The Gibbs ensemble of a vortex filament

TL;DR

This paper develops a statistical ensemble framework for a single vortex filament in a 3D incompressible fluid, modeling its core with a stochastic process and establishing the partition function's existence across certain temperature ranges.

Contribution

It introduces a novel statistical ensemble for vortex filaments with a stochastic core model and proves the existence of the partition function for specific temperature ranges.

Findings

Partition function exists for positive temperatures.

Partition function exists for a limited range of negative temperatures.

Framework applies to a generic stochastic process model of vortex core.

Abstract

We introduce a statistical ensemble for a single vortex filament of a three dimensional incompressible fluid. The core of the vortex is modelled by a quite generic stochastic process. We prove the existence of the partition function for both positive and a limited range of negative temperatures.