Steady Gravity‐Capillary Waves On Deep Water—1. Weakly Nonlinear Waves

Abstract

The form of weakly nonlinear waves of permanent form on deep water is considered under the effect of both surface tension and gravity. The Wilton ripple phenomenon is reexamined and shown to be associated with a bifurcation in which a wave of permanent form can double its period. It is shown further that Wilton's ripples are a special case of a more general phenomenon in which bifurcation into subharmonics and fractional higher harmonics can occur.