  The present study tests the efficacy of the well-known viscous drag reduction
strategy of imposing spanwise wall oscillations to reduce pressure drag
contributions in a transitional- and fully-rough turbulent wall flow. This is
achieved by conducting a series of direct numerical simulations of a turbulent
flow over two-dimensional (spanwise aligned) semi-cylindrical rods, placed
periodically along the streamwise direction with varying streamwise spacing.
Surface oscillations, imposed at fixed viscous-scaled actuation parameters
optimum for smooth wall drag reduction, are found to yield substantial drag
reduction (>25%) for all the rough wall cases, maintained at matched roughness
Reynolds numbers. While the total drag reduction is due to a drop in both
viscous and pressure drag in the case of transitionally-rough flow (i.e. with
large inter-rod spacing), it is solely associated with pressure drag reduction
for the fully-rough cases (i.e. with small inter-rod spacings), with the latter
being reported for the first time. The study finds that pressure drag reduction
in all cases is caused by the attenuation of the vortex shedding activity in
the roughness wake, in response to wall-oscillation frequencies that are of the
same order as the vortex shedding frequencies. Contrary to speculations in the
literature, this study confirms that the mechanism behind pressure drag
reduction, achieved via imposition of spanwise oscillations, is independent
from the viscous drag reduction. This mechanism is responsible for weakening of
the Reynolds stresses and increase in base pressure in the roughness wake,
explaining the pressure drag reduction observed by past studies, across varying
roughness heights and geometries.
