Homogeneous Turbulence in Superfluid 4He in the Low-Temperature Limit: Experimental Progress

Golov, A. I.; Walmsley, P. M.

doi:10.1007/s10909-009-9896-9

Cited by 23 publications

(17 citation statements)

References 92 publications

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“…However, following the original spin-down experiment, there were a number of potential issues identified regarding the interpretation of the experiment and the extracted value of ν at low temperatures [45,46]. The absence of normal fluid means that there was serious uncertainty regarding how quickly the energy of rotation was converted into turbulence and what the effect was on the turbulent decay due to any long-lived rotating state [47].…”

Section: Decay Of Turbulencementioning

confidence: 99%

Dynamics of quantum turbulence of different spectra

Walmsley

Zmeev

Pakpour

et al. 2014

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

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Turbulence in a superfluid in the zero-temperature limit consists of a dynamic tangle of quantized vortex filaments. Different types of turbulence are possible depending on the level of correlations in the orientation of vortex lines. We provide an overview of turbulence in superfluid 4 He with a particular focus on recent experiments probing the decay of turbulence in the zero-temperature regime below 0.5 K. We describe extensive measurements of the vortex line density during the free decay of different types of turbulence: ultraquantum and quasiclassical turbulence in both stationary and rotating containers. The observed decays and the effective dissipation as a function of temperature are compared with theoretical models and numerical simulations.Superfluid helium is an ordered fluid with truly zero viscosity. Its local velocity is v s ðr; tÞ = Z m4 ∇θ, where θðr; tÞ is the macroscopically coherent phase of the complex order parameter (here we refer to the common isotope 4 He with atomic mass m 4 ). As a result, the velocity circulation around any closed contour through the superfluid is always quantized in units of κ ≡ h=m 4 . This allows stable topological defects-quantized vortex lines, i.e., vortices with precisely one quantum of circulation around their filamentary cores with a thickness of just a 0 ∼ 1 Å (inside which the order parameter is suppressed) (1, 2). Such a line can bend, move, and reconnect with another line when they come very close to each other. An array of vortex lines appears naturally as the equilibrium state of a superfluid rotating with the container (3-5). However, vortices can also form nonequilibrium tangles, known as "quantum turbulence" (QT) (6), that possesses excess energy. As in any nonequilibrium system, the presence and structure of the vortex tangle is a result of the history of generation of vortices and flow in the liquid.In contrast to vortex lines, particle-like excitations (phonons and rotons) are in thermal equilibrium, so their density increases with temperature. These scatter off the cores of vortex lines exerting the mutual friction force on the superfluid. At temperatures below about 0.5 K, the excitations are too depleted to affect vortex dynamics and can be neglected. Between about 0.5 and 0.7 K, they are nearly ballistic and can be treated as a small dissipative perturbation that damps Kelvin waves (helical perturbations of the shape of vortex lines) (2, 7) of wavelengths smaller than η q ðTÞ, which decreases with decreasing T (8). At higher temperatures, excitations form a fluid of low viscosity (the normal component). The normal component can move at velocity v n ðrÞ that is different from v s ðrÞ. The presence of two coexisting but weakly interacting (they only interact in the presence of quantized vortices) fluids, superfluid and normal (both of which can be independently turbulent), is a unique feature of superfluid helium. At high temperatures, Kelvin waves of all wavelengths are damped. With decreasing temperature between some 0.7 and 0.5 K, first larger...

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Section: Decay Of Turbulencementioning

confidence: 99%

Dynamics of quantum turbulence of different spectra

Walmsley

Zmeev

Pakpour

et al. 2014

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

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“…For example, the fact that upon large amplitude Kelvin waves vortex rings can slow down and even reverse their translational motion has been recognised only recently [22,7]. Alongside the traditional interest for problems in classical fluid mechanics, additional interest is motivated by current work on superfluid helium [42,9,17,13] and atomic Bose-Einstein condensates [41,27,19].…”

Section: Introductionmentioning

confidence: 99%

Velocity, energy, and helicity of vortex knots and unknots

et al. 2010

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In this paper we determine the velocity, the energy and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number w, given by the ratio of the number of meridian wraps to that of the longitudinal wraps. We find that for w < 1 vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for w > 1 knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by the writhe contribution. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, that are found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid 4 He.

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“…In recent years there has been overwhelming evidence that vorticity tends to get organized into coherent vortex filaments and tubes (the 'sinews of turbulence'), in both classical and quantum fluids. Numerical and observational experiments (Golov andWalmsley 2009, Uddin et al 2009) on the insurgence and permanence of isotropic turbulence demonstrate that this is characterized by relatively long-lived complex tangles of filaments, that are randomly distributed in the bulk of the fluid, before final dissipation. Such evidence has been further confirmed (Baggaley et al 2012) by recent enhanced visualization techniques and refined numerical codes, coupled with increased computational power and modern diagnostic methods (Hauser et al 2007).…”

Section: Vorticity Localization In Classical and Quantum Fluidsmentioning

confidence: 99%

The Jones polynomial as a new invariant of topological fluid dynamics

Ricca¹,

Liu²

2014

Fluid Dyn. Res.

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A new method based on the use of the Jones polynomial, a well-known topological invariant of knot theory, is introduced to tackle and quantify topological aspects of structural complexity of vortex tangles in ideal fluids. By re-writing the Jones polynomial in terms of helicity, the resulting polynomial becomes then function of knot topology and vortex circulation, providing thus a new invariant of topological fluid dynamics. Explicit computations of the Jones polynomial for some standard configurations, including the Whitehead link and the Borromean rings (whose linking numbers are zero), are presented for illustration. In the case of a homogeneous, isotropic tangle of vortex filaments with same circulation, the new Jones polynomial reduces to some simple algebraic expression, that can be easily computed by numerical methods. This shows that this technique may offer a new setting and a powerful tool to detect and compute topological complexity and to investigate relations with energy, by tackling fundamental aspects of turbulence research. |

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Homogeneous Turbulence in Superfluid 4He in the Low-Temperature Limit: Experimental Progress

Cited by 23 publications

References 92 publications

Dynamics of quantum turbulence of different spectra

Dynamics of quantum turbulence of different spectra

Velocity, energy, and helicity of vortex knots and unknots

The Jones polynomial as a new invariant of topological fluid dynamics

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