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.
arXiv comment13 pages + appendix. v2: Improved derivation of the linearised Chern-Simons action. References added and typos fixed. v3: Improved explanations. References added
References in corpus (19)
- Null energy condition and superluminal propagation
- A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
- Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion
- Topological Origin of Equatorial Waves
- Topological waves in fluids with odd viscosity
- Lectures on the Quantum Hall Effect
- Supersymmetric Fluid Mechanics
- Conformal Edge Currents in Chern-Simons Theories
- Anomalous bulk-edge correspondence in continuous media
- A bulk-interface correspondence for equatorial waves
- Topology in shallow-water waves: a violation of bulk-edge correspondence
- Boundary Conditions and Unitarity: the Maxwell-Chern-Simons System in AdS_3/CFT_2
- Wave topology brought to the coast
- Clebsch (String) Parameterization of 3-Vectors and Their Actions
- Topology in shallow-water waves: A spectral flow perspective
- Topological waves in passive and active fluids on curved surfaces: a unified picture
- Topological modes in relativistic hydrodynamics
- Simplified Two-Dimensional Model for Global Atmospheric Dynamics
- Topological fluids with boundaries and fractional quantum Hall edge dynamics: A fluid dynamics derivation of the chiral boson action
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- Gauge theory for topological waves in continuum fluids with odd viscosity