The drift velocity of water waves

Abstract

The important role of viscosity in producing second-order Eulerian drift currents in the presence of small-amplitude water waves was first recognized by Longuet-Higgins (1953). The theoretical and experimental background is first reviewed. It is then shown that, contrary to previous belief, the presence of surface contamination must greatly enhance the drift velocity of short waves. We then solve an initial-value problem for the drift current associated with temporally decaying waves, thereby resolving questions raised by the work of Liu & Davis (1977), whose solution exhibits anomalous singularities. Next, the steady drift velocity of spatially decaying waves is calculated and shown to bear a close resemblance to Longuet-Higgins’ ‘conduction solution’ for unattenuated waves. Finally, we establish that unidirectional drift currents of both surface and inter-facial waves are sure to be unstable to spanwise-periodic disturbances; the instability mechanism being identical to that first proposed by Craik (1977), and recently developed by Leibovich & Paolucci (1981), to explain the generation of Langmuir circulations.