  We study a generalized Navier-Stokes model describing the thin-film flows in
non-dilute suspensions of ATP-driven microtubules or swimming bacteria that are
enclosed by a moving ring-shaped container. Considering Stokes' second problem,
which concerns the motion of an oscillating boundary, our numerical analysis
predicts that a periodically rotating ring will oscillate at a higher frequency
in an active fluid than in a passive fluid, due to an activity-induced
reduction of the fluid inertia. In the case of a freely suspended
fluid-container system that is isolated from external forces or torques, active
fluid stresses can induce large fluctuations in the container's angular
momentum if the confinement radius matches certain multiples of the intrinsic
vortex size of the active suspension. This effect could be utilized to
transform collective microscopic swimmer activity into macroscopic motion in
optimally tuned geometries.
