Oscillatory flow beneath a free surface

We consider the two-dimensional fluid flow induced by a submerged oscillating circular cylinder under a free surface; the depth of the fluid is finite and the amplitude of the movement of the cylinder is assumed to be small compared to its diameter. Thus, the solution may be pursued by perturbation methods. Particular attention is focused on the induced steady streaming motion about the cylinder, at both high Reynolds number and in the inviscid-flow limit.