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 momentum flux, measured by the wall shear stress, for a given Re is a non-monotonic function of rotation number, Ro. For low-to-moderate Reynolds numbers, we find a maximum that is associated with flow fields that are dominated by downstream vortices and calculations of 2D vortices capture the maximum also quantitatively. For higher 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 3D structure and cannot be captured by 2D vortex studies. As the Reynolds number increases, this maximum becomes stronger and eventually overtakes the one associated with the 2D flow state.
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