  To study the Reynolds stresses which describe turbulent momentum transport
from turbulence affected by large-scale shear and rotation. Three-dimensional
numerical simulations are used to study turbulent transport under the
influences of large-scale shear and rotation in homogeneous, isotropically
forced turbulence. We study three cases: one with only shear, and two others
where in addition to shear, rotation is present. These cases differ by the
angle (0 or 90\degr) the rotation vector makes with respect to the z-direction.
Two subsets of runs are performed with both values of \theta where either
rotation or shear is kept constant. When only shear is present, the
off-diagonal stress can be described by turbulent viscosity whereas if the
system also rotates, nondiffusive contributions (\Lambda-effect) to the stress
can arise. Comparison of the direct simulations are made with analytical
results from a simple closure model. We find that the turbulent viscosity is of
the order of the first order smoothing result in the parameter regime studied
and that for sufficiently large Reynolds numbers the Strouhal number,
describing the ratio of correlation to turnover times, is roughly 1.5. This is
consistent with the closure model based on the minimal tau-approximation which
produces a reasonable fit to the simulation data for similar Strouhal numbers.
In the cases where rotation is present, separating the diffusive and
nondiffusive components of the stress turns out to be challenging but taking
the results at face value, we can obtain nondiffusive contributions of the
order of 0.1 times the turbulent viscosity. We also find that the simple
closure model is able to reproduce most of the qualitative features of the
numerical results provided that the Strouhal number is of the order of unity.
