University of Newcastle, UK Collisions of superfluid vortex rings Carlo F. Barenghi Nick Proukakis...
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Transcript of University of Newcastle, UK Collisions of superfluid vortex rings Carlo F. Barenghi Nick Proukakis...
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)