1. University of Newcastle, UK Collisions of superfluid vortex rings Carlo F. Barenghi Nick Proukakis David Samuels Christos Vassilicos Charles Adams Demos Kivotides Mark Leadbeater Nick Parker

2. VORTEX RING AS TOY MODEL of more complicated vortex structures in superfluid turbulence

3. Liquid helium is the intimate mixture of two fluid components: -the normal fluid (thermal excitations) -the superfluid (quantum ground state) The normal fluid (hence viscous effects) is negligible at low temperatures (say T<1 K in 4 He)

4. -superfluid turbulence created in 4 He at T =0.01 Tc (where Tc=2.17K is the critical temperature) by a moving grid quickly decays (Davis et al, Physica B 280, 43, 2000). -superfluid turbulence created in 3 He-B at T=0.1 Tc (where Tc≈1mK) by a vibrating wire diffuses away in space (Fisher et al, Phys. Rev. Lett. 86, 244, 2001). Despite the absence of viscous dissipation, experiments at low T show that: Why ? What is the ultimate mechanism to destroy kinetic energy near T=0 ? What is the energy sink ?

5. The ultimate sink of kinetic energy is sound Early simulations of vortex tangle using the GP model showed that the level of acoustic energy increased as the kinetic energy decreased (Nore, Abid & Brachet, Phys. Rev. Lett. 78, 3896, 1997) Possibility of detecting large temperature increase due to kinetic energy of vortices transformed into phonons (Samuels and Barenghi, Phys. Rev. Lett. 81, 4381, 1998) Aim of this talk: Numerical studies of collisions of vortex rings highlight the role played by vortex reconnections in the transformation of kinetic energy into sound energy (Vinen & Niemela, JLTP 128, 167, 2002)

6. 1 st model: Vortex dynamics Velocity at point S(ξ,t): Vortex reconnections are performed “ad hoc” when two vortex lines are sufficiently close to each other

7. Let where 2 nd model: Gross-Pitaevskii equation where and get

8. Kelvin wave Helical displacement of the vortex core wave number k=2π/λ angular frequency ω~ k² Sound power radiated by Kelvin wave ~ ω 3 ~ k 6 How to generate high k ?

9. Kelvin waves cascade reconnections cusps high k sound Kivotides, Vassilicos, Samuels & Barenghi, Phys. Rev. Lett. 86, 3080 (2001) Vinen, Tsubota & Mitani, Phys. Rev. Lett. 91, 135301 (2003) Kozik & Svistunov, Phys. Rev. Lett. 92, 035301 (2004)

10. Leadbeater, Winiecki, Samuels, Barenghi & Adams, Phys. Rev. Lett. 86, 1410 (2001) Direct sound burst at vortex reconnection Rarefaction pulse moves away from reconnection point R=radius D=impact parameter

11. Vortex line length destroyed (in units of healing length) as a function of the reconnection angle θ

12. In general, sound is created by both reconnection bursts and Kelvin waves

13. Kinetic energy loss Leadbeater, Samuels, Barenghi &Adams, Phys. Rev. A 67, 015601 (2003)

14. Three-vortex interaction Sound burst produced by close approach of a vortex-antivortex pair with a third vortex Parker, Proukakis, Barenghi and Adams, JLTP 2005

15. Left: acceleration experienced by a vortex of the pair as a function of the impact parameter d for d=0 (solid line),1,2,4 Right: final radius of the pair as fraction of the initial radius as a function of d. The energy loss is apparent as reduction in size of the pair

16. S.N. Fisher, A.J.Hale, A.M.Guénault, and G.R.Pickett, PRL 86, 244, 2001 Superfluid turbulence created at low T in 3He-B by a vibrating wire diffuses away in space.

17. Barenghi & Samuels, Phys. Rev. Lett. 89, 155302 (2002) (a) 0.06 cm(b) 0.06 cm (c) 0.20 cm(d) 0.40 cm “Evaporation” of a packet of vortex loops

18. 2-dim example

19. Conclusion Sound is the sink of kinetic energy in a pure superfluid near absolute zero Vortex reconnections trigger: 1) direct sound bursts at each reconnection event, 2) Kelvin wave cascade to wavenumbers large enough for sound radiation Reconections are responsible for “diffusion” of inhomogeneous quantised vorticity (evaporation of small loops)