Formal Analogy Between Maxwell's Equations and Vortex Dynamics in Weakly Viscous Media

This paper investigates the possibility of constructing a formal mathematical analogy between the dynamics of vortex structures in an ideal or weakly viscous fluid and the structure of Maxwell’s equations in electrodynamics. The Hill’s spherical vortex is considered as a localized structure carrying energy and momentum, and traveling at constant speed. Analogous quantities are proposed between hydrodynamic variables and electromagnetic potentials and fields, including dissipation as a crucial ingredient. The resulting formalism leads to a structurally identical system to Maxwell’s equations. Experimental verification is proposed in systems such as quantum fluids, superfluid helium, and ultracold atoms.