Equilibrium rotation of a vortex bundle terminating on a lateral wall

TL;DR

This paper explores the conditions under which a vortex bundle can achieve equilibrium solid-body rotation within a container, analyzing from single vortices to multi-layered structures and considering both equilibrium and near-equilibrium states.

Contribution

It introduces a comprehensive analysis of vortex bundle equilibrium, including the effects of vortex interactions, thermodynamic potentials, and non-equilibrium dynamics.

Findings

Equilibrium requires equal thermodynamic potentials in vortex and vortex-free regions.

Vortex front velocity depends on friction between vortices and the container.

The study extends from single vortices to complex multi-layered vortex bundles.

Abstract

The paper investigates possibility of equilibrium solid-body rotation of a vortex bundle diverging at some height from a cylinder axis and terminating on a lateral wall of a container. Such a bundle arises when vorticity expands up from a container bottom eventually filling the whole container. The analysis starts from a single vortex, then goes to a vortex sheet, and finally addresses a multi-layered crystal vortex bundle. The equilibrium solid-body rotation of the vortex bundle requires that the thermodynamic potentials in the vortex-filled and in the vortex-free parts of the container are equal providing the absence of a force on the vortex front separating the two parts. The paper considers also a weakly non-equilibrium state when the bundle and the container rotate with different angular velocities and the vortex front propagates with the velocity determined by friction between vortices and the container or the normal liquid moving together with the container.