The effects of turbulence on magnetic reconnection are investigated by two‐dimensional spectral method magnetohydrodynamic computations. The nonlinear evolution of the periodic sheet pinch configuration is studied as an initial value problem. Turbulence is initiated by including a low level of broadband fluctuations in the initial data. Nonlinear features of the evolution, appropriately described as turbulence, are seen early in the solutions and persist throughout the runs. Small‐scale, unsteady coherent electric current and vorticity structures develop in the reconnection zone, resulting in enhanced viscous and resistive dissipation. Unsteady and often spatially asymmetric fluid flow develops. Large‐scale magnetic islands produced by reconnection activity, undergo internal pulsations. Small‐scale magnetic islands, or ‘‘bubbles’’ develop near the reconnection zone, prodcing multiple X points. Large‐amplitude electric field fluctuations, often several times larger than the reconnection electric field, are produced by large island pulsations and by motion of magnetic bubbles. Spectral analysis of the fluctuations show development of broad band excitations, reminiscent of inertial and dissipation range spectra in homogeneous turbulence. Two‐dimensional spectra indicate that the turbulence is broadband in both spatial directions. It is suggested that the turbulence that develops from the randomly perturbed sheet pinchbears a strong resemblence to homogeneous magnetohydrodynamic turbulence, and that analytical theories of reconnection must incorporate these effects.

1.
R.
Giovanelli
,
Mon. Not. R. Astron. Soc.
107
,
338
(
1947
).
2.
J.
Dungey
,
Philos. Mag., Ser.
7
44
,
725
(
1953
).
3.
P. Sweet, in Electromagnetic Phenomena in Cosmical Plasmas, edited by B. Lehnert (Cambridge U.P., London, 1958), p. 123.
4.
E.
Parker
,
J. Geophys. Res.
62
,
509
(
1957
).
5.
E.
Parker
,
Astrophys. J. Suppl. Ser.
8
,
177
(
1963
).
6.
J.
Dungey
,
Phys. Rev. Lett.
6
,
47
(
1961
).
7.
B.
Kadomtsev
,
Sov. J. Plasma Phys.
1
,
389
(
1975
).
8.
W. H.
Matthaeus
and
D. C.
Montgomery
,
Proc. N. Y. Acad. Sci.
357
,
203
(
1980
).
9.
V.
Vasyliunas
,
Rev. Geophys. Space Phys.
13
,
303
(
1975
).
10.
B. Sonnerup, in Solar Terrestrial Physics—Present and Future, edited by D. Butler and K. Papadopoulos (NASA, Washington, DC, 1984), pp. 1.3‐1.7.
11.
J. Dungey, Cosmic Electrodynamics (Cambridge U.P., Cambridge, 1958), pp. 98–102.
12.
H. Petschek, in AAS‐NASA Symposium on the Physics of Solar Flares, NASA SP‐50, p. 425 (1964).
13.
E. Parker, Cosmical Magnetic Fields (Clarendon, Oxford, 1979).
14.
H.
Furth
,
J.
Killeen
, and
M.
Rosenbluth
,
Phys. Fluids
6
,
459
(
1963
).
15.
B.
Sonnerup
,
J. Plasma Phys.
4
,
161
(
1970
).
16.
B.
Sonnerup
and
E.
Priest
,
J. Plasma Phys.
14
,
283
(
1975
).
17.
T.
Yeh
and
I.
Axford
,
J. Plasma Phys.
4
,
207
(
1970
).
18.
E.
Parker
,
J. Plasma Phys.
9
,
49
(
1973
).
19.
W. H.
Matthaeus
and
D. C.
Montgomery
,
J. Plasma Phys.
25
,
11
(
1981
).
20.
S. Kahler, in Solar Terrestrial Physics—Present and Future, edited by D. Butler and K. Papadopoulos (NASA, Washington, DC, 1984), pp. 1.31— 1.35.
21.
H.
Furth
,
Phys. Fluids.
28
,
1595
(
1985
).
22.
P.
Baum
and
A.
Bratenahl
,
J. Plasma Phys.
18
,
257
(
1977
).
23.
R.
Stenzel
and
W.
Gekelman
,
J. Geophys. Res.
86
,
649
(
1981
).
24.
R.
Stenzel
,
W.
Gekelman
, and
N.
Wild
,
J. Geophys. Res.
88
,
4793
(
1983
).
25.
C.
Russell
and
R.
McPherron
,
Space Sci. Rev.
15
,
205
(
1973
).
26.
E.
Hones
,
J. Geophys. Res.
82
,
5633
(
1977
).
27.
E.
Hones
,
J.
Birn
,
S.
Bame
,
G.
Paschmann
, and
C.
Russell
,
Geophys. Res. Lett.
9
,
203
(
1982
).
28.
J.
Bieber
,
E.
Stone
,
E.
Hones
,
D.
Baker
,
S.
Bame
, and
R.
Lepping
,
J. Geophys. Res.
89
,
6705
(
1984
).
29.
J.
Bercham
and
C.
Russell
,
J. Geophys. Res.
89
,
6689
(
1984
).
30.
B.
Sonnerup
,
G.
Paschmann
,
I.
Papapmastorakis
,
N.
Sckopke
,
G.
Haerendel
,
S.
Bame
,
J.
Ashbridge
,
J.
Gosling
, and
C.
Russell
,
J. Geophys. Res.
86
,
10049
(
1981
).
31.
R.
White
,
D.
Monticello
,
M.
Rosenbluth
, and
B.
Waddell
,
Phys. Fluids
20
,
800
(
1977
).
32.
D.
Schnack
and
J.
Killeen
,
J. Comp. Phys.
35
,
110
(
1980
).
33.
B.
Waddell
,
M.
Rosenbluth
,
D.
Monticello
, and
R.
White
,
Nucl. Fusion
16
,
528
(
1976
).
34.
W. Park, in Solar Terrestrial Physics‐Present and Future, edited by D. Butler and K. Papadopoulos (NASA, Washinton, DC, 1984), pp. 1.52‐1.60.
35.
D.
Biskamp
,
Z. Naturforsch.
37
,
840
(
1982
).
36.
R.
Steinolfson
and
G.
Van Hoven
,
Phys. Fluids
27
,
1207
(
1984
).
37.
T.
Sato
and
T.
Hayashi
,
Phys. Fluids
22
,
1189
(
1979
).
38.
J.
Finn
and
P.
Kaw
,
Phys. Fluids
20
,
72
(
1977
).
39.
P.
Pritchett
and
C.
Wu
,
Phys. Fluids
22
,
2140
(
1979
).
40.
D.
Biskamp
and
H.
Welter
,
Phys. Rev. Lett.
44
,
1069
(
1980
).
41.
J.
Birn
,
J. Geophys. Res.
85
,
1214
(
1980
).
42.
J.
Birn
and
E.
Hones
,
J. Geophys. Res.
86
,
6802
(
1981
).
43.
D. Biskamp and H. Welter, in Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1982), Vol. 3, pp. 373–382.
44.
T.
Forbes
and
E.
Priest
,
Solar Phys.
84
,
169
(
1983
).
45.
R.
Dahlburg
,
T.
Zang
, and
D.
Montgomery
,
J. Fluid Mech.
169
,
71
(
1986
).
46.
D.
Fyfe
and
D.
Montgomery
,
J. Plasma Phys.
16
,
181
(
1976
).
47.
D.
Fyfe
,
G.
Joyce
, and
D.
Montgomery
,
J. Plasma Phys.
17
,
317
(
1977
).
48.
D.
Fyfe
,
D.
Montgomery
, and
G.
Joyce
,
J. Plasma Phys.
17
,
369
(
1977
).
49.
R.
Kraichnan
and
D.
Montgomery
,
Rep. Prog. Phys.
43
,
547
(
1980
).
50.
G. K. Batchelor, Theory of Homogeneous Turbulence (Cambridge U.P., Cambridge, U.K., 1970).
51.
W.
Matthaeus
,
Geophys. Res. Lett.
9
,
660
(
1982
).
52.
W. Matthaeus, in Solar Terrestrial Physics—Present and Future, edited by D. Butler and K. Papadopoulos (NASA, Washington, DC, 1984), pp. 1.40‐1.44.
53.
W.
Matthaeus
and
S.
Lamkin
,
Phys. Fluids
28
,
303
(
1985
).
54.
W.
Matthaeus
and
M.
Goldstein
,
J. Geophys. Res.
87
,
6011
(
1982
).
55.
S.
Orszag
,
Stud. Appl. Math.
50
,
293
(
1971
).
56.
S.
Orszag
and
G.
Patterson
,
Phys. Rev. Lett.
28
,
76
(
1972
).
57.
D.
Korn
and
J.
Lambiotte
,
Math. Comp.
33
,
977
(
1979
).
58.
U.
Frisch
,
A.
Pouquet
,
J.
Leorat
, and
A.
Mazure
,
J. Fluid Mech.
68
,
769
(
1975
);
A.
Pouquet
and
G.
Patterson
,
J. Fluid Mech.
85
,
305
(
1978
).
59.
U. Frisch, A. Pouquet, P‐L. Sulem, and M. Meneguzzi, J. Mech. Theor. Appl. Numero special, 191 (1983).
60.
S.
Orszag
and
C.‐M.
Tang
,
J. Fluid Mech.
90
,
129
(
1978
).
61.
M.
Hossain
,
W.
Matthaeus
, and
D.
Montgomery
,
J. Plasma Phys.
30
,
479
(
1983
).
62.
M.
Menneguzzi
,
U.
Frisch
, and
A.
Pouquet
,
Phys. Rev. Lett.
47
,
1060
(
1981
).
63.
S.
Riyopoulos
,
A.
Bondeson
, and
D.
Montgomery
,
Phys. Fluids
25
,
107
(
1982
).
64.
D.
Montgomery
,
L.
Turner
, and
G.
Vahala
,
Phys. Fluids
21
,
757
(
1978
).
65.
J.
Dahlburg
,
D.
Montgomery
, and
W.
Matthaeus
,
J. Plasma Phys.
34
,
1
(
1985
).
66.
R.
Horuichi
and
T.
Sato
,
Phys. Rev. Lett.
55
,
211
(
1985
).
67.
N. Van Kampen, Stochastic Processes in Physics and Chemistry (North‐Holland, Amsterdam, 1981).
68.
A.
Hasegawa
,
Adv. Phys.
34
,
1
(
1985
).
69.
W.
Matthaeus
,
M.
Goldstein
, and
J.
King
,
J. Geophys. Res.
91
,
59
(
1986
).
70.
R.
Kraichnan
,
Phys. Fluids
7
,
1030
(
1964
).
71.
A. Ting, W. Matthaeus, and D. Montgomery, Phys. Fluids (in press).
72.
C.‐M.
Ho
and
L.‐S.
Huang
,
J. Fluid Mech.
119
,
443
(
1982
).
73.
P.
Patnaik
,
F.
Sherman
, and
G.
Corcos
,
J. Fluid Mech.
73
,
215
(
1976
).
74.
S.
Zweben
,
C.
Menyuk
, and
R.
Taylor
,
Phys. Rev. Lett.
42
,
1270
(
1979
).
75.
D.
Biskamp
,
Phys. Lett. A
87
,
357
(
1982
).
76.
M.
Brachet
,
D.
Meiron
,
S.
Orszag
,
B.
Nickel
,
R.
Morf
, and
U.
Frisch
,
J. Fluid Mech.
130
,
411
(
1983
).
77.
R.
Kraichnan
,
Phys. Fluids
8
,
1385
(
1965
).
78.
E.
Parker
,
Astrophys. J.
174
,
499
(
1972
).
79.
E.
Parker
,
Geophys. Astrophys. Fluid Dyn.
22
,
195
(
1982
).
80.
J.
Dahlburg
,
D.
Montgomery
,
G.
Doolen
, and
W.
Matthaeus
,
J. Plasma Phys.
35
,
1
(
1986
).
81.
W.
Matthaeus
,
J.
Ambrosiano
, and
M.
Goldstein
,
Phys. Rev. Lett.
53
,
1449
(
1984
);
M.
Goldstein
,
W.
Matthaeus
, and
J.
Ambrosiano
,
Geophys. Res. Lett.
13
,
205
(
1986
).
82.
T. Forbes (private communication).
83.
J.‐I.
Sakai
,
J. Plasma Phys.
30
,
109
(
1983
).
84.
T.
Sato
,
T.
Hayashi
, and
T.
Tamao
,
Phys. Rev. Lett.
41
,
1548
(
1978
).
85.
T.
Forbes
and
E.
Priest
,
J. Geophys. Res.
88
,
863
(
1983
).
86.
E. Priest, in Magnetic Reconnection in Space and Laboratory Plasmas, edited by E. Hones, Jr. (American Geophysical Union, Washington, DC, 1984), p. 63.
87.
T.
Tajima
,
F.
Brunei
, and
J.
Sakai
,
Astrophys. J.
258
,
L45
(
1982
).
88.
T.
Sato
and
A.
Hasegawa
,
Geophys. Res. Lett.
9
,
52
(
1982
).
89.
T.
Sato
,
R.
Walker
, and
M.
Ashour‐Abdalla
,
J. Geophys. Res.
89
,
9761
(
1984
).
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