Steady streaming of viscous surface layer in waves

Abstract

An investigation of the drift velocity induced by water waves of a contminated surface layer is carried out. The theoretical analysis is based on a thin boundary layer on the free surface. The results of the analysis reveal that the drift velocity of a viscous layer on the water surface is 7/4 times the Stokes prediction ofc(ak)2 wherec is the wave celerity andak the wave slope. The present experimental investigation confirms the validity of the theoretical prediction for the drift velocity for a lightly contaminated surface layer; however, for a heavily contaminated surface layer, the experimental results exceed the theoretical prediction. An investigation for a heavily contaminated layer is carried out assuming an inextensible surface layer. Thus, in the experiment, vinyl sheets are used to substitute the contaminated layers. By balancing the wave-induced mean thrust force with the mean drag force, the drift velocity is obtained and compared with the experimental results. Based on the theoretical and experimental analyses, formulae for predicting the drift velocities for laminar and turbulent flow conditions are proposed.