coexists with a flow at the (smaller) scale of the topography. The condensate arises through a supercritical bifurcation as the conserved energy of the initial condition exceeds a threshold value, a prediction that we quantitatively validate using direct numerical simulations. We then consider the forced–dissipative case, showing how weak forcing and dissipation select a single dissipative state out of the continuum of solutions to the energy-conserving system predicted by selective decay. As the forcing strength increases, the condensate arises through a supercritical bifurcation for topographic-scale forcing and through a subcritical bifurcation for domain-scale forcing, both predictions being quantitatively validated by direct numerical simulations. This method provides a way of determining the equilibrated state of forced–dissipative flows based on variational approaches to the associated energy-conserving system, such as the statistical mechanics of two-dimensional flows or selective decay. |
| ArticleNumber | A13 |
| Author | Gallet, Basile |
| Author_xml | – sequence: 1 givenname: Basile orcidid: 0000-0002-4366-3889 surname: Gallet fullname: Gallet, Basile email: basile.gallet@cea.fr organization: Université Paris-Saclay, CNRS, CEA, Service de Physique de l'Etat Condensé, 91191 Gif-sur-Yvette, France |
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| CitedBy_id | crossref_primary_10_1029_2024JC021713 crossref_primary_10_1103_PhysRevLett_134_204001 crossref_primary_10_1017_jfm_2024_633 crossref_primary_10_1029_2024JC021990 |
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| Keywords | ocean processes topographic effects quasi-geostrophic flows |
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| Snippet | We consider two-dimensional flows above topography, revisiting the selective decay (or minimum enstrophy) hypothesis of Bretherton and Haidvogel. We derive a... |
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| SubjectTerms | Approximation Bifurcations Condensates Cyclones Decay Direct numerical simulation Dissipation Energy Energy conservation Enstrophy JFM Papers Lagrange multiplier Phase transitions Simulation Statistical mechanics Topography Turbulence Two dimensional flow Vortices |
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| Title | Two-dimensional turbulence above topography: condensation transition and selection of minimum enstrophy solutions |
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| Volume | 988 |
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