Abstract
A statistically stationary turbulence with a mean shear gradient is realized in a flow driven by suitable body forces. The flow domain is periodic in downstream and spanwise directions and bounded by stress-free surfaces in the normal direction. Except for small layers near the surfaces the flow is homogeneous. The fluctuations in turbulent energy are less violent than in the simulations using remeshing, but the anisotropy on small scales as measured by the skewness of derivatives is similar and decays weakly with increasing Reynolds number.