A Gauge Theory for Shallow Water

Understand

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.