Kelvin-Wave Cascade on a Vortex in Superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mn>4</mml:mn></mml:mmultiscripts></mml:math>at a Very Low Temperature

Vinen, W. F.; Tsubota, Makoto; Mitani, Akira

doi:10.1103/physrevlett.91.135301

Cited by 142 publications

(173 citation statements)

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“…Consequently nonlinear interactions between different Kelvin wavenumbers can transfer energy from small to large wavenumbers, which constitutes a Kelvinwave cascade. This idea was first suggested by Svistunov [52] and later developed and confirmed through theoretical and numerical work by Kivotides et al [53], Vinen et al [54], and Kozik and Svistunov [55,56,57].…”

Section: T) (10)mentioning

confidence: 83%

Quantum turbulence—from superfluid helium to atomic Bose–Einstein condensates

Tsubota

2009

J. Phys.: Condens. Matter

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This article reviews recent developments in quantum fluid dynamics and quantum turbulence (QT) for superfluid helium and atomic Bose-Einstein condensates. Quantum turbulence was discovered in superfluid 4 He in the 1950s, but the field moved in a new direction starting around the mid 1990s. Quantum turbulence is comprised of quantized vortices that are definite topological defects arising from the order parameter appearing in Bose-Einstein condensation. Hence QT is expected to yield a simpler model of turbulence than does conventional turbulence. A general introduction to this issue and a brief review of the basic concepts are followed by a description of vortex lattice formation in a rotating atomic Bose-Einstein condensate, typical of quantum fluid dynamics. Then we discuss recent developments in QT of superfluid helium such as the energy spectra and dissipative mechanisms at low temperatures, QT created by vibrating structures, and the visualization of QT. As an application of these ideas, we end with a discussion of QT in atomic Bose-Einstein condensates.

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Section: T) (10)mentioning

confidence: 83%

Quantum turbulence—from superfluid helium to atomic Bose–Einstein condensates

Tsubota

2009

J. Phys.: Condens. Matter

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“…However, the most remarkable feature in the spectrum is the excitation of a broad range of modes compatible with the dispersion relation of Kelvin waves, and the excitation of sound waves only at high frequencies. The broad and continuous range of Kelvin wave modes indicates the development of a non-linear Kelvin wave cascade [26]: as multiple modes are excited, they can interact non-linearly and transfer their energy to larger wavenumbers, where the energy in the modes (and their helicity) can be dissipated by phonon emission [31]. Indeed, the Kelvin waves fade away once helicity reaches its new steady state value of ≈ 2 quanta in Fig.…”

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confidence: 99%

Helicity, topology, and Kelvin waves in reconnecting quantum knots

Leoni

Mininni

Brachet³

2016

Phys. Rev. A

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Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes and ribbons. As such, it has found myriads of applications in astrophysics and solar physics, in fluid dynamics, in atmospheric sciences, and in biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of vortex lines can be downright impossible to apply in complex and turbulent scenarios. We present a new definition of helicity which overcomes these problems. With it, we show that only certain reconnection events conserve helicity. In other cases helicity can change abruptly during reconnection. Furthermore, we show that these events can also excite Kelvin waves, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum turbulence. Although helicity is perfectly conserved in barotropic ideal fluids, in real fluids [13,14] and in superfluids [15,16] vortex reconnection events, which alter the topology of the flow, can take place. It is unclear how well helicity is preserved under reconnection. As a few examples, experiments of vortex knots in water have shown that center line helicity remains constant throughout reconnection events [17], while theoretical arguments indicate that writhe (one component of the helicity) should be conserved in anti-parallel reconnection events [18], a fact later confirmed in numerical simulations of a few specific quantum vortex knots [19]. However, numerical studies of Burgers-type vortices indicate that helicity is not conserved [20]. While experiments studying helicity in quantum flows have not been done yet, the recent experimental creation of quantum knots in a Bose-Einstein condensate in the laboratory [21] is a significant step in that direction.Recently, quantum flows have been used as a testbed for many of these ideas [17,19], as vorticity in a quantum flow is concentrated along vortex lines with quantized circulation, and as these vortex lines can reconnect without dissipation. However, the lack of a fluid-like definition of helicity for a quantum flow requires complex topological measurements of the linking and knottedness of vortex lines [17], or artificial filtering of the fields [19] to prevent spurious values of helicity resulting from the singularity near quantum vortices. Moreover, helicity in quantum flows has an interest per se, as reconnection events in superfluid turbulence can excite Kelvin waves [22]. These are helical perturbations that travel along the vortex lines first predicted for classical vortices by Lord Kelvin (see [23]). Kelvin waves are believed to be responsible for the generation of an energy cascade [24,25] leading to Kelvin wave turbulence [26]. Possible links between helicity and the development of Kelvin wave turbulence have remain obscure as a result of the difficulties i...

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“…Our experiments with second sound (temperature-entropy) waves in He II show that, contrary to the conventional wisdom, acoustic wave energy can sometimes flow in the opposite direction too. We note that inverse energy cascades are known in 2-dimensional incompressible liquids and Bose gases [9], and have been considered for quantized vortices [10].We find that energy backflow in our acoustic system is attributable to a decay instability (cf. the kinetic instability in turbulent systems [11]), controlled mainly by nonlinear decay of the wave into two waves of lower frequency governed by the energy (frequency) conservation law [2] !…”

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Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium

et al. 2008

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We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments. DOI: 10.1103/PhysRevLett.101.065303 PACS numbers: 67.25.dk, 47.20.Ky, 47.27.ÿi, 67.25.dt A highly excited state of a system with numerous degrees of freedom, characterized by a directional energy flux through frequency scales, is referred to as turbulent [1,2]. Like the familiar manifestations of vortex turbulence in fluids, turbulence can also occur in systems of waves, e.g., turbulence of sound waves in oceanic waveguides [3], magnetic turbulence in interstellar gases [4], shock waves in the solar wind and their coupling with Earth's magnetosphere [5], and phonon turbulence in solids [6]. Following the ideas of Kolmogorov, the universally accepted picture says that nonlinear wave interactions give rise to a cascade of wave energy towards shorter and shorter wavelengths until, eventually, it becomes possible for viscosity to dissipate the energy as heat. Experiments and calculations show that, most of the time, the Kolmogorov picture is correct [2,7,8].We demonstrate below that this picture is incomplete. Our experiments with second sound (temperature-entropy) waves in He II show that, contrary to the conventional wisdom, acoustic wave energy can sometimes flow in the opposite direction too. We note that inverse energy cascades are known in 2-dimensional incompressible liquids and Bose gases [9], and have been considered for quantized vortices [10].We find that energy backflow in our acoustic system is attributable to a decay instability (cf. the kinetic instability in turbulent systems [11]), controlled mainly by nonlinear decay of the wave into two waves of lower frequency governed by the energy (frequency) conservation law [2] ! 1 ! 2 ! 3 . Here ! i u 20 k i is the frequency of a linear wave of wave vector k i and u 20 is the second sound velocity at negligibly small amplitude. The instability manifests itself in the generation of subharmonics. A quite similar parametric process, due to 4-wave scattering (modulation instability), is thought to be responsible for the generation of large wind-driven ocean waves [12]. Decay instabilities (especially threshold and nearthreshold behavior) have been studied for, e.g., spin waves [13], magnetohydrodynamic waves in plasma [14], and interacting first and second sound waves in superfluid helium near the superfluid transition [15].We now discuss what happens to a system of acoustic waves far beyond the decay threshold. Modeling the resultant nonlinear wave transformations in the laboratory is a potentially fruitful approach that has already yielded important results for, e.g., the turbulent decay of capillary waves on the surface of liquid H 2 [16]. Here, we exploit the special pro...

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Kelvin-Wave Cascade on a Vortex in SuperfluidHe4at a Very Low Temperature

Cited by 142 publications

References 14 publications

Quantum turbulence—from superfluid helium to atomic Bose–Einstein condensates

Quantum turbulence—from superfluid helium to atomic Bose–Einstein condensates

Helicity, topology, and Kelvin waves in reconnecting quantum knots

Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium

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