A gauge theory for the 2+1 dimensional incompressible Euler equations

Autor:	Eling, Christopher
Rok vydání:	2023
Předmět:	High Energy Physics - Theory Physics - Atmospheric and Oceanic Physics Physics - Fluid Dynamics
Druh dokumentu:	Working Paper
Popis:	We show that in two dimensions the incompressible Euler equations can be re-expressed in terms of an abelian gauge theory with a Chern-Simons term. The magnetic field corresponds to fluid vorticity and the electric field is the product of the vorticity and the gradient of the stream function. This picture can be extended to active scalar models, including the surface quasi-geostrophic equation. We examine the theory in the presence of a boundary and show that the Noether charge algebra is a Kac-Moody algebra. We argue that this symmetry is associated with the nodal lines of zero magnetic field. Comment: 19 pages; v2: fixed minor errors, added clarifications and a section on field redefinitions, references added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.04394 Zobrazit plný text záznamu View this record from Arxiv