In his study of superfluid turbulence in the low-temperature limit, Svistunov [“Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)] derived a Hamiltonian equation for the self-induced motion of a vortex filament. Under the local induction approximation (LIA), the Svistunov formulation is equivalent to a nonlinear dispersive partial differential equation. In this paper, we consider a family of rotating vortex filament solutions for the LIA reduction of the Svistunov formulation, which we refer to as the 2D LIA (since it permits a potential formulation in terms of two of the three Cartesian coordinates). This class of solutions holds the well-known Hasimoto-type planar vortex filament [H. Hasimoto, “Motion of a vortex filament and its relation to elastica,” J. Phys. Soc. Jpn. 31, 293 (1971)] as one reduction and helical solutions as another. More generally, we obtain solutions which are periodic in the space variable. A systematic analytical study of the behavior of such solutions is carried out. In the case where vortex filaments have small deviations from the axis of rotation, closed analytical forms of the filament solutions are given. A variety of numerical simulations are provided to demonstrate the wide range of rotating filament behaviors possible. Doing so, we are able to determine a number of vortex filament structures not previously studied. We find that the solution structure progresses from planar to helical, and then to more intricate and complex filament structures, possibly indicating the onset of superfluid turbulence.
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June 2014
Research Article|
June 17 2014
General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation
Robert A. Van Gorder
Robert A. Van Gorder
a)
Department of Mathematics,
University of Central Florida
, Orlando, Florida 32816-1364, USA
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a)
Author to whom correspondence should be addressed. Electronic mail: rav@knights.ucf.edu
Physics of Fluids 26, 065105 (2014)
Article history
Received:
January 26 2014
Accepted:
June 04 2014
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Citation
Robert A. Van Gorder; General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation. Physics of Fluids 1 June 2014; 26 (6): 065105. https://doi.org/10.1063/1.4883749
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