Patterns of ship waves. II. Gravity-capillary waves
In a previous paper [4], Yih's formulas [3] were used to obtain patterns of gravity waves, or of capillary waves in a thin fluid sheet, created by a moving disturbance. In this paper the effects of surface tension are taken into account in finding the patterns of capillary-gravity waves in deep water with a free surface created by a moving disturbance, and much more extensive results than those of Rayleigh [2] have been obtained. The most important feature of the waves is that there are capillary waves behind the disturbance, which have very short wavelengths at high values of the speed U of the disturbance and which are confined to a wedge of an angle that decreases as U increases. Of interest too is the existence of two cusps in the phase lines on either side of the centerline at high values of U (relative to a minimum wave velocity defined in the paper) for those waves which are entirely behind the disturbance.