Capillary–gravity waves produced by a wavemaker

Abstract

Surface waves in a channel can be produced by the horizontal motion of a plane wavemaker at one end of the channel. The amplitude and the frequency of the waves depend on both surface tension and gravity, as well as on the condition imposed at the contact line between the free surface and the wavemaker. Some of the previous work on the generation of capillary–gravity waves has been based on the unjustified assumption that the slope of the free surface at the contact line can be prescribed. A more acceptable condition is one that relates the slope to the motion of the contact line relative to the wavemaker; in this way the dynamic properties of the contact angle can be incorporated. The waves generated by a plane wavemaker in fluid of infinite depth and in fluid of a depth equal to that of the wavemaker are determined. An important reason for including surface tension is that in its absence the transient motion initiated by an impulsive start is singular; when surface tension is included this singularity is removed.