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

Sonin, É. B.

doi:10.1103/physrevb.85.024515

Cited by 17 publications

(30 citation statements)

References 15 publications

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“…The Vinen spectrum E Vinen (k) ∼ k −1 , was derived under the assumption of critical balance where the linear and nonlinear time-scales of KW are of the same order. Finally, It was suggested by E. Sonin [16] that no universally can be expected for the KW spectrum.…”

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confidence: 96%

Kelvin-wave cascade and dissipation in low-temperature superfluid vortices

Krstulovic

2012

Phys. Rev. E

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We study the statistical properties of the Kelvin waves propagating along quantized superfluid vortices driven by the Gross-Pitaevskii equation. No artificial forcing or dissipation is added. Vortex positions are accurately tracked. This procedure directly allows us to obtain the Kevin-waves occupation-number spectrum. Numerical data obtained from long time integration and ensembleaverage over initial conditions supports the spectrum proposed in [L'vov and Nazarenko, JETP Lett 91, 428 (2010)]. Kelvin wave modes in the inertial range are found to be Gaussian as expected by weak-turbulence predictions. Finally the dissipative range of the Kelvin-wave spectrum is studied. Strong non-Gaussian fluctuations are observed in this range. PACS numbers: 67.25.dk, 47.37.+q, 67.25.dt, 03.75.Kk Superfluid turbulence has been the subject of many experimental and theoretical works for the last decades. In particular a lot of progress has been done in experimental techniques and it is now possible to realize tur- , a turbulent Kolmogorov cascade has been observed experimentally and numerically. In superfluids, this takes place at scales larger than the mean inter-vortex distance [6][7][8]. At very low temperature, when damping due to mutual friction is negligible, it is believed that dissipation at small scales is carried by phonon radiation which dissipates energy into heat [9]. At scales smaller than the energy is transferred down by a series of reconnection processes of quantized vortices that excite waves on the filaments. These perturbations called Kelvin waves (KW), have been known for more than one century [10] in the broader context of fluid dynamics. These waves obey a set of non-linear equations where the energy transfer towards small scales is carried by a wave-turbulence cascade. How the energy is distributed along different scales is crucial for the understanding of the dissipative processes in superfluids. The energy spectrum of such a cascade is not yet fully-determined, except in the limit of small amplitude KW, where the theory of weak turbulence is applicable [11]. However, a heated debate on the locality of KW energy transfer has taken place in the last years [12][13][14][15][16][17]. Two different groups, Kozik & Stvistunov [18] and L'vov & Nazarenko [19], starting from the very same equations and by using the same theory, have derived two different spectra (hereafter KS and LN spectra repectivelly). The origin of this controversy is mainly due to a symmetry argument by KS (tilt of a vortex line) that eventually leads to a vanishing vertex in the perturbative expansion. This leads to locality in the energy transfer and makes the 6-wave interaction theory realizable. The energy spectrum found by KS iswhere is the energy flux, κ the circulation quantum and k the wavevector. This symmetry argument was questioned by LN and they claimed that the energy transfer is non-local. They derived an effective 4-wave interaction theory that leads to the energy spectrumwhere Ψ ∼ (1/κ) E LN (k)dk is the mean-square angul...

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confidence: 96%

Kelvin-wave cascade and dissipation in low-temperature superfluid vortices

Krstulovic

2012

Phys. Rev. E

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“…The systematic deviation of the model from the experimental data in the range (0.25-0.35)T c in Fig. 8 may be caused by an oversimplified treatment of the angular momentum balance in the turbulent front that does not yet include all contributions considered for the laminar front (34). An important message is conveyed by the residual values for α en = 0:20 andα am = 0:002, which describe the T → 0 contribution to effective friction from turbulence and possibly from surface friction.…”

Section: Energy Dissipation and Momentum Transfermentioning

confidence: 89%

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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“…In particular, we will clarify several issues and past results which appear to have been misinterpreted in Ref. 14…”

Section: Introductionmentioning

confidence: 91%

Comment on “Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in theT=0superfluid turbulence”

L’vov

Nazarenko

2012

Phys. Rev. B

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We comment on the paper by E. B. Sonin, PRB 85, 104516 (2012) with which we find ourselves in serious disagreement. We use this option to shed light on some important issues of a theory of Kelvin wave turbulence, touched in E. B. Sonin's paper, in particular, on the relation between the Vinen spectrum of strong-and the L'vov-Nazarenko spectrum of weak-turbulence of Kelvin waves. We also discuss the role of our explicit calculation of the Kelvin wave interaction Hamiltonian and of the "symmetry arguments" that are supposed to resolve a contradiction between the Kozik-Svistunov and L'vov-Nazarenko spectrum of weak turbulence of Kelvin waves.

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

Cited by 17 publications

References 15 publications

Kelvin-wave cascade and dissipation in low-temperature superfluid vortices

Kelvin-wave cascade and dissipation in low-temperature superfluid vortices

Quantum turbulence in superfluids with wall-clamped normal component

Comment on “Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in theT=0superfluid turbulence”

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