Fractal dimension of superuid turbulence: A random-walk toy model

Michele Sciacca, David Jou, Maria Stella Mongiovi

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


This paper deals with the fractal dimension of a superuid vortex tangle. It extends a previous model [1] (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.
Original languageEnglish
Article number471
JournalCommunications in Applied and Industrial Mathematics
Publication statusPublished - 1 Jan 2014


  • Fractal Dimension
  • Quantum Vortices
  • Random Walks
  • Superfluid Turbulence


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