VORTEX RECONNECTIONS AND STRETCHING IN QUANTUM FLUIDS

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

2. VORTICES IN QUANTUM FLUIDS order parameter density velocity quantisation of circulation core radius a~ healing length ξ = ħ(mE0)-1/2

3. 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)

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

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

6. 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/(mE0 r²) ~1 for r~ξ In 4He: ξ≈10-8 cm << vortex separation δ≈10-3 or 10-4 cm superfluid = reconnecting Euler fluid

7. Example of role played by reconnections: rotating counterflow in 4He Ω=0.01 s-1 Ω=0.05 s-1 Ω=0 Tsubota, Araki & Barenghi, PRL 90, 205301, 2003; PRB 69, 134515, 2004

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

9. CLASSICAL TURBULENCE Kolmogorov energy spectrum E(k)≈ε2/3 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

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

11. 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

12. 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

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

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

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

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

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

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

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

20. Alamri, Youd & Barenghi, 2008 NLSE model Reconnection of vortex bundles Note that length increases by 30 % while energy is conserved within 0.1 % Length

21. 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.