2023/10/19 by Christopher Eling, Eling, Christopher · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2310.12475
openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the incompressible Euler equations in three spatial dimensions can be expressed in terms of an abelian gauge theory with a topological BF term. A crucial part of the theory is a 3-form field strength, which is dual to a material invariant local helicity in the fluid. In one version of the theory, there is an additional 2-form field strength, with the magnetic field corresponding to fluid vorticity and the electric field identified with the cross-product of the velocity and the vorticity. In the second version, the 2-form field strength is instead expressed in terms of Clebsch scalars. We discuss the theory in the presence of the boundary and argue that edge modes may be present in the dual description of fluid flows with a boundary.