  A review of recent studies on a new mechanism of generation of large-scale
magnetic field in a sheared turbulent plasma is presented. This mechanism is
associated with the shear-current effect which is related to the W x J-term in
the mean electromotive force. This effect causes the generation of the
large-scale magnetic field even in a nonrotating and nonhelical homogeneous
sheared turbulent convection whereby the alpha effect vanishes. It is found
that turbulent convection promotes the shear-current dynamo instability, i.e.,
the heat flux causes positive contribution to the shear-current effect.
However, there is no dynamo action due to the shear-current effect for small
hydrodynamic and magnetic Reynolds numbers even in a turbulent convection, if
the spatial scaling for the turbulent correlation time is k^{-2}, where k is
the small-scale wave number. We discuss here also the nonlinear mean-field
dynamo due to the shear-current effect and take into account the transport of
magnetic helicity as a dynamical nonlinearity. The magnetic helicity flux
strongly affects the magnetic field dynamics in the nonlinear stage of the
dynamo action. When the magnetic helicity flux is not small, the saturated
level of the mean magnetic field is of the order of the equipartition field
determined by the turbulent kinetic energy. The obtained results are important
for elucidation of origin of the large-scale magnetic fields in astrophysical
and cosmic sheared turbulent plasma.
