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A fundamental problem in the field of turbulent skin-friction drag reductionis to determine the performance of the available control techniques at highvalues of the Reynolds number $Re$. We consider active, predeterminedstrategies based on spanwise forcing (oscillating wall and streamwise-travelingwaves applied to a plane channel flow), and explore via Direct NumericalSimulations (DNS) up to $Re_\tau=2100$ the rate at which their performancedeteriorates as $Re$ is increased. To be able to carry out a comprehensiveparameter study, we limit the computational cost of the simulations byadjusting the size of the computational domain in the homogeneous directions,compromising between faster computations and the increased need oftime-averaging the fluctuating space-mean wall shear-stress.  Our results, corroborated by a few full-scale DNS, suggest a scenario wheredrag reduction degrades with $Re$ at a rate that varies according to theparameters of the wall forcing. In agreement with already availableinformation, keeping them at their low-$Re$ optimal value produces a relativelyquick decrease of drag reduction. However, at higher $Re$ the optimalparameters shift towards other regions of the parameter space, and theseregions turn out to be much less sensitive to $Re$. Once this shift isaccounted for, drag reduction decreases with $Re$ at a markedly slower rate. Ifthe slightly favorable trend of the energy required to create the forcing isconsidered, a chance emerges for positive net energy savings also at largevalues of the Reynolds number.

Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number