  Context: Differential rotation in stars is driven by turbulent transport of
angular momentum. Aims: To measure and parametrize the non-diffusive
contribution to turbulent stress, known as $\Lambda$ effect, and its quenching
as a function of rotation and magnetic field. Methods: Simulations of
homogeneous, anisotropically forced turbulence in fully periodic cubes are used
to extract the turbulent Reynolds and Maxwell stresses. Magnetic fields are
introduced by imposing a uniform large-scale field on the system. Turbulent
transport coefficients pertaining to the $\Lambda$ effect are obtained by
fitting. Results: The numerical results agree qualitatively with analytic ones
at slow rotation and low Reynolds numbers. This entails that vertical
(horizontal) transport is downward (equatorward). The existence of a
significant meridional $\Lambda$ effect is confirmed. Large-scale vorticity
generation is found at rapid rotation when the Reynolds number exceeds a
threshold value. The $\Lambda$ effect is severely quenched by large-scale
magnetic fields due to the tendency of the Reynolds and Maxwell stresses to
cancel each other. Rotational (magnetic) quenching of $\Lambda$ occurs at more
rapid rotation (at lower field strength) in simulations than in theory.
Conclusions: The current results largely confirm the earlier theoretical
results but they also offer new insights: the non-negligible meridional
$\Lambda$ effect possibly plays a role in the maintenance of meridional
circulation in stars and the appearance of large-scale vortices raises the
question of their effect on the angular momentum transport in stars. The
results regarding magnetic quenching are consistent with the strong decrease of
differential rotation in recent semi-global simulations and highlight the
importance of including magnetic effects in differential rotation models.
(abridged)
