  The temporal linear stability of plane Poiseuille flow modified by spanwise
forcing applied at the walls is considered. The forcing consists of a
stationary streamwise distribution of spanwise velocity that generates a steady
transversal Stokes layer, known to reduce skin-friction drag in a turbulent
flow with little energetic cost. A large numerical study is carried out, where
the effects of both the physical and the discretization parameters are
thoroughly explored, for three representative subcritical values of the
Reynolds number Re. Results show that the spanwise Stokes layer significantly
affects the linear stability of the system. For example, at Re=2000 the wall
forcing is found to more than double the negative real part of the least-stable
eigenvalue, and to decrease by nearly a factor of four the maximum transient
growth of perturbation energy. These observations are Re-dependent and further
improve at higher $Re$. Comments on the physical implications of the obtained
results are provided, suggesting that spanwise forcing might be effective to
obtain at the same time a delayed transition to turbulence and a reduced
turbulent friction.
