Shallow Water Memory: Stokes and Darwin Drifts

TL;DR

This paper explores the gauge symmetry and conserved charges in shallow water systems, revealing connections to Kelvin circulation, current algebra, and drift phenomena as memory effects within a gauge theory framework.

Contribution

It demonstrates the gauge symmetry as area-preserving diffeomorphisms in the Lagrange description and links shallow water drifts to gauge memory effects.

Findings

Surface charges form a u(1) current algebra with level proportional to the Coriolis parameter.

Kelvin circulation theorem is reinterpreted in terms of conserved charges.

Euler, Stokes, and Darwin drifts are understood as gauge memory effects.

Abstract

It has been shown in \cite{Tong:2022gpg} that shallow water in the Euler description admits a dual gauge theory formulation. We show in the Lagrange description this gauge symmetry is a manifestation of the 2 dimensional area-preserving diffeomorphisms. We find surface charges associated with the gauge symmetry and their algebra, and study their physics in the shallow water system. In particular, we provide a reinterpretation of the Kelvin circulation theorem in terms of conserved charges. In the linear shallow water case, the charges form a u(1) current algebra with level proportional to the Coriolis parameter over the height of the fluid. We also study memory effect for the gauge theory description of the linearized shallow water and show Euler, Stokes and Darwin drifts can be understood as a memory effect and/or change of the surface charges in the gauge theory description.