A three‐dimensional direct simulation of inhomogeneous magnetohydrodynamic (MHD) turbulence is carried out to investigate the turbulent dynamo effect. The velocity field is driven by an external force so that the velocity and magnetic fields are statistically inhomogeneous in one direction and homogeneous in the other two directions. Several statistical quantities are obtained such as the mean magnetic field, the turbulent energy, and the turbulent electromotive force. The data are used to examine the modeling of the dynamo effect in the four‐equation turbulence model. It is shown that the dynamo term related to the cross helicity is more important than the well‐known α dynamo term. Some model constants in the four‐equation model are estimated using the least‐square method.

1.
H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge U. P., Cambridge, 1978).
2.
F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, 1980).
3.
H. A. B.
Bodin
and
A. A.
Newton
, “
Reversed-field-pinch research
,”
Nucl. Fusion
20
,
1255
(
1980
).
4.
A.
Pouquet
and
G. S.
Patterson
, “
Numerical simulation of helical magnetohydrodynamic turbulence
,”
J. Fluid Mech.
85
,
305
(
1978
).
5.
M.
Meneguzzi
,
U.
Frisch
, and
A.
Pouquet
, “
Helical and nonhelical turbulent dynamos
,”
Phys. Rev. Lett.
47
,
1060
(
1981
).
6.
S.
Kida
,
S.
Yanase
, and
J.
Mizushima
, “
Statistical properties of MHD turbulence and turbulent dynamo
,”
Phys. Fluids A
3
,
457
(
1991
).
7.
J. P.
Dahlburg
,
D.
Montgomery
,
G. D.
Doolen
, and
L.
Turner
, “
Turbulent relaxation of a confined magnetofluid to a force-free state
,”
J. Plasma Phys.
37
,
299
(
1987
).
8.
J. P.
Dahlburg
,
D.
Montgomery
,
G. D.
Doolen
, and
L.
Turner
, “
Driven, steady-state RFP computations
,”
J. Plasma Phys.
40
,
39
(
1988
).
9.
A. Y.
Aydemir
,
D. C.
Barnes
,
E. J.
Caramana
,
A. A.
Mirin
,
R. A.
Nebel
,
D. D.
Schnack
, and
A. G.
Sgro
, “
Compressibility as a feature of field reversal maintenance in the reversed-field pinch
,”
Phys. Fluids
28
,
898
(
1985
).
10.
K.
Kusano
and
T.
Sato
, “
Non-linear coupling effects on the relaxation process in the reversed field pinch
,”
Nucl. Fusion
27
,
821
(
1987
).
11.
P.
Kirby
, “
Numerical simulation of the reversed field pinch
,”
Phys. Fluids
31
,
625
(
1988
).
12.
M. Meneguzzi and A. Pouquet, “Convective turbulent dynamos without rotation,” in Turbulence and Nonlinear Dynamics in MHD Flows, edited by M. Meneguzzi, A. Pouquet, and P. L. Sulem (North-Holland, Amsterdam, 1989), pp. 41–48.
13.
V. Carbone and P. Veltri, “Decay of fully developed anisotropic MHD turbulence,” in Ref. 12, pp. 241–246.
14.
A.
Yoshizawa
and
F.
Hamba
, “
A turbulent dynamo model for the reversed field pinches of plasma
,”
Phys. Fluids
31
,
2276
(
1988
).
15.
F.
Hamba
, “
One-dimensional calculation of a turbulent dynamo model for reversed field pinches
,”
Phys. Fluids B
2
,
3064
(
1990
).
16.
A.
Yoshizawa
, “
Self-consistent turbulent dynamo modeling of reversed field pinches and planetary magnetic fields
,”
Phys. Fluids B
2
,
1589
(
1990
).
17.
A.
Yoshizawa
, “
Turbulent transport processes in tokamak’s high-mode confinement
,”
Phys. Fluids B
3
,
2723
(
1991
).
18.
B. E. Launder and D. B. Spalding, Mathematical Models, of Turbulence (Academic, London, 1972).
19.
P. Bradshaw, T. Cebici, and J. H. Whitelaw, Engineering Calculation Methods for Turbulent Flow (Academic, London, 1981).
20.
A.
Pouquet
,
U.
Frisch
, and
J.
Leorat
, “
Strong MHD helical turbulence and the nonlinear dynamo effect
,”
J. Fluid Mech.
77
,
321
(
1976
).
21.
F.
Hamba
, “
Estimate of constants in the k−ε model of turbulence by using large eddy simulation
,”
J. Phys. Soc. Jpn.
56
,
3405
(
1987
).
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