VORTEX RECONNECTIONS AND STRETCHING IN QUANTUM FLUIDS

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VORTEX RECONNECTIONSAND STRETCHING IN QUANTUM
FLUIDS
Carlo F. Barenghi
School of Mathematics, Newcastle
University, Newcastle upon Tyne, UK
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VORTICES IN QUANTUM FLUIDS
order parameter
density
velocity
quantisation of circulation
core radius a healing length ? h(mE0)-1/2
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QUANTUM TURBULENCE
isotropic vortex tangle
twisted vortex state
Hanninen, Eltsov, Krusius et al
CFB
Reconnections Postulated by Schwarz 1985 (vortex
filament model) Confirmed by Koplik Levine 1993
(NLSE model)
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Example Reconnection of vortex ring with vortex
line (NLSE)
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Example Reconnection of vortex ring with vortex
line (NLSE)
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SUPERFLUID vs EULER FLUID
Substitute
and
into NLSE
and get
classical Continuity and (quasi) Euler equations
where
and
? reconnections
At scale r, quantum stress/pressure h²/(mE0 r²)
1 for r? In 4He ?10-8 cm ltlt vortex
separation d10-3 or 10-4 cm
superfluid reconnecting Euler fluid
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Example of role played by reconnections rotating
counterflow in 4He
O0.01 s-1
O0.05 s-1
O0
Tsubota, Araki Barenghi, PRL 90, 205301, 2003
PRB 69, 134515, 2004
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Example of role played by reconnections rotating
counterflow in 4He
Tsubota, Araki Barenghi, PRL 90, 205301, 2003
PRB 69, 134515, 2004
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CLASSICAL TURBULENCE
Kolmogorov energy spectrum E(k)e2/3
k-5/3 wavenumber k1/r, energy dissipation rate
e
Maurer Tabeling, EPL 43, 29, 1998 Experiment
Araki, Tsubota Nemirowskii, PRL 89, 145301,
2002 Vortex filament model
Kobayashi Tsubota, PRL 94, 665302, 2005 NLSE
model
Nore, Abid Brachet, PRL 78, 3896, 1997 NLSE
model
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CLASSICAL TURBULENCE
Vortex stretching drives the energy cascade
Vorticity
Vorticity equation
Intensification of vorticity (angular velocity)
through conservation of angular momentum
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CLASSICAL TURBULENCE
Coherent structures
She, Jackson Orszag, Nature 344, 226,
1990 Vincent Meneguzzi JFM 225, 1, 1991 Farge
et, PRL 87, 054501, 2001
S. Goto, JFM 605, 355, 2008 Energy cascade can
be caused by stretching of smaller-scale vortices
in larger-scale strains existing between vortex
pairs
Problem there is no classical stretching for
quantised vortices
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CLASSICAL TURBULENCE
Coherent structures
She, Jackson Orszag, Nature 344, 226,
1990 Vincent Meneguzzi JFM 225, 1, 1991 Farge
et, PRL 87, 054501, 2001
S. Goto, JFM 605, 355, 2008 Energy cascade can
be caused by stretching of smaller-scale vortices
in larger-scale strains existing between vortex
pairs
Problem there is no classical stretching for
quantised vortices
Solution think of quantised vortex bundles
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Evidence for bundles ?
Kivotides, PRL 96 175301, 2006
Morris, Koplik Rouson, PRL 101, 015301, 2008
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Alamri, Youd Barenghi, 2008
NLSE model
Reconnection of vortex bundles
7 strands
Alamri Youd Barenghi, 2008
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Alamri, Youd Barenghi, 2008
NLSE model
Reconnection of vortex bundles
5 strands
Alamri Youd Barenghi, 2008
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Alamri, Youd Barenghi, 2008
NLSE model
Reconnection of vortex bundles
9 strands
Alamri Youd Barenghi, 2008
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vortex filament model
Alamri, Youd Barenghi, 2008
Reconnection of vortex bundles
Alamri Youd Barenghi, 2008
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vortex filament model
Alamri, Youd Barenghi, 2008
Reconnection of vortex bundles
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vortex filament model
Alamri, Youd Barenghi, 2008
Reconnection of vortex bundles
Length
Curvature
PDF of curvature
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Alamri, Youd Barenghi, 2008
NLSE model
Reconnection of vortex bundles
Note that length increases by 30 while energy
is conserved within 0.1
Length
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Conclusions
1. Concept of quantised vortex bundle strengthens
the analogy between quantum turbulence and
classical turbulence. 2. Quantised vortex
bundles are so robust that they can undergo
reconnections. 3. Large amount of coiling of
vortex strands confirms Kerr (Nonlinearity 9,
271, 1996) and the conjecture by Holm and Kerr
(PRL 88, 244501, 2002) on the generation of
helicity in nearly singular events of the
Euler equation.