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Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature

Lookup NU author(s): Dr Michele Sciacca, Professor Carlo Barenghi

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Abstract

By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. Finally, for the sake of more concrete illustration, we relate the fractal dimension of the tangle to the scaling exponents of amplitude and wavelength of a cascade of Kelvin waves.

Publication metadata

Author(s): Jou D, Mongiovi MS, Sciacca M, Barenghi CF

Publication type: Article

Publication status: Published

Journal: Journal of Physics A: Mathematical and Theoretical

Year: 2010

Volume: 43

Issue: 20

Print publication date: 30/04/2010

ISSN (print): 1751-8113

ISSN (electronic): 1751-8121

Publisher: Institute of Physics Publishing Ltd.

URL: http://dx.doi.org/10.1088/1751-8113/43/20/205501

DOI: 10.1088/1751-8113/43/20/205501

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