  We perform a detailed numerical study of modal and non-modal stability in
oblique Couette-Poiseuille profiles, which are among the simplest examples of
three-dimensional boundary layers. Through a comparison with the Orr-Sommerfeld
operator for the aligned case, we show how an effective wall speed succinctly
characterizes modal stability. Large-scale parameter sweeps reveal that the
misalignment between the pressure gradient and wall motion is, in general,
destabilizing. For flows that are sufficiently oblique, the instability is
found to depend exclusively on the direction of wall motion and not on its
speed, a conclusion supported, in part, by the perturbation energy budget and
the evolution of the critical layers. Closed forms for the critical parameters
in this regime are derived using a simple analysis. Finally, a modified
long-wavelength approximation is developed, and the resulting asymptotic
eigenvalue problem is used to show that there is no cutoff wall speed for
unconditional stability whenever the angle of wall motion is non-zero, in stark
contrast to the aligned case. From a non-modal perspective, pseudo-resonance is
examined through the resolvent and the $\epsilon$-pseudospectra. An analysis of
the unforced initial value problem shows that the maximum energy gain is highly
dependent on both the magnitude and direction of the wall velocity. However,
the strongest amplification is always achieved for configurations that are only
weakly skewed. Finally, the optimal perturbations appear to develop via a
lift-up effect induced by an Orr-like mechanism.
