Some effects of surface tension on steep water waves. Part 2

Abstract

This paper continues an investigation of the effects of surface tension on steep water waves in deep water begun in Hogan (1979a). A Stokes-type expansion method is given which can be applied to most wavelengths. For capillary waves (2 cm or less) it is found that the surface of the highest wave encloses a bubble of air, as was found for pure capillary waves by Crapper (1957). For intermediate waves (20 cm) the wave profiles are similar to those of pure gravity waves and the wave properties increase monotonically. For gravity waves (200 cm) the wave properties all exhibit a maximum just short of the maximum wave height obtained by the method. The integral properties for all the waves are drawn and given in numerical form in the appendix.