2023/05/07 by Christopher Eling, Eling, Christopher · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Atmospheric and Oceanic Physics (physics.ao-ph) #Black Holes and Theoretical Physics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2305.04394
openalex publication_date 2023/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.