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A Gauge Theory for Shallow Water

by David Tong

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): David Tong
Submission information
Preprint Link: scipost_202212_00069v1  (pdf)
Date accepted: 2023-02-15
Date submitted: 2022-12-23 18:38
Submitted by: Tong, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Fluid Dynamics
  • High-Energy Physics - Theory
Approach: Theoretical

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 Abelian gauge theory. The magnetic field corresponds to the conserved height of the fluid, while the electric charge corresponds to the conserved vorticity. 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.

Author comments upon resubmission

Dear Editor,

Please find attached a revised version of this paper.

Best Wishes and Happy Holidays
David

List of changes

-- I made minor changes to the discussion of currents to include the definition of potential vorticity in (2.3)

-- The non-linear action (2.9) is no longer written in terms of two gauge fields, but instead in terms of the two scalars \alpha and \beta. The description in terms of the Clebsch gauge field that I previously called \tilde{A} is postponed to (2.14). This also involved minor changing to the wording in the abstract and introduction.

-- Footnote 1 on page 6 describes what happens when the Coriolis force is time dependent.

-- I added a brief discussion of time reversal and parity in (2.13) and (2.14)

-- I separated out the discussion of the flat band and Poincare waves in Section 3.2 more clearly. In addition, I added an effective action (3.15) for the flat band

-- I expanded the discussion of edge modes in classical Chern-Simons theory and Maxwell-Chern-Simons theory in Section 3.3

-- I added a discussion Section 4.

Published as SciPost Phys. 14, 102 (2023)


Reports on this Submission

Report #2 by Brad Marston (Referee 1) on 2023-1-10 (Invited Report)

Report

The revisions to the manuscript address my concerns, and I recommend publication. It is a very nice paper.

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Report #1 by Anonymous (Referee 3) on 2023-1-7 (Invited Report)

Report

I thank the author for addressing my comments and recommend the publication of the paper in SciPost Physics in the present form.

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