Classical and quantum regimes of superfluid turbulence

Volovik, G. E.

doi:10.1134/1.1641478

Cited by 69 publications

(67 citation statements)

References 18 publications

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“…The working superfluid is 4 He; similar mathematical models are also applicable to 3 He-B, although the typical phenomenology of 3 He-B flows is expected to differ from the 4 He case since the material properties that enter as parameters in these equations differ significantly between the two fluids [8,41]. We fix the temperature at T = 1.3 K so that ν n = 2.3303 × 10 −3 cm 2 /s, h 1 = 0.04093, and h 2 = −0.02175.…”

Section: Resultsmentioning

confidence: 99%

Elementary Vortex Processes in Thermal Superfluid Turbulence

Kivotides

Wilkin

2009

J Low Temp Phys

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By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics.

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Section: Resultsmentioning

confidence: 99%

Elementary Vortex Processes in Thermal Superfluid Turbulence

Kivotides

Wilkin

2009

J Low Temp Phys

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“…In Refs. [5] and [13] the effect of the mutual friction on the high momentum tail was overestimated, which led to the incorrect result for the spectrum of dissipation at high momenta. However, some general features suggested in Ref.…”

Section: Recent Experiments Inmentioning

confidence: 99%

“…In the second scenario suggested in Refs. [5] and [13], at qN ≪ 1 the turbulent state is completely reconstructed and the so called Vinen state emerges. This state introduced by Vinen [14] and then by Schwarz [15] contains a single scale r = κ/V and thus no cascade.…”

Section: Recent Experiments Inmentioning

confidence: 99%

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Energy spectra of developed superfluid turbulence

2004

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Turbulence spectra in superfluids are modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. We have found a new state of fully developed turbulence which occurs in some range of two Reynolds parameters characterizing the superfluid flow. This state displays both the Kolmogorov-Obukhov -scaling law E k ∝ k −5/3 and a new "3-scaling law" E k ∝ k −3 , each in a well-separated range of k.PACS numbers: 43.37.+q,47.32.Cc, 67.40.Vs, 67.57.Fg Superfluid consists of mutually penetrating components -viscous normal component and one or several frictionless superfluid components. This explains why different types of turbulent motion are possible depending on whether the normal and the superfluid components move together or separately. Here, we are interested in the most simple case when the dynamics of the normal component can be neglected. This occurs, for example, in the superfluid phases of 3 He where the normal component is so viscous that it is practically clamped to the container walls. The role of the normal component in this case is to provide the preferred heat-bath reference frame, where the normal component, and thus the heat bath, are at rest. Dissipation takes place when the vortices move with respect to this reference frame. Turbulence in such a superfluid component with the normal component at rest will be called here superfluid turbulence. Recent experiments in3 He-B [1] demonstrated that the fate of a few vortices injected into a rapidly moving superfluid depends on a dimensionless intrinsic temperaturedependent parameter q rather than on the flow velocity. At q ∼ 1, a rather sharp transition is observed between laminar evolution of the injected vortices and a turbulent many-vortex state of the whole superfluid. In this Letter we describe how the celebrated Kolmogorov-Obukhov 5 3 -law for the turbulent energy spectrum in normal fluid, E k ∝ k −5/3 , gets modified in the superfluid turbulence, giving rise the much steeper decrease, E k ∝ k −3 .As a starting point we utilize a coarse-grained hydrodynamic equation for the superfluid dynamics with distributed vortices. In this equation the parameter q characterizes the friction force between the superfluid and the normal components of the liquid, which is mediated by quantized vortices. According to this equation, turbulence develops only if the friction is relatively small compared to the inertial term, i.e. when q < 1. Here, we will study the case of developed turbulence which must occur at q ≪ 1.An important feature of superfluid turbulence is that the vorticity of the superfluid component is quantized in terms of the elementary circulation quantum κ (in 3 He-B, κ = π /m where m is the mass of 3 He atom). Thus, superfluid turbulence is a chaotic motion of welldetermined and well-separated vortex filaments [3]. Using this as starting point we can simulate the main ingredients of classical turbulence -the chaotic dynamics of the vortex degrees of freedom of the liquid. H...

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“…14), mechanical resonator techniques were developed for quantum turbulence (15)(16)(17)(18), and quantum turbulence was studied in dilute gases (19,20); there were many important theoretical developments, for example refs. [21][22][23][24][25][26], and numerical methods were enormously improved (27)(28)(29) to complement and better interpret experimental results.…”

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Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in ³ He-B

Fisher

Jackson

Sergeev

et al. 2014

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

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Andreev reflection of quasiparticle excitations provides a sensitive and passive probe of flow in superfluid 3 He-B. It is particularly useful for studying complex flows generated by vortex rings and vortex tangles (quantum turbulence). We describe the reflection process and discuss the results of numerical simulations of Andreev reflection from vortex rings and from quantum turbulence. We present measurements of vortices generated by a vibrating grid resonator at very low temperatures. The Andreev reflection is measured using an array of vibrating wire sensors. At low grid velocities, ballistic vortex rings are produced. At higher grid velocities, the rings collide and reconnect to produce quantum turbulence. We discuss spatial correlations of the fluctuating vortex signals measured by the different sensor wires. These reveal detailed information about the formation of quantum turbulence and about the underlying vortex dynamics. Quantum turbulence in superfluid 4 He has been studied for many decades (3-5). There has been a great deal of renewed interest in quantum turbulence in recent years owing to several factors: quantum turbulence was discovered in superfluid 3 He (6-8), techniques were developed to extend the study of quantum turbulence in superfluid 4 He to very low temperatures (9, 10), imaging techniques were developed to visualize superfluid turbulence at higher temperatures (11-13) (see the review in ref. 14), mechanical resonator techniques were developed for quantum turbulence (15-18), and quantum turbulence was studied in dilute gases (19,20); there were many important theoretical developments, for example refs. 21-26, and numerical methods were enormously improved (27-29) to complement and better interpret experimental results.In this article, we discuss quantum turbulence generated by vibrating grids in superfluid 3 He-B at low temperatures, where the normal fluid component is very small. The primary thermal excitations in 3 He are quasiparticle and quasihole excitations (30). At low temperatures, the excitation mean free path between collisions vastly exceeds the experimental dimensions. In this ballistic regime, excitations move independently and normally scatter only with the container walls. The normal fluid concept no longer applies because there is no collective motion of excitations.In addition to normal scattering, excitations can also undergo Andreev reflection. Andreev scattering produces nearly perfect retroreflection of excitations with very little momentum transfer: Quasiparticles become quasiholes, and vice versa. This provides an ideal probe for vortices and quantum turbulence at low temperatures. Andreev Scattering from Superfluid FlowThe dispersion curve for excitations is shown in Fig. 1A. The excitation group velocity v g = dE=dp is parallel to the momentum for quasiparticles that have p > p F , where p F is the Fermi momentum and is antiparallel to the momentum for quasiholes that have p < p F . The dispersion curve is tied to the reference frame of the superfluid. So, accordi...

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Classical and quantum regimes of superfluid turbulence

Cited by 69 publications

References 18 publications

Elementary Vortex Processes in Thermal Superfluid Turbulence

Elementary Vortex Processes in Thermal Superfluid Turbulence

Energy spectra of developed superfluid turbulence

Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in ³ He-B

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Classical and quantum regimes of superfluid turbulence

Cited by 69 publications

References 18 publications

Elementary Vortex Processes in Thermal Superfluid Turbulence

Elementary Vortex Processes in Thermal Superfluid Turbulence

Energy spectra of developed superfluid turbulence

Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in 3 He-B

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Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in ³ He-B