Minimum-enstrophy solutions in topographic quasi-geostrophic flow on the rotating sphere
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910174205181952 |
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| author | Ephrati, Sagy Jansson, Erik |
| author_facet | Ephrati, Sagy Jansson, Erik |
| contents | The minimum-enstrophy theory of Bretherton and Haidvogel postulates that two-dimensional turbulent systems evolve to a state that minimises enstrophy at a fixed energy level. We extend this to the rotating spherical quasi-geostrophic setting, accounting for bottom topography and the fully nonlinear Coriolis effect, resulting in latitude-dependent effects not present in planar approximations. We prove existence and nonlinear stability of minimum-enstrophy solutions and describe analytically asymptotic regimes for certain rates of rotation, topography scales, and energy values. We compute the minimum-enstrophy solutions by a structure-preserving method for the quasi-geostrophic equations on the sphere. We apply the method to a range of parameter values, including those describing Jupiter's atmosphere. The results reveal a distinct latitude dependence of the flow, with a tendency for topographical trapping near the poles and zonal flow near the equator, depending on the chosen parameters. The predicted nonlinear stability is confirmed numerically by integrating perturbed solutions using a structure-preserving time discretisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25600 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimum-enstrophy solutions in topographic quasi-geostrophic flow on the rotating sphere Ephrati, Sagy Jansson, Erik Fluid Dynamics Numerical Analysis Mathematical Physics 76U05, 53D50, 35Q35, 67U60 The minimum-enstrophy theory of Bretherton and Haidvogel postulates that two-dimensional turbulent systems evolve to a state that minimises enstrophy at a fixed energy level. We extend this to the rotating spherical quasi-geostrophic setting, accounting for bottom topography and the fully nonlinear Coriolis effect, resulting in latitude-dependent effects not present in planar approximations. We prove existence and nonlinear stability of minimum-enstrophy solutions and describe analytically asymptotic regimes for certain rates of rotation, topography scales, and energy values. We compute the minimum-enstrophy solutions by a structure-preserving method for the quasi-geostrophic equations on the sphere. We apply the method to a range of parameter values, including those describing Jupiter's atmosphere. The results reveal a distinct latitude dependence of the flow, with a tendency for topographical trapping near the poles and zonal flow near the equator, depending on the chosen parameters. The predicted nonlinear stability is confirmed numerically by integrating perturbed solutions using a structure-preserving time discretisation. |
| title | Minimum-enstrophy solutions in topographic quasi-geostrophic flow on the rotating sphere |
| topic | Fluid Dynamics Numerical Analysis Mathematical Physics 76U05, 53D50, 35Q35, 67U60 |
| url | https://arxiv.org/abs/2604.25600 |