  The three-dimensional temporal instability of rotating boundary layer flows
is investigated by computing classical normal modes as well as by evaluating
the transient growth of optimal disturbances. The flows examined are the
rotating Blasius (RB) and the rotating asymptotic suction layers (RAS), with
the rotation axis normal to the basic flow plane. In agreement with an inviscid
criterion, streamwise unstable modes are found in both flow cases for
anti-cyclonic rotation: at high Reynolds numbers, one obtains the Rossby number
unstable range 0<1/Ro<0.57 for RB, or 0<1/Ro<1 for RAS. Critical Reynolds and
Rossby numbers are also determined in both instances. Moreover the dependence
of transient growth with respect to wavenumbers, Rossby and Reynolds numbers is
presented for both cyclonic and anti-cyclonic r\'egimes. In particular, the
{\it peak} transient growth is computed for a wide range of parameter values
within the cyclonic regime and is shown to be reduced by rotation. A scaling
analysis with respect to the Reynolds number is performed showing that the
standard Re^2 scaling is recovered only at very weak rotation. Optimal
disturbances resemble oblique vortices. At weak rotation, they are almost
streamwise vortices though their structure departs from the classical
non-rotating case. Strong rotation imposes two-dimensionality and the optimal
disturbances vary weakly in the spanwise direction and exhibit growth by the
Orr mechanism.
