  This work studies the effects of skin-friction drag reduction in a turbulent
flow over a curved wall, with a view to understanding the relationship between
the reduction of friction and changes to the total aerodynamic drag. Direct
numerical simulations (DNS) are carried out for an incompressible turbulent
flow in a channel where one wall has a small bump; two bump geometries are
considered, that produce mildly separated and attached flows. Friction drag
reduction is achieved by applying streamwise-travelling waves of spanwise
velocity (StTW).
  The local friction reduction produced by the StTW is found to vary along the
curved wall, leading to a global friction reduction that, for the cases
studied, is up to 10\% larger than that obtained in the plane-wall case.
Moreover, the modified skin friction induces non-negligible changes of pressure
drag, which is favorably affected by StTW and globally reduces by up to 10\%.
The net power saving, accounting for the power required to create the StTW, is
positive and, for the cases studied, is one half larger than the net saving of
the planar case. The study suggests that reducing friction at the surface of a
body of complex shape induces further effects, a simplistic evaluation of which
might lead to underestimating the total drag reduction.
