A Gauge Theory for Shallow Water
High Energy Physics - Theory
2023-05-10 v3 Strongly Correlated Electrons
Atmospheric and Oceanic Physics
Fluid Dynamics
Abstract
The shallow water equations describe the horizontal flow of a thin layer of fluid with varying height. We show that the equations can be rewritten as a d=2+1 dimensional gauge theory with a Chern-Simons term. The theory contains two Abelian gauge fields, corresponding to the conserved height and conserved vorticity of the fluid. In a certain linearised approximation, the shallow water equations reduce to relativistic Maxwell-Chern-Simons theory. This describes Poincar\'e waves. The chiral edge modes of the theory are identified as coastal Kelvin waves.
Cite
@article{arxiv.2209.10574,
title = {A Gauge Theory for Shallow Water},
author = {David Tong},
journal= {arXiv preprint arXiv:2209.10574},
year = {2023}
}
Comments
13 pages + appendix. v2: Improved derivation of the linearised Chern-Simons action. References added and typos fixed. v3: Improved explanations. References added