Quasiparticle-scattering measurements of laminar and turbulent vortex flow in the spin-down of superfluid ${}^{3}$He-$B$

Quasiparticle-scattering measurements of laminar and turbulent vortex flow in the spin-down of superfluid $^{3}$ He- $B$

J. J. Hosio, V. B. Eltsov, M. Krusius, and J. T. Mäkinen

Phys. Rev. B 85, 224526 – Published 21 June 2012

Abstract

The dynamics of quantized vortices is studied in superfluid $^{3}$ He-B after a rapid stop of rotation. We use Andreev reflection of thermal excitations to monitor vortex motion with quartz tuning-fork oscillators in two different experimental setups at temperatures below $0.2 T_{c}$ . Deviations from ideal cylindrical symmetry in the flow environment cause the early decay to become turbulent. This is identified from a rapid initial overshoot in the vortex density above the value before the spin-down and its subsequent decay with a $t^{- 3 / 2}$ time dependence. The high polarization of the vortices along the rotation axis significantly suppresses the effective turbulent kinematic viscosity $ν^{'}$ below the values reported for more homogeneous turbulence and leads to a laminar late-time response. The laminar dissipation down to $T < 0.15 T_{c}$ is determined from the precession frequency of the polarized vortex configuration. In the limit of vanishing normal-component density, it is found to approach a temperature-independent value, whose origin is currently under discussion.

Received 30 April 2012

DOI:https://doi.org/10.1103/PhysRevB.85.224526

Authors & Affiliations

J. J. Hosio^*, V. B. Eltsov, M. Krusius, and J. T. Mäkinen

O.V. Lounasmaa Laboratory, P.O. Box 15100, FI-00076 AALTO, Finland

^*jaakko.hosio@aalto.fi

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Vol. 85, Iss. 22 — 1 June 2012

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Images

Figure 1
Left: Experimental setup for the bolometric measurement of the early turbulent spin-down response. The upper experimental volume modeled as a bolometer is separated from the heat-exchanger volume at the bottom by the lower division plate with a small 0.3-mm-diameter orifice. The upper division plate with a 0.75-mm-diameter aperture secures laminar spin-down flow in the topmost section. The quartz tuning forks are calibrated to measure the heat transport to the refrigerator. Right: Setup without division plates for the measurement of the late laminar part of the spin-down response.Reuse & Permissions
Figure 2
Temperature $T$ in the bolometer and an estimate for the lower limit of the vortex density $L$ after bringing the container to rest from $Ω_{ini} = 0.5$ rad/s at $t = 0$ . The vortex density is inferred from the fraction of Andreev-reflected thermal excitations, as discussed in the text. The solid line is a fit to $L \propto {(t + τ)}^{- 3 / 2}$ dependence after the initial overshoot in the data. The inset shows the principle of the measurement: The vortices below the orifice reflect some fraction of the thermal excitations back to the bolometer. The fraction depends on the density and configuration of these vortices at the lower temperature $T < 0.14 T_{c}$ . The measurement is performed at 29 bar liquid $^{3}$ He pressure.Reuse & Permissions
Figure 3
Left: Lower limit of the vortex density $L$ as a function of time after bringing the container to rest for four initial velocities $Ω_{ini}$ (see text for details). A simple moving-average filtering is used to reduce the noise in the data. The upper limit of $L$ at each value of $Ω_{ini}$ obtained from a calibration measurement with rectilinear vortices at a known density is a few times higher. Right: Lower and upper limits for the maximum vortex density generated in spin-down together with the initial steady-state value $2 Ω_{ini} / κ$ .Reuse & Permissions
Figure 4
Response of the resonance width of the quartz tuning-fork oscillator to a rapid spin-down from $Ω_{ini} =$ 1.02 rad/s to rest. The initial increase arises mainly owing to Andreev reflection from the rapidly decaying turbulent vortex configuration generated in the early part of the spin-down. The inset shows the zoomed view of the oscillations in the laminar late response caused by a periodic variation of the thermal excitation density in the vicinity of the fork. These oscillations result from the Andreev scattering from an asymmetric vortex cluster precessing at angular velocity $Ω_{s} (t)$ . The measurement is performed at 0.5 bar liquid $^{3}$ He pressure.Reuse & Permissions
Figure 5
Superfluid angular velocity $Ω_{s}$ as a function of time after bringing the container to rest at $t = 0$ . The response fits perfectly to the laminar flow model [Eq. (6)] shown by the dashed line with $Ω_{0} \approx 0.80 Ω_{ini}$ and $α \approx 6.45 \times 10^{- 4}$ . The inset shows the dissipative mutual-friction parameter $α$ as a function of the linewidth of the tuning-fork oscillator (bottom axis) or temperature (top axis). The value of $α$ , whose uncertainty is of the order of $\pm 5 \times 10^{- 5}$ , is extracted from the precession frequency of the vortex cluster, as discussed in the text, and averaged over 2–4 measurements at different rotation velocities in the range $Ω_{ini} = 0.6$ – $1.5$ rad/s at the given temperature.Reuse & Permissions

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