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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].

Keywords

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;

R2 v1 2026-06-23T19:25:52.061Z