Conserved Pseudomomenta in Linear Quasigeostrophic Fluid Flows From Noether's Theorem

Abstract

Hamiltonian and Lagrangian formulations for the two-dimensional quasi-geostrophic equations linearized about a zonally-symmetric basic flow are presented. The Lagrangian and Hamiltonian exhibit an infinite U(1) symmetry due to the absence of wave + wave -> wave interactions in the linearized approximation. By Noether's theorem the symmetry has a corresponding infinite set of conservation laws which are the well-known pseudomomenta. There exist separately conserved pseudomomenta at each zonal wavenumber, a point that has sometimes been obscured in past treatments.