University of Newcastle, UK

Collisions of superfluid vortex rings

Carlo F. Barenghi

Nick ProukakisDavid SamuelsChristos Vassilicos

Charles AdamsDemos KivotidesMark LeadbeaterNick Parker

VORTEX RING AS TOY MODEL of more complicated vortex structures in

superfluid turbulence

Liquid helium is the intimate mixture of two fluid components:-the normal fluid (thermal excitations)-the superfluid (quantum ground state)

The normal fluid (hence viscouseffects) is negligible at low temperatures (say T<1 K in 4He)

-superfluid turbulence created in 4He 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 3He-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 ?

The ultimate sink of kinetic energy is sound

Early simulations of vortex tangle using the GP modelshowed 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 reconnectionsin the transformation of kinetic energy into sound energy

(Vinen & Niemela, JLTP 128, 167, 2002)

1st model: Vortex dynamics

3][

)(

4),(

RZ

ZdRZtRS

dt

d

Velocity at point S(ξ,t):

Vortex reconnections are performed “ad hoc” when two vortex lines are sufficiently close to each other

2mAs

EV

mti

2

02

2||

2

Let iSAe Sm

vs

0)(

sss vt

k

jk

jk

sjsk

sjs xx

p

x

vv

t

v

)(

kj

ssjk

s

xxmm

Vp

ln

4,

2

2

2

2

2

20 where

2nd model: Gross-Pitaevskii equation

where

and get

Kelvin waveHelical displacement

of the vortex core

wave number k=2π/λ angular frequency ω~ k²

Sound power radiated by Kelvin wave ~ ω3 ~k6

How to generate high k ?

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)

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=radiusD=impact parameter

Vortex line length destroyed(in units of healing length)

as a function of the reconnection angle θ

In general, sound is createdby both reconnection

bursts and Kelvin waves

Kinetic energy loss

Leadbeater, Samuels, Barenghi &Adams,Phys. Rev. A 67, 015601 (2003)

Three-vortex interaction

Sound burst produced by close approach ofa vortex-antivortex pair with a third vortex

Parker, Proukakis, Barenghi and Adams, JLTP 2005

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

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.

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

2-dim example

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)