  A cylindrical container partially filled with a liquid in orbital shaking
motion, i.e. in circular translation with fixed orientation with respect to an
inertial frame of reference, generates, along with a rotating sloshing wave, a
mean flow rotating in the same direction as the wave. Here we investigate
experimentally the structure and the scaling of the wave flow and the
Lagrangian mean flow in the weakly nonlinear regime, for small forcing
amplitude and for forcing frequency far from the resonance, using conventional
and stroboscopic particle image velocimetry. The Lagrangian mean flow is
composed of a strong global rotation near the center and a non trivial pattern
of poloidal recirculation vortices of weaker amplitude, mostly active near the
contact line. The global rotation near the center is robust with respect to
changes in viscosity and forcing frequency, and its amplitude compares well
with the predicted Stokes drift for an inviscid rotating sloshing wave. On the
other hand, the spatial structure of the poloidal vortices show strong
variation with viscosity and forcing frequency, suggesting that it results from
the streaming flow driven by the complex oscillatory boundary layers near the
contact line.
