Counterflow in rotating superfluid helium

Yarmchuk, E. J.; Glaberson, W. I.

doi:10.1007/bf00118714

Cited by 40 publications

(8 citation statements)

References 20 publications

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“…Following a similar line of reasoning, Yarmchuk and Glaberson (1979) questioned whether one could rely on the Bekarevich-Khalatnikov condition at all. This caution is entirely justified in the region where the onset of depinning occurs.…”

Section: Ivd)mentioning

confidence: 99%

Vortex oscillations and hydrodynamics of rotating superfluids

Sonin

1987

Rev. Mod. Phys.

361

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This review covers the progress in the study of vortex oscillations in rotating superfluids. The paper deals with the theory as its principal coricern, but the experimerits that one can compare with the theory considered are also discussed. Attention is focused mainly on the d'fects of crystalline order in the vorte~lattice (the Tkachenko waves especially) and on the boundary problems arising in studies of vortex oscillations in finite containers. The approach is based mostly on the continuum hydrodynamic theory dealing with dense vortex arrays, and considerable attention is devoted to discussion of this theory in order to understand better the principles upon which the obtained results rest. The theory is traced from the simple description of a rotating classical fluid with continuous vorticity, through that of a perfect fluid with quantized vorticity in the form of an array of vortex lines, then the two-fluid theory of an isotropic superfluid, and finally the theory of rotating anisotropic superfluids such as He-A. Applications of the theory to He II, the superfluid phases of He, and the superfluid neutron matter in pulsars are discussed. CONTENTS

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Section: Ivd)mentioning

confidence: 99%

Vortex oscillations and hydrodynamics of rotating superfluids

Sonin

1987

Rev. Mod. Phys.

361

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“…But if vortices are pinned, in a boundary layer of width k~ -~ -k~ ~ superfluid velocities as well as displacements rL and angles drL/dz increase proportionally to d. One might expect that the onset of depinning would be determined by the condition that one of these quantities reaches some critical value independent of bulk properties. 3 In this case the critical mean flow density for depinning should be inversely proportional to d. But the experiment shows 3 that the critical density flow is inversely proportional to x/d. Probably this suggests that some sort of bulk turbulence has an effect on the onset of depinning.…”

Section: Vt~vxt+ivytmentioning

confidence: 99%

“…1'2 The direct measurement of the temperature gradients in stationary thermal flow also has been recently done. 3 The theory of mutual friction has been developed following the ideas of the pioneering paper by Hall and Vinen 1"4-6 (for additional references see Refs. 3 and 6).…”

Section: Introductionmentioning

confidence: 99%

Mutual friction force in rotating helium II at low temperatures and near the ?-point

Sonin¹

1981

J Low Temp Phys

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Mutual friction parameters in rotating HeH are derived for the case of vortices kept at rest by external forces (surface pinning forces). They are different from those obtained in the theory of Hall and Vinen for the case of free vortices with the total momentum of the fluid being conserved. The difference increases if the temperature increases. In the critical region Hall and Vinen' s theory fails and the mutual friction problem is solved with the help of the phenomenological theory of superfluidity fitted to the critical behavior of known physical quantities. The theory is in satisfactory quantitative agreement with experimental data on the critical behavior of the mutual friction parameters B and B'. The theory predicts a strong effect of the vortex pinning on the thermal counterflow in the critical region.

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“…As AJL^ -> 0, \v n -v s \ must drop below the critical value before A^ = 0. Measurements and theory have shown that when the L-K equations apply, Vju = 0 [4]. Further inspection of the nonlinear term shows that v s does not have an entrance region because v s -Vv s <x Vv s 2 and a steady state solution would not produce a constant mass flow averaged over a cross section.…”

Section: The Problemmentioning

confidence: 97%

“…The thermodynamic variables are the temperature, pressure and entropy: T, p, and s. The gravitational acceleration is g and c p is the specific heat. We have simplified equation (4) for the conservation of entropy by removing the pressure dependence of s and the thermal conductivity of He II, both of which are negligible for our application. We omitted the second viscosity terms of Khalatnikov since they are negligible in steady flow.…”

Section: The Problemmentioning

confidence: 99%

Critical Velocities for HE II

Snyder

2004

AIP Conference Proceedings

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We propose a model to calculate the mass and heat flow of He II in a pipe connecting two baths. The each bath is maintained at constant temperature and pressure. The chemical potential difference is nonzero. When the velocities of the normal and superfluid components are above the critical value, the Gorter-Mellink equations provide a good approximation. These equations have unique solutions and the method is straightforward. When the velocities are below critical, the Landau equations are appropriate. These equations have no steady state solution when the chemical potential is nonzero. The equations do not specify how to find the velocity of the superfluid component and it is not clear how to determine when the flow is above or below the critical velocity. The model envisages two flow regimes in different parts of the flow path. One regime is above critical and is a solution of the Gorter-Mellink equations. It brings the chemical potential difference to zero. The remainder of the flow path is below critical with no gradient of chemical potential. There is a change in the profile of the superfluid component where the transition of flow regimes occurs and this allows a conservation of mass and heat flow.

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Counterflow in rotating superfluid helium

Cited by 40 publications

References 20 publications

Vortex oscillations and hydrodynamics of rotating superfluids

Vortex oscillations and hydrodynamics of rotating superfluids

Mutual friction force in rotating helium II at low temperatures and near the ?-point

Critical Velocities for HE II

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