vortex instability and the onset of superfluid turbulence
DESCRIPTION
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: - PowerPoint PPT PresentationTRANSCRIPT
Vortex instability and the onset of superfluid turbulenceN.B. Kopnin
Low Temperature Lab., HUT, Finland,L.D. Landau Institute for Theoretical Physics, Moscow.
Collaboration
Experiment: M. Krusius, V. Eltsov, A. Finne, HUTL. Skrbek, Charles University, Prague
Theory:T. Araki, M. Tsubota, Osaka University G. Volovik, HUT
Contents
New class of superfluid turbulence.
Experiment in superfluid He 3 B: Onset independent of the Reynolds number
(Res 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
Superfluid turbulence. Results.[ Finne et al., Nature 424, 1022 (2002)]
Forces on vortices
• Magnus force
• Force from the normal component
Mutual friction parameters d, d’
Force balance
couples the velocities:
Hall and Vinen mutual friction parameters
Mutual friction force on the superfluid
Mutual friction parameters in He-3 B.
Microscopic theory [Rep. Prog. Phys (2002)]
Mutual friction parameters
Distance between the CdGM states
Effective relaxation time
Mutual friction parameters in He-3 B.
Experiment [Hook, Hall, et al. (1997)]
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
Numerical results: High temperatures, high friction
Parameters• Rotation velocity rad/s
• Superfluid “Reynolds number”
• Temperature and the MF ratio
Numerical results: Low temperatures, low friction
Rotation velocity and the Reynolds number
Temperature and the MF ratio
Evolution time
Enormous multiplication of vortices !
Numerical simulations of vortex evolution in a rotating container
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
linesCompetition between vortex
multiplication and their extraction into the bulk
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
Total vortex evolution
MF parameters
Superflow velocity
The counterflow velocityThe self-induced velocity
Finally,
Similarly to the Vinen equation (1957)
Another approach: Vorticity equationNavier—Stokes equation
Vorticity equation
In superfluids: mutual friction force instead of viscosity
Superfluid vorticity equation
Averaged over random vortex loops assuming
Vortex instabilityEvolution equation
Two regimes of evolution:
Low temperatures,
Solution saturates at
Instability towards turbulent vortex tangle
Higher temperatures,
No multiplication of vortices
Summary:Superfluid turbulence in other
systems He-3 A: High vortex friction; q>>1 except for very low
temperatures T<<Tc .
No turbulence. Superconductors: High vortex friction; q>>1 except for
very clean materials, l>>(EF /Tc) , and low temperatures.
No turbulence. Superfluid He II: Low vortex friction: q<<1 except for
temperatures very close to T .
Unstable towards turbulence.