doi: 10.1685/journal.caim.471

Fractal dimension of superfluid turbulence: a random-walk toy model

Maria Stella Mongiovì, Michele Sciacca, David Jou


This paper deals with the fractal dimension of a superfluid vortex tangle. It extends a previous model [J. Phys. A: Math. Theor. 43, 205501 (2010)] (which was proposed for very low temperature), and it proposes an alternative random walk toy model, which is valid also for finite
temperature. This random walk model combines a recent Nemirovskii’s proposal, and a simple modelization of a self-similar structure of vortex loops (mimicking the geometry of the loops of several sizes which compose the tangle). The fractal dimension of the vortex tangle is then related
to the exponents describing how the vortex energy per unit length changes with the length scales, for which we take recent proposals in the bibliography. The range between 1.35 and 1.75 seems the most consistent one.

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909