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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Bibliographic Details
Published in:Journal of fluid mechanics Vol. 988
Main Author: Gallet, Basile
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 31.05.2024
Subjects:
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
ocean processes
topographic effects
quasi-geostrophic flows
ISSN:0022-1120, 1469-7645
Online Access:Get full text
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Summary: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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ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2024.365