Probabilistic representation of helicity in viscous fluids
arXiv:2010.09027 · doi:10.5802/crmeca.116
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].
v2: fixed a mistake in the setup; v3: streamlined exposition;