We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnections are time symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium and discuss the different length scales probed by the two models and by experiments.

1.
S.
Kida
and
M.
Takaoka
, “
Vortex reconnection
,”
Annu. Rev. Fluid Mech.
26
,
169
(
1994
).
2.
P. E.
Dimotakis
, “
Turbulent mixing
,”
Annu. Rev. Fluid Mech.
37
,
329
(
2005
).
3.
A. K. M. F.
Hussain
, “
Coherent structures—reality and myth
,”
Phys. Fluids
26
,
2816
(
1983
).
4.
A. K. M. F.
Hussain
, “
Coherent structures and turbulence
,”
J. Fluid Mech.
173
,
303
(
1986
).
5.
D. R.
Poole
,
H.
Scoffield
,
C. F.
Barenghi
, and
D. C.
Samuels
, “
Geometry and topology of superfluid turbulence
,”
J. Low Temp. Phys.
132
,
97
(
2003
).
6.
R. J.
Donnelly
,
Quantized Vortices in Helium II
(
Cambridge University Press
,
Cambridge
,
1991
).
7.
M. S.
Paoletti
,
M. E.
Fisher
, and
D. P.
Lathrop
, “
Reconnection dynamics for quantized vortices
,”
Physica D
239
,
1367
(
2010
).
8.
L.
Skrebk
and
K. R.
Sreenivasan
, “
Developed quantum turbulence and its decay
,”
Phys. Fluids
24
,
011301
(
2012
).
9.
F.
Hussain
and
K.
Duraisamy
, “
Mechanics of viscous vortex reconnection
,”
Phys. Fluids
23
,
021701
(
2011
).
10.
S. C.
Crow
, “
Stability theory for a pair of trailing vortices
,”
AIAA J.
8
,
2172
(
1970
).
11.
T.
Fohl
and
J. S.
Turner
, “
Colliding vortex rings
,”
Phys. Fluids
18
,
433
(
1975
).
12.
Y.
Oshima
and
S.
Asaka
, “
Interaction of two vortex rings along parallel axes in air
,”
J. Phys. Soc. Jpn.
42
,
708
(
1977
).
13.
Y.
Oshima
and
N.
Izutsu
, “
Cross-linking of two vortex rings
,”
Phys. Fluids
31
,
2401
(
1988
).
14.
W. I.
Ashurst
and
D. I.
Meiron
, “
Numerical study of vortex reconnection
,”
Phys. Rev. Lett.
58
,
1632
(
1987
).
15.
P. G.
Saffman
,
Vortex Dynamics
(
Cambridge University Press
,
Cambridge
,
1992
).
16.
A.
Pumir
and
R. M.
Kerr
, “
Numerical simulation of interacting vortex tubes
,”
Phys. Rev. Lett.
58
,
1636
(
1987
).
17.
J.
Marshall
,
P.
Brancher
, and
A.
Giovannini
, “
Interaction of unequal anti-parallel vortex tubes
,”
J. Fluid Mech.
446
,
229
(
2001
).
18.
P.
Chatelain
,
D.
Kivotides
, and
A.
Leonard
, “
Reconnection of colliding vortex rings
,”
Phys. Rev. Lett.
90
,
054501
(
2003
).
19.
D.
Kivotides
and
A.
Leonard
, “
Computational model of vortex reconnection
,”
Europhys. Lett.
63
,
354
(
2003
).
20.
N. K.-R.
Kevlahan
, “
Stochastic differential equation models of vortex merging and reconnection
,”
Phys. Fluids
17
,
065107
(
2005
).
21.
B. K.
Shivamoggi
, “
Vortex stretching and reconnection in a compressible fluid
,”
Eur. Phys. J. B
49
,
483
(
2006
).
22.
R. P.
Feynman
, “
Application of quantum mechanics to liquid helium
,” in
Progress in Low Temperature Physics
, edited by
C. J.
Gorter
(
North-Holland
,
Amsterdam
,
1955
), Vol. 1.
23.
K. W.
Schwarz
, “
Three-dimensional vortex dynamics in superfluid 4He: Line-line and line-boundary interactions
,”
Phys. Rev. B
31
,
5782
(
1985
).
24.
K. W.
Schwarz
, “
Three-dimensional vortex dynamics in superfluid 4He: Homogeneous superfluid turbulence
,”
Phys. Rev. B
38
,
2398
(
1988
).
25.
R. L.
Ricca
, “
The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics
,”
Fluid. Dyn. Res.
18
,
245
(
1996
).
26.
J.
Koplik
and
H.
Levine
, “
Vortex reconnection in superfluid helium
,”
Phys. Rev. Lett.
71
,
1375
(
1993
).
27.
A. T. A. M.
de Waele
and
R. G. K. M.
Aarts
, “
Route to vortex reconnection
,”
Phys. Rev. Lett.
72
,
482
(
1994
).
28.
M.
Leadbeater
,
T.
Winiecki
,
D. C.
Samuels
,
C. F.
Barenghi
, and
C. S.
Adams
, “
Sound emission due to superfluid vortex reconnections
,”
Phys. Rev. Lett.
86
,
1410
(
2001
).
29.
W. F.
Vinen
, “
Decay of superfluid turbulence at very low temperature: The radiation of sound from a Kelvin wave on a quantized vortex
,”
Phys. Rev. B
64
,
134520
(
2001
).
30.
M.
Leadbeater
,
D. C.
Samuels
,
C. F.
Barenghi
, and
C. S.
Adams
, “
Decay of superfluid turbulence via Kelvin-wave radiation
,”
Phys. Rev. A
67
,
015601
(
2003
).
31.
W. F.
Vinen
and
J. J.
Niemela
, “
Quantum turbulence
,”
J. Low Temp. Phys.
128
,
167
(
2002
).
32.
R.
Tebbs
,
A. J.
Youd
, and
C. F.
Barenghi
, “
The approach to vortex reconnection
,”
J. Low Temp. Phys.
162
,
314
(
2011
).
33.
M.
Kursa
,
K.
Bajer
, and
T.
Lipniacki
, “
The approach to vortex reconnection
,”
Phys. Rev. B
83
,
014515
(
2011
).
34.
R. M.
Kerr
, “
Vortex stretching as a mechanism for quantum kinetic energy decay
,”
Phys. Rev. Lett.
106
,
224501
(
2011
).
35.
P. H.
Roberts
and
N. G.
Berloff
, “
The nonlinear Schrödinger equation as a model of superfluidity
,” in
Quantized Vortex Dynamics and Superfluid Turbulence
,
Lecture Notes in Physics
Vol. 571, edited by
C. F.
Barenghi
,
R. J.
Donnelly
, and
W. F.
Vinen
(
Springer-Verlag
,
2001
), pp.
235
257
.
36.
M.
Sadd
,
G. V.
Chester
, and
L.
Reatto
, “
Structure of a vortex in superfluid 4He
,”
Phys. Rev. Lett.
79
,
2490
(
1997
).
37.
G. W.
Reyfield
and
F.
Reif
, “
Quantized vortex rings in superfluid helium
,”
Phys. Rev.
136
,
A1194
(
1964
).
38.
C. F.
Barenghi
,
R. J.
Donnelly
, and
W. F.
Vinen
, “
Friction on quantized vortices in helium II. A review
,”
J. Low Temp. Phys.
52
,
189
(
1983
).
39.
N. G.
Berloff
, “
Padè approximations of solitary wave solutions of the Gross-Pitaevskii equation
,”
J. Phys. A
37
,
1617
(
2004
).
40.
A. W.
Baggaley
,
L. K.
Sherwin
,
C. F.
Barenghi
, and
Y. A.
Sergeev
, “
Thermally and mechanically driven quantum turbulence in helium II
,”
Phys. Rev. B
86
,
104501
(
2012
).
41.
A. W.
Baggaley
and
C. F.
Barenghi
, “
Spectrum of turbulent Kelvin-waves cascade in superfluid helium
,”
Phys. Rev. B
83
,
134509
(
2011
).
42.
A. W.
Baggaley
and
C. F.
Barenghi
, “
Vortex-density fluctuations in quantum turbulence
,”
Phys. Rev. B
84
,
020504
R
(
2011
).
43.
A. W.
Baggaley
, “
The sensitivity of the vortex filament method to different reconnection models
,”
J. Low Temp. Phys.
168
,
18
(
2012
).
44.
A. W.
Baggaley
,
C. F.
Barenghi
,
A.
Shukurov
, and
Y. A.
Sergeev
, “
Coherent vortex structures in quantum turbulence
,”
Europhys. Lett.
98
,
26002
(
2012
).
45.
A. W.
Baggaley
and
C. F.
Barenghi
, “
Tree method for quantum vortex dynamics
,”
J. Low Temp. Phys.
166
,
3
(
2012
).
46.
M.
Tsubota
and
H.
Adachi
, “
Simulation of counterflow turbulence by vortex filament
,”
J. Low Temp. Phys.
162
,
367
(
2011
).
47.
W.
Bao
,
D.
Jaksch
, and
P.
Markowich
, “
Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation
,”
J. Comp. Phys.
187
,
318
(
2003
).
48.
M.
Thalhammer
,
M.
Caliari
, and
C.
Neuhauser
, “
High-order time-splitting Hermite and Fourier spectral methods for the Gross–Pitaevskii equation
,”
J. Comp. Phys.
228
,
822
(
2009
).
49.
H.
Yoshida
, “
Construction of higher order symplectic integrators
,”
Phys. Lett. A
150
,
262
(
1990
).
50.
G.
Strang
, “
On the construction and comparison of difference schemes
,”
SIAM J. Numer. Anal.
5
,
506
(
1968
).
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