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Physical Review Letters

Superfluid Dissipation in Rotating He3 - B

Henry Edgar Hall, P. L. Gammel, J. D. Reppy

Published May 7, 1984• 23 citations
Publisher

Abstract

Additional dissipation of oscillatory superflow has been observed in uniformly rotating $^{3}\mathrm{He}$-$B$. The damping increases linearly with angular velocity and is interpreted in terms of vortex-induced mutual friction similar to that observed in superfluid $^{4}\mathrm{He}$. In the nonrotating state the damping is amplitude dependent, and may contain a contribution from remanent vorticity.

DOI
10.1103/physrevlett.52.1701

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Additional dissipation of oscillatory superflow has been observed in uniformly rotating 3He^{3}\mathrm{He}3He-BBB. The damping increases linearly with angular velocity and is interpreted in terms of vortex-induced mutual friction similar to that observed in superfluid 4He^{4}\mathrm{He}4He. In the nonrotating state the damping is amplitude dependent, and may contain a contribution from remanent vorticity.
A satellite peak has been observed in the NMR spectrum of rotating 3He^{3}\mathrm{He}3He-AAA; the peak intensity depends linearly on $\ensuremath{\Omega}$ at the high angular velocities, $\ensuremath{\Omega}=0.6\ensuremath{-}1.5$ rad/s, needed to resolve it. The frequency shift of the satellite is independent of $\ensuremath{\Omega}$. These results strongly suggest the existence of vortices in rotating 3He^{3}\mathrm{He}3He-AAA with the vortex density proportional to $\ensuremath{\Omega}$. Another satellite peak also has been observed which probably is due to solitons.
Insight in the dynamics of quantized vortex lines has been obtained by performing NMR measurements in uniformly rotating superfluid 3B^{3}\mathit{B}3B. Compared to superfluid 4He^{4}\mathrm{He}4He, in 3B^{3}\mathit{B}3B the viscosity of the normal component is three orders of magnitude larger and the pinning of vortices is weaker. The collective modes governing the hydrodynamic response of an array of vortex lines are highly overdamped. Two distinct modes are identified: (1) a relatively fast mutual-friction-resisted mode, which controls the redistribution of the vortex density on a time scale of a few seconds, and (2) an exponentially relaxing slow mode with a time constant of a few minutes, which governs asymptotically the approach to equilibrium at nearly constant vortex density. Measurement of the fast motion allows us to extract the dissipative mutual friction. The slow mode is dominated by the elastic tension along the vortex line and by weak pinning at the top and bottom surfaces of the rotating container. With increasing vortex density the surface pinning becomes a collective process, in which coherently moving groups of vortices are pinned in unison. Collective pinning is a result of the shear elasticity related to the crystalline order of the vortex lattice. Our measurements on the slow mode indicate that the crystalline correlation extends over many lattice spacings.
In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3 He-B, that q = α/(1 − α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/ q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al. , the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.
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The dynamics of quantized vortices in rotating 3^33He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at 0.5Tc0.5 T_{\rm c}0.5Tc​. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of numerical calculations we suggest a mechanism responsible for vortex formation at low temperatures and identify the mutual friction parameter which governs its abrupt temperature dependence.
We have used torsional oscillators, containing disk-shaped slabs of superfluid (3)He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating. Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity Ω(0) is left behind after stopping rotation. The bias toward a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation. When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation relative to that of l. A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when the angular velocity, Ω, is parallel to l.