  We analyze the motion of an overdamped classical particle in a
multidimensional periodic potential, driven by a weak external noise. We
demonstrate that in steady-state, the presence of temporal correlations in the
noise and spatial asymmetry within a period of the potential could lead to
particle rotation. The rotation is a direct consequence of a change in sign of
the noise-induced drift motion in each dimension. By choosing different
potentials, we can generate a variety of flow patterns from laminar drifts to
rotations.
