VORTEX RECONNECTIONS AND STRETCHING IN QUANTUM FLUIDS Carlo F. Barenghi School of Mathematics,...
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Transcript of VORTEX RECONNECTIONS AND STRETCHING IN QUANTUM FLUIDS Carlo F. Barenghi School of Mathematics,...
VORTEX RECONNECTIONSAND STRETCHING
IN QUANTUM FLUIDS
Carlo F. Barenghi
School of Mathematics, Newcastle University,
Newcastle upon Tyne,
UK
VORTICES IN QUANTUM FLUIDS
density velocity
order parameter
quantisation of circulation
core radius a~ healing length ξ = ħ(mE0)-1/2
QUANTUM TURBULENCE
Reconnections Postulated by Schwarz 1985 (vortex filament model)Confirmed by Koplik & Levine 1993 (NLSE model)
CFB Hanninen, Eltsov, Krusius et al
isotropic vortex tangle twisted vortex state
Example:Reconnection of vortex ring with vortex line
(NLSE)
Example:Reconnection of vortex ring with vortex line
(NLSE)
Substitute
classical Continuity and (quasi) Euler equations:
where
At scale r, quantum stress/pressure ~ ħ²/(mE0 r²) ~1 for r~ξIn 4He: ξ≈10-8 cm << vortex separation δ≈10-3 or 10-4 cm
and
into NLSE and get
and → reconnections
SUPERFLUID vs EULER FLUID
superfluid = reconnecting Euler fluid
Example of role played by reconnections:rotating counterflow in 4He
Tsubota, Araki & Barenghi, PRL 90, 205301, 2003; PRB 69, 134515, 2004
Ω=0
Ω=0.05 s-1
Ω=0.01 s-1
Tsubota, Araki & Barenghi, PRL 90, 205301, 2003; PRB 69, 134515, 2004
Example of role played by reconnections:rotating counterflow in 4He
Maurer & Tabeling, EPL 43, 29, 1998
Experiment
Araki, Tsubota & Nemirowskii,PRL 89, 145301, 2002Vortex filament model
Kobayashi & Tsubota,PRL 94, 665302, 2005
NLSE model
CLASSICAL TURBULENCE
Nore, Abid & Brachet,PRL 78, 3896, 1997
NLSE model
Kolmogorov energy spectrumE(k)≈ε2/3 k-5/3
wavenumber k~1/r, energy dissipation rate ε
CLASSICAL TURBULENCEVortex stretching drives the energy cascade
Intensification of vorticity (angular velocity) through conservation
of angular momentum
Vorticity Vorticity equation
Coherent structures
S. Goto, JFM 605, 355, 2008: Energy cascade can be caused by stretching of smaller-scalevortices in larger-scale strainsexisting between vortex pairs
CLASSICAL TURBULENCE
She, Jackson & Orszag, Nature 344, 226, 1990Vincent & Meneguzzi JFM 225, 1, 1991
Farge & et, PRL 87, 054501, 2001
Problem: there is no classical stretching for quantised vortices
Coherent structures
S. Goto, JFM 605, 355, 2008: Energy cascade can be caused by stretching of smaller-scalevortices in larger-scale strainsexisting between vortex pairs
CLASSICAL TURBULENCE
She, Jackson & Orszag, Nature 344, 226, 1990Vincent & Meneguzzi JFM 225, 1, 1991
Farge & et, PRL 87, 054501, 2001
Problem: there is no classical stretching for quantised vortices
Solution: think of quantised vortex bundles
Evidence for bundles ?
Kivotides, PRL 96 175301, 2006 Morris, Koplik & Rouson, PRL 101, 015301, 2008
Alamri Youd & Barenghi, 2008
Reconnection of vortex bundlesAlamri, Youd & Barenghi,
2008
NLSEmodel
7 strands
Alamri Youd & Barenghi, 2008
Reconnection of vortex bundlesAlamri, Youd & Barenghi,
2008
NLSEmodel
5 strands
Alamri Youd & Barenghi, 2008
Reconnection of vortex bundlesAlamri, Youd & Barenghi,
2008
NLSEmodel
9 strands
Alamri Youd & Barenghi, 2008
Reconnection of vortex bundlesAlamri, Youd & Barenghi,
2008
vortexfilamentmodel
Reconnection of vortex bundlesAlamri, Youd & Barenghi,
2008
vortexfilamentmodel
Alamri, Youd & Barenghi,
2008
vortexfilamentmodel
Reconnection of vortex bundles
Length Curvature PDF of curvature
NLSEmodelReconnection of vortex bundles
Length
Alamri, Youd & Barenghi,
2008
Note that length increases by 30 % while energy is conserved within 0.1 %
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.