Generalized fluid dynamics and the boundary condition

TL;DR

This paper develops a comprehensive relativistic fluid dynamics framework incorporating vorticity and boundary effects, highlighting topological contributions and vortex sheets, with implications for superfluid and boundary physics.

Contribution

It introduces a general formulation of relativistic fluid dynamics with vorticity on manifolds with boundaries, emphasizing topological terms and vortex sheet analysis.

Findings

Inclusion of topological terms in relativistic fluid equations.

Representation of vortex sheets as co-exact forms.

Discussion of boundary conditions for vortex dynamics.

Abstract

We present the general formulation of the relativistic fluid dynamics with vorticity (including relativistic superfluid) on a manifold with boundary. Making use of the Hodge decomposition, we emphasize that the equations of motion include a term due to non-trivial topology, while the pure vortex term introduced by Carter and Langlois will be presented merely by a co-exact form. We also consider a vortex sheet combined of individual vortices and discuss the boundary problem.