Wall-oscillation conditions for drag reduction in turbulent channel flow
  The drag reduction properties of a turbulent channel flow modified by spanwise sinusoidal oscillations of the walls are investigated by direct numerical simulations. The work is based on the linear relation between the drag reduction and the parameter $S$, function of the maximum wall velocity and the period of the oscillation. This quantity has been found through physical arguments pertaining to the action of the oscillating Stokes layer on the near-wall turbulence dynamics. The predictive potential of the scaling parameter is exploited to gain insight into the drag-reducing effects of the oscillating wall technique. The period of oscillation which guarantees the maximum drag reduction for a given maximum wall displacement is studied for the first time. The issue of the minimum intensity of wall forcing required to produce a non-zero drag reduction effect and the dependence of the drag reduction on the Reynolds number are also addressed. The drag reduction data available in the literature are compared with the prediction given by the scaling parameter, thus attaining a comprehensive view of the state of the art. 
Pierre Ricco, Maurizio Quadrio