  Coriolis force effects on shear flows are important in geophysical and
astrophysical contexts. We here report a study on the linear stability and the
transient energy growth of the plane Couette flow with system rotation
perpendicular to the shear direction. External rotation causes linear
instability. At small rotation rates, the onset of linear instability scales
inversely with the rotation rate and the optimal transient growth in the
linearly stable region is slightly enhanced, ~Re^2. The corresponding optimal
initial perturbations are characterized by roll structures inclined in the
streamwise direction and are twisted under external rotation. At large rotation
rates, the transient growth is significantly inhibited and hence linear
stability analysis is a reliable indicator for instability.
