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

This paper deals with the fractal dimension of a superfluid vortextangle. It extends a previous model [J. Phys. A: Math. Theor. {\bf43}, 205501 (2010)] (which was proposed for very low temperature),and it proposes an alternative random walk toy model, which is validalso for finite temperature. This random walk model combines arecent Nemirovskii's proposal, and a simple modelization of aself-similar structure of vortex loops (mimicking the geometry of the loops ofseveral sizes which compose the tangle). The fractal dimension ofthe vortex tangle is then related to the exponents describing howthe 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.