Mutual-friction induced instability of normal-fluid vortex tubes in superfluid helium-4

Kivotides, Demosthenes

doi:10.1016/j.physleta.2018.03.051

Cited by 6 publications

(4 citation statements)

References 29 publications

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“…They should melt, changing into a highly irregular structure. Other example is a series of numerical simulations by Kivotides [13], [14], [15], [16]), who studied the exact (not HVBK) dynamics of quantum vortices in the turbulent flows (at finite temperature) and concluded "that the results do not show that a turbulent normal-fluid with a Kolmogorov energy spectrum induces superfluid vortex bundles in the superfluid". In paper [15] Kivotides reported about observation of clusters with weakly polarized vortex lines and associated Kolmogorov -type spectra E(k) ∝ k 5/3 .…”

Section: Hvbk Approach a Hvbk Approach For Rotating Superfluidsmentioning

confidence: 99%

Coarse-grained Hydrodynamics of turbulent superfluids: HVBK approach and the bundle structure of the vortex tangle

Nemirovskii¹

2019

Preprint

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In the paper I develop a critical analysis of the use of the HVBK method for the study of three-dimensional turbulent flows of superfluids. The conception of the vortex bundles forming the structure of quantum turbulence is controversial and does not justify the use of the HVBK method. In addition, this conception is counterproductive, because it gives incorrect ideas about the structure of the vortex tangle as a set of bundles containing parallel lines. The only type of dynamics of vortex filaments inside these bundles is possible, namely, Kelvin waves running along the filaments. At the same time, as shown in numerous numerical simulations, a vortex tangle consists of a set of entangled vortex loops of different sizes and having a random walk structure. These loops are subject to large deformations (due to highly nonlinear dynamics), they reconnect with each other and with the wall, split and merge, creating a lot of daughter loops. They also bear Kelvin waves on them, but the latter have little impact.I also propose and discuss an alternative variant of study of three-dimensional turbulent flows, in which the vortex line density L(r, t) is not associated with ∇ × vs, but it is an independent equipollent variable described by a separate equation.

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Section: Hvbk Approach a Hvbk Approach For Rotating Superfluidsmentioning

confidence: 99%

Coarse-grained Hydrodynamics of turbulent superfluids: HVBK approach and the bundle structure of the vortex tangle

Nemirovskii¹

2019

Preprint

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“…Indeed, it was shown that, under typical conditions, normal-fluid inertia overpowers the mutual-friction force, hence, the latter cannot efficiently correlate superfluid vorticity with the normal-fluid one. In a similar vein, it was shown that, as a result of its interactions with ambient quantized vortices, a straight normal-fluid tube becomes unstable, and only a small percentage of generated superfluid vorticity is eventually trapped by the unstable normal tube mimicking its structure[20]. Instead, the majority of superfluid vorticity propagates in the intervortex space.…”

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confidence: 94%

“…In other words, the normal-fluid and superfluid vortex structures are locally different from each other. The crucial role of flow instabilities in this phenomenology has been indicated in reference [20].…”

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confidence: 94%

“…The purpose of this article is to advance further the direct approach by developing a new model for the coupling between topological defects and normal-fluid hydrodynamics, whose sole empirical input requirement are the standard material properties of the quantum of circulation, superfluid-vortex core radius, and normal-fluid viscosity. Hence, the model is genuinely predictive, and its solutions can (a) directly be compared with experiments which measure local normal-fluid velocities and vortex tangle densities or detect individual superfluid vortices, (b) guide the development of new coarse-grained models [20]. We apply numerical analysis to the new dynamical equations, and solve them algorithmically.…”

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Superfluid helium-4 hydrodynamics with discrete topological defects

Kivotides

2018

Phys. Rev. Fluids

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In superfluid helium-4, a model of normal-fluid hydrodynamics and their coupling with topological defects (quantized vortices) of the order parameter (superfluid) is formulated. The model requires only material properties as input, and applies to both laminar and turbulent flows, to both dilute and dense superfluid vortex tangles. By solving the model for the case of a normal-fluid vorticity Hopf-link interacting with systems of quantized vortices, two vortex dynamical mechanisms of energy transfer from the normal-fluid to the superfluid are indicated: (a) small superfluid rings expand to the size of the normal-fluid vortex link tubes, and (b) superfluid rings with diameters similar to the diameters of the normal-fluid tubes succumb to axial-flow instabilities that excite small amplitude wiggles which subsequently evolve into spiral-waves along the superfluid vortex contours. The normal-fluid vorticity scale determines the upper size of the generated superfluid vorticity structures. A key role in energy transfer processes is played by an axial-flow instability of a superfluid vortex due to mutual-friction excitation by the normal-fluid, which mirrors the instability of normal-fluid tubes due to mutual-friction excitation by the superfluid. Although the sites of superfluid vorticity generation are always in the neighbourhood of intense normal-fluid vorticity events, the superfluid vortices do not mimic the normal-fluid vorticity structure, and perform different motions. These vortex dynamical processes provide explanations for the phenomenology of fully developed finite temperature superfluid turbulence. PROLOGUE Due to quantum decoherence and the loss of quantum interference effects [1, 2], the hydrodynamics of many quantum systems (e.g., quark-gluon plasmas [3] or helium-4 liquids above the critical temperature of T = 2.17 K) follow similar equations with those that apply to classical gases and liquids. In the helium-4 case however, below T = 2.17 K (the so-called lambda point), the global U (1) symmetry of the microscopic quantum system is spontaneously broken (Bose-Einstein Condensation), and low-frequency, long-wavelength Nambu-Goldstone modes appear, that need vanishingly little energy to excite, and are referred to as order-parameter dynamics [4]. These modes are of different nature than the (normal-fluid) hydrodynamics corresponding to conservation laws. Although spontaneous symmetry breaking is also a feature of classical systems (e.g., topological defect networks in liquid crystals: Poiseuille flow [5] or simple shear flow [6]), in helium-4, the broken symmetry corresponds to the conservation of particle number, and the corresponding order parameter obeys a nonlinear Schroedinger equation that depicts an inviscid, compressible superfluid populated with topological defects (vortices). In other words, the order parameter is a material field, a rather intriguing physics case. The term material field indicates that, rather than been (for example) a quality like the net magnetization in a ferromagnetic system...

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On the Closure Problem of the Coarse-Grained Hydrodynamics of Turbulent Superfluids

Nemirovskii

2020

J Low Temp Phys

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Mutual-friction induced instability of normal-fluid vortex tubes in superfluid helium-4

Cited by 6 publications

References 29 publications

Coarse-grained Hydrodynamics of turbulent superfluids: HVBK approach and the bundle structure of the vortex tangle

Coarse-grained Hydrodynamics of turbulent superfluids: HVBK approach and the bundle structure of the vortex tangle

Superfluid helium-4 hydrodynamics with discrete topological defects

On the Closure Problem of the Coarse-Grained Hydrodynamics of Turbulent Superfluids

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