Probabilistic representation of helicity in viscous fluids
Fluid Dynamics
2022-06-20 v3 Mathematical Physics
math.MP
Probability
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].
Cite
@article{arxiv.2010.09027,
title = {Probabilistic representation of helicity in viscous fluids},
author = {Simon Hochgerner},
journal= {arXiv preprint arXiv:2010.09027},
year = {2022}
}
Comments
v2: fixed a mistake in the setup; v3: streamlined exposition;