Asymptotic motion of a single vortex in a rotating cylinder

Karimäki, J. M.; Hänninen, Risto; Thuneberg, E. V.

doi:10.1103/physrevb.85.224519

Cited by 5 publications

(9 citation statements)

References 39 publications

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“…19 The results are in a qualitative agreement with those obtained here using the local-induction approximation. In particular, expansion of the expression (11) of Ref.…”

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

confidence: 91%

“…In particular, expansion of the expression (11) of Ref. 19 for the front velocity (noted as v Lz there) with respect to − 0 gives v f ≈ 0.741αR( − 0 ), which does not differ essentially from Eq. (64).…”

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

confidence: 97%

“…(64). A more quantitative comparison requires more numerical data for lower angular velocities ∼ 0 , while available data 19 focus on high angular velocities 0 . Another useful approximation is to assume that the shape of the end vortex segment in the front is close to a horizontal straight line between the axis (r = 0) and the wall (r = R).…”

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

confidence: 99%

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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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“…19 The results are in a qualitative agreement with those obtained here using the local-induction approximation. In particular, expansion of the expression (11) of Ref.…”

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

confidence: 91%

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

confidence: 97%

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

confidence: 99%

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

Sonin

2012

Phys. Rev. B

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“…The front precesses azimuthally at a lower angular velocity than the bundle behind it, and consequently, they both are twisted. 19 The effects of vortex curvature, both collective 20,21 and the single-vortex effects, 22 somewhat reduce the propagation velocity V f of the front from that in Eq. ( 2) at temperatures down to T ≈ 0.45 T c .…”

Section: Superfluid Vortex Frontmentioning

confidence: 99%

Thermal Detection of Turbulent and Laminar Dissipation in Vortex Front Motion

2012

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We report on direct measurements of the energy dissipated in the spinup of the superfluid component of 3 He-B. A vortex-free sample is prepared in a cylindrical container, where the normal component rotates at constant angular velocity. At a temperature of 0.20 T c , seed vortices are injected into the system using the shear-flow instability at the interface between 3 He-B and 3 He-A. These vortices interact and create a turbulent burst, which sets a propagating vortex front into motion. In the following process, the free energy stored in the initial vortexfree state is dissipated leading to the emission of thermal excitations, which we observe with a bolometric measurement. We find that the turbulent front contains less than the equilibrium number of vortices and that the superfluid behind the front is partially decoupled from the reference frame of the container. The final equilibrium state is approached in the form of a slow laminar spin-up as demonstrated by the slowly decaying tail of the thermal signal.

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“…1A. They continuously expand, until they become fully rectilinear line vortices, as their ends move with an axial velocity V lam ≈ αΩR or somewhat smaller, depending on the curvature of the vortex (18,19).…”

Section: Coarse-grained Superfluid Dynamics and Mutual Frictionmentioning

confidence: 99%

Quantum turbulence in superfluids with wall-clamped normal component

Eltsov

Hänninen

Krusius

2014

Proc. Natl. Acad. Sci. U.S.A.

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In Fermi superfluids, such as superfluid 3 He, the viscous normal component can be considered to be stationary with respect to the container. The normal component interacts with the superfluid component via mutual friction, which damps the motion of quantized vortex lines and eventually couples the superfluid component to the container. With decreasing temperature and mutual friction, the internal dynamics of the superfluid component becomes more important compared with the damping and coupling effects from the normal component. As a result profound changes in superfluid dynamics are observed: the temperature-dependent transition from laminar to turbulent vortex motion and the decoupling from the reference frame of the container at even lower temperatures.superfluid Reynolds number | vortex tension | vortex front | rotating flow | pipe flow I n this paper, we consider the motion of quantized vortices in superfluids, where the normal component is clamped to the walls of the container; that is, it is stationary in a reference frame moving with the wall. This situation can be experimentally realized in superfluid 3 He. In such systems, turbulent motion can occur only in the superfluid component and thus, in principle, is easier to analyze. Here the role of the normal fluid is twofold: first, it provides friction in the superfluid motion, which is mediated by quantized vortices and works over a wide range of length scales. Second, it provides a coupling to the container walls, which acts uniformly over the whole volume of the superfluid. This situation is quite unlike classical turbulence, where viscous dissipation operates only at the small Kolmogorov scale and coupling to the walls is provided by thin boundary layers.As a result, a variety of new phenomena is observed in experiments and numerical simulations as a function of temperature. These phenomena are controlled by the normal-fluid density. At the highest temperatures, turbulent motion is suppressed completely. When the temperature decreases, a sharp transition to turbulence is seen. The transition can be characterized by a superfluid Reynolds number, which is composed of the internal friction parameters of the superfluid and is independent of velocity. When turbulence is triggered by a localized perturbation of the laminar flow, the critical value of the Reynolds number is found to scale with the strength of the perturbation.When the temperature decreases further, friction from the normal component rapidly vanishes. The overall dissipation rate in quantum turbulence remains nevertheless finite, owing to the contribution from the turbulent energy cascade, and reaches a temperatureindependent value in the zero-temperature limit. This zero-temperature dissipation can be characterized by an effective viscosity or friction. It is found, however, that coupling to the walls is not essentially improved by the turbulence and can potentially become very small. At the lowest temperatures the concept of a single effective friction breaks down; for the proper descriptio...

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Asymptotic motion of a single vortex in a rotating cylinder

Cited by 5 publications

References 39 publications

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

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

Thermal Detection of Turbulent and Laminar Dissipation in Vortex Front Motion

Quantum turbulence in superfluids with wall-clamped normal component

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