Probabilistic representation of helicity in viscous fluids

TL;DR

This paper demonstrates that the helicity in viscous incompressible fluids can be represented through the linking of initial vorticity and a stochastic mean field expectation, connecting fluid dynamics with stochastic particle systems.

Contribution

It introduces a novel probabilistic representation of helicity in viscous fluids using stochastic mean field limits and Lagrangian path analysis.

Findings

Helicity linked to stochastic mean field expectation.

Connection established between vorticity linking and stochastic particle systems.

Provides a new perspective on viscous fluid helicity analysis.

Abstract

It is shown that the helicity of three dimensional viscous incompressible flow can be identified with the overall linking of the fluid's initial vorticity to the expectation of a stochastic mean field limit. The relevant mean field limit is obtained by following the Lagrangian paths in the stochastic Hamiltonian interacting particle system of [S. Hochgerner, Proc. R. Soc. A 474:20180178].