  An oscillating spanwise pressure gradient is imposed numerically to control
the flow separation and reduce the drag of a turbulent flow in a channel with
square bars. The transverse flow produces a maximum drag reduction of 25\%, due
to lower pressure and skin-friction drag forces. The pressure drag reduction
reaches a maximum of 22\% and is due to a decrease of the positive high
pressure in front of the bars and an increase of the low negative pressure
behind the bars. The skin-friction drag reduction is caused by a lower
wall-shear stress along the cavity between the bars where the flow is fully
attached, while the wall-shear stress on the crest of the bars and in the
separated region behind the bars is unaffected. The spanwise laminar flow
obtained by neglecting the nonlinear terms involving the turbulent velocity
fluctuations is used to compute the power spent for oscillating the fluid along
the spanwise direction and an excellent agreement is found with the power spent
obtained by the averaged turbulent flow. A marginal or negative net power saved
is found by subtracting the power employed for controlling the flow from the
power saved thanks to the transverse flow. The control reduces the total drag
as the integral of the Reynolds stresses along the horizontal line connecting
the corners of two consecutive bars is decreased, which in turn impacts on the
pressure and wall-shear stress reductions.
