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Transition to Turbulence in Alternating Boundary Flow of Superfluid 4 He

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LOW TEMPERATURES 2008, 28 Mar 2008

Transition to Turbulence in Alternating Boundary Flow of Superfluid 4He

- 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

Osaka City UniversityHideo Yano

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

200 μm

Oscillating obstacles can easily generate turbulence in superfluid 4He.

Microsphere

Grid

Wire

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. B75, 012502 (2007).

J. Jager, B. Shuderer, W. Schoepe, Phys. Rev. Lett.74, 566 (1995).

F

vibrating wire

B

F : Lorentz force

B : magnetic field

I : electric current

I

Generation of turbulence by a vibrating wire

Response of a vibrating wire

turbulence

HY, N. Hashimoto, et al, Phys. Rev. B75, 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 of60 m/s.

Remanent vortices should cause the generation of turbulence !!

Sample cell

Lead Lines

Thermal Link

4

Stycast1266

He Filling Line

Heat Exchanger

B

1.6mm

A

30mK

1.8mm

1.0mm

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

Vortex-free vibrating wire

Response of a vibrating wire

No transition to turbulence even above 1 m/s !

Effectively free of remanent vortices

See alsoN. Hashimoto, R. Goto, HY, et al, Phys. Rev. B76, 020504 (2007).

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

f : resonance frequency

k : spring constant

m : effective mass

Bridged vortex lines

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. B76, 020504 (2007).

Initial

condition

sphere

vortex lines

oscillating

superfluid

flow

Turbulence due to oscillation of a bridged vortex

Time evolution of turbulencesimulated 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)

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

1.4 m/s

Experimental setup

after 48 hours filling of superfluid 4He

vibrating wireA

vibrating wireB

Detector

Generator of turbulence

Generator of vortex rings

Generation of turbulence

No turbulent transition

B

vortex-free wire

remanent vortices attaching to a wire

A

OFF

Laminar

Transition to turbulence triggered by vortex rings

Free vortex ring from Generator

Detector

In turbulent flow

In turbulent flow

Detector @30mK

generator

OFF

Turbulence

OFF

detector

Laminar

Turbulence

The Detector keep the generation of turbulence without free vortex rings coming from the Generator.

Transition to turbulence triggered by vortex rings

Detector @30mK

Vortex rings trigger

the transition to turbulence.

generator OFF

generator

generator ON

detector

generator OFF

generator OFF

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)

v : Self-induced velocity

r0：Ring radius

κ：Quantum of circulation

ξ：Core radius

r0

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

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

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 (< Tl=2.17 K)
- Control of a normal fluid component
- Using a vortex-free vibrating wire

Transition to superfluid turbulence triggered by temperature sweep

Turbulent transition

- Normal fluid flow should affect the superfluid flow.
- Turbulent transition requires:
- T > 1.05 K (rn > 1 %)
- Reynolds number (~KC) > 15
- wire velocity > critical velocity of the superfluid turbulence

- Flow patterns behind a cylinder
- in a classical fluid

Normal fluid component

- Normal fluid flow should affect the superfluid flow.
- Turbulent transition requires:
- T > 1.05 K (rn > 1 %)
- Reynolds number (~KC) > 15
- wire velocity > critical velocity of the superfluid turbulence

Normal fluid eddies might induce superfluid vortices.

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