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A simple Lagrangian for shallow water equations with constant potential vorticity
Abstract
Inspired by a recent gauge field description of shallow water equations [SciPost Phys. 14 (2023) 102], in this work we build a simple Lagrangian formulation for the case of constant potential vorticity. An attractive feature of the construction is that it does not appeal to a Clebsch-like parametrization or the use of auxiliary fields. It is also emphasized that on the equator, where the Coriolis parameter vanishes, the shallow water equations exhibit extra SO(2,1) conformal invariance. Using the group-theoretic method, a new exact solution is found, which is associated with the scaling symmetry transformation entering the conformal group.
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BibTeX
@misc{galajinsky2026simple,
title = {{A simple Lagrangian for shallow water equations with constant potential vorticity}},
author = {Anton Galajinsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05904},
eprint = {2610.05904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05904},
}
RIS
TY - UNPB
TI - A simple Lagrangian for shallow water equations with constant potential vorticity
AU - Anton Galajinsky
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05904
UR - https://arxiv.org/abs/2610.05904
AB - Inspired by a recent gauge field description of shallow water equations [SciPost Phys. 14 (2023) 102], in this work we build a simple Lagrangian formulation for the case of constant potential vorticity. An attractive feature of the construction is that it does not appeal to a Clebsch-like parametrization or the use of auxiliary fields. It is also emphasized that on the equator, where the Coriolis parameter vanishes, the shallow water equations exhibit extra SO(2,1) conformal invariance. Using the group-theoretic method, a new exact solution is found, which is associated with the scaling symmetry transformation entering the conformal group.
ER -