  A turbulent channel flow modified by the motion of discs that are free to
rotate under the action of wall turbulence is studied numerically. The
Navier-Stokes equations are coupled nonlinearly with the dynamical equation of
the disc motion, which synthesizes the fluid-flow boundary conditions and is
driven by the torque exerted by the wall-shear stress. We consider discs that
are fully exposed to the fluid and discs for which only half of the surface
interfaces the fluid. The disc motion is thwarted by the fluid torque in the
housing cavity and by the torque of the ball bearing that supports the disc.
For the full discs, no drag reduction occurs because of the small angular
velocities. The most energetic disc response occurs for disc diameters that are
comparable with the spanwise spacing of the low-speed streaks. A perturbation
analysis for small disc-tip velocities reveals that the two-way nonlinear
coupling has an intense attenuating effect on the disc response. The
reduced-order results show excellent agreement with the nonlinear results for
large diameters. The half discs rotate with a finite angular velocity, leading
to large reduction of the turbulence activity and of the skin-friction drag
over the spinning portion of the discs, while the maximum drag reduction over
the entire walls is 5.6%. The dependence of the drag reduction on the wall-slip
velocity and the spatial distribution of the wall-shear stress qualitatively
match results based on the only available experimental data.
