  The addition of suitable volume forces to the Navier-Stokes equation allows
to simulate flows in the presence of a homogeneous shear. Because of the
explicit form of the driving the flows are accessible to rigorous mathematical
treatment and to accurate quantitative modelling in their global properties.
The statistics of the fluctuations provide insight into generic behaviour of
non-equilibrium systems and into the presistence of anisotropies at small
scales. Correlation functions can be used to identify dominant large scale
dynamical processes that are relevant for most of the momentum transport across
the shear. The numerical studies of homogeneous shear flows complement
analytical and experimental investigations and contribute to bridging the gap
between ideal homogeneous isotropic turbulence and the more realistic
heterogeneous turbulence.
