Momentum and pseudomomentum in a shallow water equation

TL;DR

This paper analyzes a variable-topography shallow water system using a Lagrangian approach to derive momentum, energy, and pseudomomentum equations, highlighting symmetry properties and their physical implications.

Contribution

It provides a Lagrangian derivation of momentum, energy, and pseudomomentum balances for shallow water equations with variable topography, revealing symmetry structures.

Findings

Derived a two-dimensional momentum equation from a Lagrangian perspective

Identified broken and preserved symmetries in the system

Formulated additional energy and pseudomomentum equations

Abstract

A basic shallow water system with variable topography is analyzed from the point of view of a Lagrangian derivation of momentum, energy, and pseudomomentum balances. A two-dimensional action and associated momentum equation are derived. The latter is further manipulated to derive additional equations for energy and pseudomomentum. This revealed structure emphasizes broken symmetries in space and a reference configuration, and preserved symmetry in time.