VORTEX RECONNECTIONS AND STRETCHING IN QUANTUM FLUIDS Carlo

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VORTEX RECONNECTIONS AND STRETCHING IN QUANTUM FLUIDS Carlo F. Barenghi School of Mathematics, Newcastle

VORTEX RECONNECTIONS AND STRETCHING IN QUANTUM FLUIDS Carlo F. Barenghi School of Mathematics, Newcastle University, Newcastle upon Tyne, UK

VORTICES IN QUANTUM FLUIDS order parameter density velocity quantisation of circulation core radius a~

VORTICES IN QUANTUM FLUIDS order parameter density velocity quantisation of circulation core radius a~ healing length ξ = ħ(m. E 0)-1/2

QUANTUM TURBULENCE isotropic vortex tangle CFB twisted vortex state Hanninen, Eltsov, Krusius et al

QUANTUM TURBULENCE isotropic vortex tangle CFB twisted vortex state Hanninen, Eltsov, Krusius et al Reconnections Postulated by Schwarz 1985 (vortex filament model) Confirmed by Koplik & Levine 1993 (NLSE model)

Example: Reconnection of vortex ring with vortex line (NLSE)

Example: Reconnection of vortex ring with vortex line (NLSE)

Example: Reconnection of vortex ring with vortex line (NLSE)

Example: Reconnection of vortex ring with vortex line (NLSE)

SUPERFLUID vs EULER FLUID Substitute and into NLSE and get classical Continuity and (quasi)

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 ~ ħ²/(m. E 0 r²) ~1 for r~ξ In 4 He: ξ≈10 -8 cm << vortex separation δ≈10 -3 or 10 -4 cm superfluid = reconnecting Euler fluid

Example of role played by reconnections: rotating counterflow in 4 He Ω=0. 01 s-1

Example of role played by reconnections: rotating counterflow in 4 He Ω=0. 01 s-1 Ω=0. 05 s-1 Ω=0 Tsubota, Araki & Barenghi, PRL 90, 205301, 2003; PRB 69, 134515, 2004

Example of role played by reconnections: rotating counterflow in 4 He Tsubota, Araki &

Example of role played by reconnections: rotating counterflow in 4 He Tsubota, Araki & Barenghi, PRL 90, 205301, 2003; PRB 69, 134515, 2004

CLASSICAL TURBULENCE Kolmogorov energy spectrum E(k)≈ε 2/3 k-5/3 wavenumber k~1/r, energy dissipation rate ε

CLASSICAL TURBULENCE Kolmogorov energy spectrum E(k)≈ε 2/3 k-5/3 wavenumber k~1/r, energy dissipation rate ε Maurer & Tabeling, EPL 43, 29, 1998 Experiment Nore, Abid & Brachet, PRL 78, 3896, 1997 NLSE model Araki, Tsubota & Nemirowskii, PRL 89, 145301, 2002 Vortex filament model Kobayashi & Tsubota, PRL 94, 665302, 2005 NLSE model

CLASSICAL TURBULENCE Vortex stretching drives the energy cascade Vorticity equation Intensification of vorticity (angular

CLASSICAL TURBULENCE Vortex stretching drives the energy cascade Vorticity equation Intensification of vorticity (angular velocity) through conservation of angular momentum

CLASSICAL TURBULENCE Coherent structures She, Jackson & Orszag, Nature 344, 226, 1990 Vincent &

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

CLASSICAL TURBULENCE Coherent structures She, Jackson & Orszag, Nature 344, 226, 1990 Vincent &

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

Evidence for bundles ? Kivotides, PRL 96 175301, 2006 Morris, Koplik & Rouson, PRL

Evidence for bundles ? Kivotides, PRL 96 175301, 2006 Morris, Koplik & Rouson, PRL 101, 015301, 2008

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles 7 strands Alamri Youd &

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles 7 strands Alamri Youd & Barenghi, 2008 NLSE model

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles 5 strands Alamri Youd &

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles 5 strands Alamri Youd & Barenghi, 2008 NLSE model

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles 9 strands Alamri Youd &

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles 9 strands Alamri Youd & Barenghi, 2008 NLSE model

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles Alamri Youd & Barenghi, 2008

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles Alamri Youd & Barenghi, 2008 vortex filament model

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles vortex filament model

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles vortex filament model

Alamri, Youd & Barenghi, 2008 Length Reconnection of vortex bundles Curvature vortex filament model

Alamri, Youd & Barenghi, 2008 Length Reconnection of vortex bundles Curvature vortex filament model PDF of curvature

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles NLSE model Note that length

Alamri, Youd & Barenghi, 2008 Reconnection of vortex bundles NLSE model Note that length increases by 30 % while energy is conserved within 0. 1 % Length

Conclusions 1. Concept of quantised vortex bundle strengthens the analogy between quantum turbulence and

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.