Probabilistic representation of helicity in viscous fluids

Simon Hochgerner

Published 2020-10-18Version 1

It is shown that the helicity of $3D$ 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 [8].