SciPost Submission Page
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: |
|
| 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
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 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.