Generalized Symmetries in Shallow Water

TL;DR

This paper reveals that generalized global symmetries, including subsystem symmetries, naturally occur in shallow water systems, linking classical fluid dynamics with modern symmetry concepts and uncovering new algebraic structures.

Contribution

It demonstrates the emergence of subsystem symmetries in shallow water flows and connects these symmetries to conservation laws and algebraic structures like Kac-Moody algebras.

Findings

Potential vorticity conservation stems from subsystem symmetry.

Kelvin circulation theorem is rooted in these symmetries.

Charge algebra forms a Kac-Moody current algebra.

Abstract

Recent developments have extended the concept of global symmetries in several directions, offering new perspectives across a wide range of physical systems. This work shows that generalized global symmetries naturally emerge in shallow water systems. In particular, we demonstrate that two subsystem symmetries-previously studied primarily in exotic field theories-arise intrinsically in the dynamics of shallow water flows. A central result is that the local conservation of potential vorticity follows directly from the first subsystem symmetry, revealing that the classic Kelvin circulation theorem is rooted in these symmetries. Notably, the associated charge algebra forms a Kac-Moody current algebra, with the level determined by the spatial variation of the Coriolis parameter. Beyond the first subsystem symmetry, we also identify a second one, construct the corresponding Noether charges, and explore their potential applications.