Turbulent Drag Reduction at High Reynolds Numbers

Abstract

Direct numerical simulations were performed to study the effect of streamwise travelling waves of spanwise wall velocity on turbulent channel flow. Simulations with various control parameters, scaled by wall units, are performed at four Reynolds numbers, corresponding to \( {\text{Re}}_{\tau } = 200,\,400,\,800,\,1600 \). As the Reynolds number is increased the intensity of both the drag reduction and drag increase is reduced. This reduction does not scale universally, and the drag reduction deteriorates quickly with increased Reynolds number when the parameters used are close to optimal. The consequence of this variation in Reynolds scaling is that the value of the optimal forcing parameters change, even in wall units, with increased Reynolds number.