  We study the steady streaming between two infinitely long circular cylinders
produced by small amplitude transverse vibrations of the inner cylinder about
the axis of the outer cylinder. The Vishik-Lyusternik method is employed to
construct an asymptotic expansion of the solution of the Navier-Stokes
equations in the limit of high-frequency vibrations for Reynolds numbers of
order of unity. The effect of the Stokes drift of fluid particles is also
studied. It is shown that it is nonzero not only within the boundary layers but
also in higher order terms of the expansion of the averaged outer flow.
