  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.
