Comment on “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation” [Phys. Fluids 26, 065105 (2014)]

Hietala, Niklas; Hänninen, Risto

doi:10.1063/1.4900584

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…Mathematically, this means that the solutions Ψ will not always have time-independent modulus (as they did in [28]). The need to consider translating waves was discussed in the correspondence [29,30].…”

Section: Introductionmentioning

confidence: 99%

Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation

Gorder

2015

Physics of Fluids

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In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [Svistunov, Phys. Rev. B 52 (1995) 3647]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motion. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [Van Gorder, Phys. Fluids 26 (2014) 065105], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions, and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments, and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self-similar solutions to the model, and demonstrate that these types of solutions can model vortex kinks that gradually smooth and radiate Kelvin waves as time increases. Such solutions qualitatively agree with what one might expect from post-reconnection events.

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Section: Introductionmentioning

confidence: 99%

Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation

Gorder

2015

Physics of Fluids

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“…3 are correct in that the solutions discussed in Sec. III (and beyond) exhibit no translational motion.…”

Section: Introductionmentioning

confidence: 65%

“…If one then includes translation (as suggested in Ref. 3 and discussed above), we still obtain a valid system of Eqs. (4) and (5).…”

Section: Extensions For the Non-stationary Vortex Filament Casementioning

confidence: 99%

Response to “Comment on ‘General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation’” [Phys. Fluids 26, 119101 (2014)]

Gorder

2014

Physics of Fluids

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Comment on “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation” [Phys. Fluids 26, 065105 (2014)]

Cited by 2 publications

References 9 publications

Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation

Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation

Response to “Comment on ‘General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation’” [Phys. Fluids 26, 119101 (2014)]

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