Statistics of a Vortex Filament Model

Franco Flandoli (Università di Pisa, Italy)
Massimiliano Gubinelli (Università di Pisa, Italy)


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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Pages: 865-900

Publication Date: July 14, 2005

DOI: 10.1214/EJP.v10-267


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