Transition to Turbulence in Alternating Boundary Flow of Superfluid 4 He

1. 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 University Hideo 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

2. 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).

3. 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 !!

4. Sample cell Lead Lines Thermal Link 4 Stycast1266 He Filling Line Heat Exchanger B 1.6mm A 30mK 1.8mm 1.0mm 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

5. 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).

6. 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

7. 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).

8. 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)

9. 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

10. 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

11. 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.

12. 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

13. 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)

14. v : Self-induced velocity r0：Ring radius κ：Quantum of circulation ξ：Core radius r0 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

15. 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

16. 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

17. Transition to superfluid turbulence triggered by temperature sweep Vibrating velocity varied with temperature sweeps

18. How does the turbulent transition occur ? 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

19. Flow patterns behind a cylinder • in a classical fluid How does the turbulent transition occur ? 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.

20. 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