Instability of vortex lines in the presence of axial normal fluid flow

Ostermeier, R.M.; Glaberson, W. I.

doi:10.1007/bf01141298

Cited by 57 publications

(35 citation statements)

References 5 publications

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“…The stretch of remnant vortices in the thermal counterflow instability may be understood more fundamentally as an instability of single quantized vortices, the Kelvin-wave instability, sometimes called the Donnelly-Glaberson instability [149,150,151]. Kelvin-wave instability can occur when there is a relative helical flow along a vortex line between normal fluid and superfluid components, which is realized by injecting a heat current along the quantized vortices.…”

Section: Hydrodynamic Instabilities In Superfluid Systemsmentioning

confidence: 99%

Quantum hydrodynamics

Tsubota¹,

Kobayashi²,

Takeuchi³

2013

Physics Reports

157

181

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Quantum hydrodynamics in superfluid helium and atomic Bose-Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function (order parameter) appears because of Bose-Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in 4 He, which has no analogue with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), "Quantized vortices in superfluid helium and atomic Bose-Einstein condensates", and other review articles.

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Section: Hydrodynamic Instabilities In Superfluid Systemsmentioning

confidence: 99%

Quantum hydrodynamics

Tsubota¹,

Kobayashi²,

Takeuchi³

2013

Physics Reports

157

181

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“…Still, it would be interesting to discuss the instability for pure Kelvin waves k = 0 when v c = (2 + ν s p 2 )/p. By analyzing the stability of a single vortex in a rotating coordinate frame, Ostermeier and Glaberson 13 obtained v c = ( + ν s p 2 )/p. The factor 2 difference in the limit p → 0 is due to long-range interaction between vortices.…”

Section: Stability Of Twisted Vortex Bundlementioning

confidence: 98%

“…However, assuming that the friction force is weak, either because d and d are small or because the difference − 0 is small, one can determine the values d z , d φ , and d zφ using the shape of the vortex line in the state of equilibrium solid-body rotation together with the container and the normal liquid [Eq. (13) in Ref. 11].…”

Section: A Single-vortex Line Terminating At the Lateral Wallmentioning

confidence: 99%

Dynamics of twisted vortex bundles and laminar propagation of the vortex front

Sonin

2012

Phys. Rev. B

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This paper studies the dynamics of twisted vortex bundles, which were detected in experimental investigations of superfluid turbulence in superfluid 3 He-B. The analysis shows that a linear torsion oscillation of a vortex bundle is a particular case of the slow vortex mode related with the inertial wave, which was already investigated in the past in connection with observation of the Tkachenko waves in superfluid 4 He and the experiments on the slow vortex relaxation in superfluid 3 He-B. This paper addresses also a twisted vortex bundle terminating at a lateral wall of a container, starting from the elementary case when the bundle reduces to a single vortex. The theory considers the laminar regime of the vortex-bundle evolution and investigates the Glaberson-Johnson-Ostermeier instability of the laminar regime, which is a precursor for the transition to the turbulent regime at strong twist of the bundle. The propagation and the rotation velocities of the vortex front (the segment of the vortex bundle diverging to the wall) can be found from the equations of balance for the linear and the angular momenta and the energy. It is demonstrated that the vortex front can move with finite velocity even in the absence of mutual friction (the T = 0 limit). The theory is compared with experimental results on vortex-front propagation in superfluid 3 He-B.

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“…It is well known that normal fluid velocity parallel to the vortex may lead to the Donnelly-Glaberson instability. [2][3][4] This instability causes the amplification of Kelvin waves. A simple derivation to show the Donnelly-Glaberson instability (in the small amplitude limit and when α = 0) can be found, for example, in an article by Barenghi et al 5 In his paper, Van Gorder fails to mention the Donnelly-Glaberson instability completely.…”

mentioning

confidence: 99%

“…The resulting dispersion relation in zero temperature is the dispersion relation for a large amplitude Kelvin wave (4). The dispersion relation with mutual friction is…”

mentioning

confidence: 99%

Comment on “Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation” [Phys. Fluids 25, 085101 (2013)]

Hietala

Hänninen

2014

Physics of Fluids

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We comment on the paper by Van Gorder [“Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation,” Phys. Fluids 25, 085101 (2013)]. We point out that the flow of the normal fluid component parallel to the vortex will often lead into the Donnelly–Glaberson instability, which will cause the amplification of the Kelvin wave. We explain why the comparison to local nonlinear equation is unreasonable, and remark that neglecting the motion in the x-direction is not reasonable for a Kelvin wave with an arbitrary wavelength and amplitude. The correct equations in the general case are also derived.

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Instability of vortex lines in the presence of axial normal fluid flow

Cited by 57 publications

References 5 publications

Quantum hydrodynamics

Quantum hydrodynamics

Dynamics of twisted vortex bundles and laminar propagation of the vortex front

Comment on “Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation” [Phys. Fluids 25, 085101 (2013)]

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