We study the flow induced by random vibration of a solid boundary in an otherwise
quiescent fluid. The analysis is motivated by experiments conducted under the low level
and random effective acceleration field that is typical of a microgravity environment.
When the boundary is planar and is being vibrated along its own plane, the variance
of the velocity field decays as a power law of distance away from the boundary. If a
low-frequency cut-off is introduced in the power spectrum of the boundary velocity,
the variance decays exponentially for distances larger than a Stokes layer thickness
based on the cut-off frequency. Vibration of a gently curved boundary results in
steady streaming in the ensemble average of the tangential velocity. Its amplitude
diverges logarithmically with distance away from the boundary, but asymptotes to a
constant value instead if a low-frequency cut-off is considered. This steady component
of the velocity is shown to depend logarithmically on the cut-off frequency. Finally, we
consider the case of a periodically modulated solid boundary that is being randomly
vibrated. We find steady streaming in the ensemble average of the first-order velocity,
with flow extending up to a characteristic distance of the order of the boundary
wavelength. The structure of the flow in the vicinity of the boundary depends strongly
on the correlation time of the boundary velocity.