  A Stokes layer, which is a flow pattern that arises in a viscous fluid
adjacent to an oscillatory boundary, was observed in an experiment using a
two-dimensional strongly coupled dusty plasma. Liquid conditions were
maintained using laser heating, while a separate laser manipulation applied an
oscillatory shear that was localized and sinusoidal. The evolution of the
resulting flow was analyzed using space-time diagrams. These figures provide an
intuitive visualization of a Stokes layer, including features such as the depth
of penetration and wavelength. Another feature, the characteristic speed for
the penetration of the oscillatory flow, also appears prominently in space-time
diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer
was generalized to describe a two-phase liquid. In our experiment, the phases
were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb
coupling. The model is found to agree with the experiment, in the appearance of
the space-time diagrams, and in the values of the characteristic speed, depth
of penetration, and wavelength.
