  A linear defect, viz. an elastic string, diffusing on a planar substrate
traversed by a travelling wave experiences a drag known as Stokes' drift. In
the limit of an infinitely long string, such a mechanism is shown to be
characterized by a sharp threshold that depends on the wave parameters, the
string damping constant and the substrate temperature. Moreover, the onset of
the Stokes' drift is signaled by an excess diffusion of the string center of
mass, while the dispersion of the drifting string around its center of mass may
grow anomalous.
