Interactions between normal-fluid and superfluid vortex rings in helium-4

Kivotides, Demosthenes

doi:10.1209/0295-5075/112/36005

Cited by 9 publications

(14 citation statements)

References 18 publications

(32 reference statements)

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“…shows normal-fluid vorticity isosurfaces (|ω| = 37000 s −1 ) as they coevolve with a dilute tangle of superfluid vortices. In agreement with previous investigations[18], the solution indicates that although the generation sites of superfluid vorticity are somewhat Normal-fluid Hopf-link interacting with superfluid vortices of similar diameters. Left:Flow energy E = (1/2V) dV V • Vversus time.…”

supporting

confidence: 91%

“…The observed instabilities appear similar to the Ostermeier-Glaberson instability [36], that Another important result (see also [18]) is that the superfluid rings do not grow at sizes quantities is expected to be small. Indeed, only mild variations of the pure normal-fluid solution are observed.…”

Section: Interactions Between Rings Of Similar Sizesupporting

confidence: 53%

“…acting with a locally averaged normal-fluid vorticity field. Notably, the governing equations and the parametrization of mutual-friction interactions in this approach are, in principle, flow dependent (e.g., different for rotating and pipe or channel flows), and, by default, not applicable to dilute tangles of a few superfluid vortices, (b) a "direct" approach [15][16][17][18][19] that models discrete topological defects and their individual interactions with the normal-fluid.…”

mentioning

confidence: 99%

“…Left: Normal-fluid velocity streamlines for the same structure. A mutualfriction induced jet at the superfluid vortex position creates two recirculating normal-flow areas adjacent to the superfluid ring contour.connection between superfluid theory and classical low Reynolds number hydrodynamics.EFFECTS OF A NORMAL-VORTICITY HOPF-LINK ON THE STRUCTURE OF SUPERFLUID TURBULENCEIt has previously been shown[18] that a key effect of single normal-fluid vortex ring on superfluid turbulence is the transfer of energy from the normal-fluid to the superfluid towards an equilibration of energies in the two fluids. This however, is not accompanied by the superfluid vorticity mimicking the normal-fluid one.…”

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confidence: 99%

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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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supporting

confidence: 91%

Section: Interactions Between Rings Of Similar Sizesupporting

confidence: 53%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Superfluid helium-4 hydrodynamics with discrete topological defects

Kivotides

2018

Phys. Rev. Fluids

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“…For example, [8] indicated that a system of viscous, reconnecting vortex tubes reproduces the Kolmogorov k −5/3 scaling of inertial range turbulence, and [9] showed that systems of vortex elements give rise to Levy rather than Gaussian distributions for turbulent flow velocity. Similar connections between vortices and spectra [10][11][12], as well as, vortices and velocity distributions [13,14] were also obtained in quantum fluids. In FTST, [12] showed that interactions between one normal-fluid and many superfluid vortex rings generate a tendency towards energy-level matching in the wavenumber intervals of the velocity spectra which correspond to the normal-fluid ring diameter scale.…”

supporting

confidence: 58%

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

Kivotides

2018

Physics Letters A

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It is shown that, as a result of its interactions with superfluid vorticity, a normal-fluid vortex tube in helium-4 becomes unstable and disintegrates. The superfluid vorticity acquires only a small (few percents of normal-fluid tube strength) polarization, whilst expanding in a front-like manner in the intervortex space of the normal-fluid, forming a dense, unstructured tangle in the process. The accompanied energy spectra scalings offer a structural explanation of analogous scalings in fully developed finite-temperature superfluid turbulence. A macroscopic mutual-friction model incorporating these findings is proposed. PROLOGUE At temperatures smaller than 2.17 K (the lambda point), the quantum field that describes helium-4 becomes Bose-Einstein condensed, giving rise to a non-zero ground state that corresponds to an inviscid fluid ("superfluid"). The superfluid coexists with the (classical-like) "normal-fluid" of the Bogoliubov quasiparticles that comprise the thermalized quantum fluctuations. Turbulence in such systems, "finite-temperature superfluid turbulence" or FTST

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Cross-Component Energy Transfer in Superfluid Helium-4

Stasiak,

Baggaley,

Krstulovic

et al. 2024

J Low Temp Phys

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The reciprocal energy and enstrophy transfers between normal fluid and superfluid components dictate the overall dynamics of superfluid 4He including the generation, evolution and coupling of coherent structures, the distribution of energy among lengthscales, and the decay of turbulence. To better understand the essential ingredients of this interaction, we employ a numerical two-way model which self-consistently accounts for the back-reaction of the superfluid vortex lines onto the normal fluid. Here we focus on a prototypical laminar (non-turbulent) vortex configuration which is simple enough to clearly relate the geometry of the vortex line to energy injection and dissipation to/from the normal fluid: a Kelvin wave excitation on two vortex anti-vortex pairs evolving in (a) an initially quiescent normal fluid, and (b) an imposed counterflow. In (a), the superfluid injects energy and vorticity in the normal fluid. In (b), the superfluid gains energy from the normal fluid via the Donnelly–Glaberson instability.

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Interactions between normal-fluid and superfluid vortex rings in helium-4

Cited by 9 publications

References 18 publications

Superfluid helium-4 hydrodynamics with discrete topological defects

Superfluid helium-4 hydrodynamics with discrete topological defects

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

Cross-Component Energy Transfer in Superfluid Helium-4

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