Conserved Pseudomomenta in Linear Quasigeostrophic Fluid Flows From Noether's Theorem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908703160008704 |
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| author | Begus, Dusan Zhang, Chenyu Marston, J. B. |
| author_facet | Begus, Dusan Zhang, Chenyu Marston, J. B. |
| contents | Hamiltonian and Lagrangian formulations for the two-dimensional quasi-geostrophic equations linearized about a zonally-symmetric basic flow are presented. The Lagrangian and Hamiltonian exhibit an infinite U(1) symmetry due to the absence of wave + wave -> wave interactions in the linearized approximation. By Noether's theorem the symmetry has a corresponding infinite set of conservation laws which are the well-known pseudomomenta. There exist separately conserved pseudomomenta at each zonal wavenumber, a point that has sometimes been obscured in past treatments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conserved Pseudomomenta in Linear Quasigeostrophic Fluid Flows From Noether's Theorem Begus, Dusan Zhang, Chenyu Marston, J. B. Fluid Dynamics Atmospheric and Oceanic Physics Hamiltonian and Lagrangian formulations for the two-dimensional quasi-geostrophic equations linearized about a zonally-symmetric basic flow are presented. The Lagrangian and Hamiltonian exhibit an infinite U(1) symmetry due to the absence of wave + wave -> wave interactions in the linearized approximation. By Noether's theorem the symmetry has a corresponding infinite set of conservation laws which are the well-known pseudomomenta. There exist separately conserved pseudomomenta at each zonal wavenumber, a point that has sometimes been obscured in past treatments. |
| title | Conserved Pseudomomenta in Linear Quasigeostrophic Fluid Flows From Noether's Theorem |
| topic | Fluid Dynamics Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2512.09061 |