Statistics of a Vortex Filament Model
Franco Flandoli, Università di Pisa, Italy
Massimiliano Gubinelli, Università di Pisa, Italy
Abstract
A random incompressible velocity field in three dimensions composed by Poisson distributed Brownian vortex filaments is
constructed. The filaments have a random thickness, length and intensity,
governed by a measure $gamma$. Under appropriate assumptions on $gamma$ we
compute the scaling law of the structure function of the field and show that, in particular, it allows for either K41-like scaling or multifractal scaling.
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