  Shearing and rotational forces in fluids can significantly alter the
transport of momentum.A numerical investigation was undertaken to study the
role of these forces using plane Couette flow subject to rotation about an axis
perpendicular to both wall-normal and streamwise directions. Using a set of
progressively higher Reynolds numbers up to Re = 5200, we find that the torque
for a given Re is a non-monotonic function of rotation number, Ro. For
low-to-moderate turbulent Reynolds numbers we find a maximum that is associated
with flow fields that are dominated by downstream vortices and calculations of
2-d vortices capture the maximum also quantitatively. For higher shear Reynolds
numbers a second stronger maximum emerges at smaller rotation numbers, closer
to non-rotating plane Couette flow. It is carried by flows with a markedly 3-d
structure and cannot be captured by 2-d vortex studies. As the Reynolds number
increases, this maximum becomes stronger and eventually overtakes the one
associated with the 2-d flow state.
