Transition to Turbulence in Alternating Boundary Flow of Superfluid 4He

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Transition to Turbulence in Alternating Boundary
Flow of Superfluid 4He
LOW TEMPERATURES 2008, 28 Mar 2008

• Osaka City University Hideo Yano

• Contents
• Vortex-free vibrating wire
• Transition to turbulence
• due to the presence of remanent vortex lines
• triggered by free vortex rings
• triggered by temperature sweep

Collaborators Experiment R. Goto, Y. Nago,
N. Hashimoto, S. Mio, M. Inui, M.
Chiba, K. Andachi, K. Obara, O. Ishikawa, T.
Hata Theory S. Fujiyama, M. Tsubota
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Oscillating obstacles can easily generate
turbulence in superfluid 4He.
Wire
Grid
Microsphere
60 mm/s
42 mm/s
50 mm/s
H.A. Nichol, L. Skrbek, P.C. Hendry, P.V.E.
McClintock, Phys. Rev. Lett. 92, 244501 (2004).
HY, N. Hashimoto, et al, Phys. Rev. B 75, 012502
(2007).
J. Jager, B. Shuderer, W. Schoepe, Phys. Rev.
Lett. 74, 566 (1995).
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Generation of turbulence by a vibrating wire
Response of a vibrating wire
turbulence
HY, N. Hashimoto, et al, Phys. Rev. B 75, 012502
(2007).

• Motivation
• Vortex-free vibrating wire
• that cannot generate turbulence.
• If we can do it, then
• Study of the transition to turbulence

The velocity of generating turbulence ( 50 mm/s)
is much lower than the Landau velocity of 60
m/s. Remanent vortices should cause the
generation of turbulence !!
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Experimental setup
Configuration of vibrating wires
Pinhole of 0.1-mm diameter
B
A
NbTi 3 mm in diameter

• How we can obtain a vortex-free vibrating wire
• using a chamber with a pinhole
• 20 hours filling of superfluid 4He below 100 mK

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Vortex-free vibrating wire
Response of a vibrating wire
No transition to turbulence even above 1 m/s
! ? Effectively free of remanent vortices
See also N. Hashimoto, R. Goto, HY, et al,
Phys. Rev. B 76, 020504 (2007).
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Study on the transition to turbulence using a
vortex-free vibrating wire

• Turbulent Transition
• Transition due to remanent vortices
• Transition triggered by free vortex rings
• Transition triggered by temperature sweep
• Creating remanent vortices
• Warming above Tl
• Cooling to 30 mK

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Transition to turbulence due to remanent vortex
lines
Response of a vibrating wire
Bridged vortex lines attach to the
wire. ? Oscillation of the bridged vortices
causes turbulence.
Vortex lines are nucleated through the
superfluid transition, attaching to the vibrating
wire.
Resonance frequency increasing by 0.3 Hz
vortex-free vibrating wire
N. Hashimoto, R. Goto, HY, et al, Phys. Rev. B
76, 020504 (2007).
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Turbulence due to oscillation of a bridged vortex
Time evolution of turbulence simulated by Tsubota
group
obstacle sphere 200 mm Oscillating
superfluid velocity 150 mm/s frequency 200 Hz
150 ms
232 ms

• Kelvin waves arise on the bridged vortex line.
• Vortex rings nucleate by reconnection.
• Turbulence develops.

326 ms
R. Hänninen, M. Tsubota, W.F. Vinen, Phys. Rev.
B 75, 064502 (2007)
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Study on the transition to turbulence using a
vortex-free vibrating wire

• Turbulent Transition
• Transition due to remanent vortices
• Transition triggered by free vortex rings
• Transition triggered by temperature sweep
• Using two vibrating wire
• Generator of free vortex rings
• Detector of the turbulence

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Experimental setup
after 48 hours filling of superfluid 4He
vibrating wire A
vibrating wire B
Generator of turbulence
Detector
Generator of vortex rings
Generation of turbulence
No turbulent transition
B
vortex-free wire
remanent vortices attaching to a wire
A
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Transition to turbulence triggered by vortex rings
Detector _at_30mK
generator
OFF
Turbulence
OFF
detector
Laminar
Turbulence
The Detector keep the generation of turbulence
without free vortex rings coming from the
Generator.
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Transition to turbulence triggered by vortex rings
Detector _at_30mK
Vortex rings trigger the transition to turbulence.
generator OFF
generator
generator ON
detector
generator OFF
generator OFF
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Transition to turbulence triggered by vortex rings
Numerical simulation by Fujiyama and Tsubota
oscillating obstacle sphere 6 mm velocity 137
mm/s frequency 1.59 kHz number of injected
vortex rings 8

• 8 rings are enough for triggering the turbulence.
• A turbulence region appears to be on the
  trajectory of the sphere.

See a joint paper R. Goto, S. Fujiyama, M.
Tsubota, HY, et al, Phys. Rev. Lett. 100, 045301
(2008)
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Delay time of the transitions
Time series of energy dissipation
Delay time Dt 16 msec (? time of flight of
vortex rings) ? v 110 mm/s (if assuming a
flight distance of 1.8 mm) vortex size 1.5 mm
Generator
?t
Detector
Size of vortex rings
Generator
Detector
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Velocity of vortex rings triggering turbulence
Delay vs. detector velocity
Velocity of vortex rings
Generator drive force 0.5 nN in laminar flow
900 mm/s in turbulent flow 50 mm/s
Velocity of vortex rings triggering turbulence ?
velocity of the detector
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Study on the transition to turbulence using a
vortex-free vibrating wire

• Turbulent Transition
• Transition due to remanent vortices
• Transition triggered by free vortex rings
• Transition triggered by temperature sweep
• Temperature control 1 1.8 K (lt Tl2.17 K)
• Control of a normal fluid component
• Using a vortex-free vibrating wire

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Vibrating velocity varied with temperature sweeps
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How does the turbulent transition occur ?
Turbulent transition

• Normal fluid flow should affect the superfluid
  flow.
• Turbulent transition requires
• T gt 1.05 K (rn gt 1 )
• Reynolds number (KC) gt 15
• wire velocity gt critical velocity of the
  superfluid turbulence

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How does the turbulent transition occur ?
Normal fluid component

• Normal fluid flow should affect the superfluid
  flow.
• Turbulent transition requires
• T gt 1.05 K (rn gt 1 )
• Reynolds number (KC) gt 15
• wire velocity gt critical velocity of the
  superfluid turbulence

Normal fluid eddies might induce superfluid
vortices.
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Summary future works

• We have successfully devised
• a vortex-free vibrating wire !!
• Transition to turbulence
• Turbulence due to remanent vortex lines
• Turbulence triggered by free vortex rings
• Turbulence triggered by temperature control
• Future works
• Critical velocity of a turbulent phase
• Superfluid turbulence in 3He-B