A Gauge Theory for Shallow Water
arXiv:2209.10574 · doi:10.21468/SciPostPhys.14.5.102
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 Poincaré waves. The chiral edge modes of the theory are identified as coastal Kelvin waves.
13 pages + appendix. v2: Improved derivation of the linearised Chern-Simons action. References added and typos fixed. v3: Improved explanations. References added
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