  A plane-shear flow in a fluid with forced turbulence is considered. If the
fluid is electrically-conducting then a mean electromotive force (EMF) results
even without basic rotation and the magnetic diffusivity becomes a highly
anisotropic tensor. It is checked whether in this case self-excitation of a
large-scale magnetic field is possible (so-called WxJ-dynamo) and the answer is
NO. The calculations reveal the cross-stream components of the EMF
perpendicular to the mean current having the wrong signs, at least for small
magnetic Prandtl numbers. After our results numerical simulations with magnetic
Prandtl number of about unity have only a restricted meaning as the Prandtl
number dependence of the diffusivity tensor is rather strong. If, on the other
hand, the turbulence field is stratified in the vertical direction then a
dynamo active alpha-effect is produced. The critical magnetic Reynolds number
for such a self-excitation in a simple shear flow is slightly above 10 like for
the other - but much more complicated - flow patterns used in existing dynamo
experiments with liquid sodium or gallium.
