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Vortex instability and the onset of superfluid turbulence N.B. Kopnin Low Temperature Lab., HUT, Finland, L.D. Landau Institute for Theoretical Physics,

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Presentation on theme: "Vortex instability and the onset of superfluid turbulence N.B. Kopnin Low Temperature Lab., HUT, Finland, L.D. Landau Institute for Theoretical Physics,"— Presentation transcript:

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2 Vortex instability and the onset of superfluid turbulence N.B. Kopnin Low Temperature Lab., HUT, Finland, L.D. Landau Institute for Theoretical Physics, Moscow. Collaboration Experiment: M. Krusius, V. Eltsov, A. Finne, HUT L. Skrbek, Charles University, Prague Theory: T. Araki, M. Tsubota, Osaka University G. Volovik, HUT

3 Contents  New class of superfluid turbulence. Experiment in superfluid He 3 B: Onset independent of the Reynolds number (Re s is the ratio of superflow and the Feynman critical velocity)  Theoretical model for vortex instability Results of numerical simulations Mutual-friction controlled onset of turbulence Normal fluid Superfluid

4 Superfluid turbulence. Results. [ Finne et al., Nature 424, 1022 (2002)]

5 Forces on vortices Magnus force Force from the normal component Mutual friction parameters d, d ’

6 Force balance couples the velocities: Hall and Vinen mutual friction parameters Mutual friction force on the superfluid

7 Mutual friction parameters in He-3 B. Microscopic theory [Rep. Prog. Phys (2002)] Mutual friction parameters Distance between the CdGM states Effective relaxation time

8 Mutual friction parameters in He-3 B. Experiment [Hook, Hall, et al. (1997)]

9 Numerical simulations  Vortex evolution is integrated from [Schwartz 1988]  The local superflow: all the Biot—Savart contributions  Boundary conditions: Image vortices  Vortex interconnections for crossing vortices

10 Numerical results: High temperatures, high friction Parameters Rotation velocity  rad/s Superfluid “Reynolds number” Temperature and the MF ratio

11 Numerical results: Low temperatures, low friction  Rotation velocity and the Reynolds number  Temperature and the MF ratio  Evolution time Enormous multiplication of vortices !

12 Numerical simulations of vortex evolution in a rotating container

13 Model for the onset of turbulence Distinguish two regions  Multiplication region: high flow velocity, high density of entangled vortex loops, vortex crossings and interconnections  Rest of the liquid (bulk): low flow velocity, polarized vortex lines  Competition between vortex multiplication and their extraction into the bulk

14 Multiplication region Loop size l 3D vortex density n~l  2D (vortex line) density L=nl=l   Multiplication due to collisions and reconnections  Extraction due to inflation

15 Total vortex evolution MF parameters Superflow velocity The counterflow velocity The self-induced velocity Finally, Similarly to the Vinen equation (1957)

16 Another approach: Vorticity equation Navier—Stokes equation Vorticity equation In superfluids: mutual friction force instead of viscosity Superfluid vorticity equation Averaged over random vortex loops assuming

17 Vortex instability Evolution equation Two regimes of evolution:  Low temperatures, Solution saturates at  Instability towards turbulent vortex tangle  Higher temperatures,  No multiplication of vortices

18 Summary: Superfluid turbulence in other systems  He-3 A: High vortex friction; q>>1 except for very low temperatures T<>1 except for very clean materials, l>>(E F /T c ) , and low temperatures. No turbulence.  Superfluid He II: Low vortex friction: q<<1 except for temperatures very close to T. Unstable towards turbulence.


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