Conserved Pseudomomenta in Linear Quasigeostrophic Fluid Flows From Noether's Theorem

Dusan Begus; Chenyu Zhang; J. B. Marston

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arXiv · 2512.09061

Conserved Pseudomomenta in Linear Quasigeostrophic Fluid Flows From Noether's Theorem

Dusan Begus·Chenyu Zhang·J. B. Marston

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Abstract

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.

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Dusan Begus, Chenyu Zhang, J. B. Marston. 2025-12-09. Conserved Pseudomomenta in Linear Quasigeostrophic Fluid Flows From Noether's Theorem. https://arxiv.org/abs/2512.09061

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