# Vortex flows on closed surfaces

## TL;DR

This paper explores the hydrodynamics of chiral vortex matter on closed surfaces, revealing the geometric origin of odd viscosity and its relation to vortex-curvature interactions.

## Contribution

It extends the understanding of chiral vortex hydrodynamics to curved geometries, highlighting the geometric nature of odd viscosity in such systems.

## Key findings

- Odd viscosity is linked to vortex-curvature interactions.
- Curved geometries reveal the geometric nature of odd viscosity.
- Hydrodynamics on closed surfaces extends previous flat-surface models.

## Abstract

We investigate the bulk hydrodynamics of the chiral vortex matter on an arbitrary closed surface, extending the ideas of [20, 41]. Placing this important example of a chiral medium onto a curved geometry reveals the geometric nature of odd viscosity. The anomalous odd viscosity of the vortex matter is associated with a special interaction of point vortices with curvature.