Turbulent Diffusion of Lines and Circulations

We study material lines and passive vectors in a model of turbulent flow at infinite-Reynolds number, the Kraichnan-Kazantsev ensemble of velocities that are white-noise in time and rough (Hoelder continuous) in space. It is argued that the phenomenon of spontaneous stochasticity'' generalizes to material lines and that conservation of circulations generalizes to a martingale property’’ of the stochastic process of lines.