Internal Capillary-Gravity Wilton Ripples

Abstract Periodic traveling waves at the interface of two incompressible, inviscid fluids subject to gravity and surface tension are studied. We focus on the case in which the linearization about the quiescent state has a two-dimensional kernel. We prove the existence of sheets of traveling waves in this circumstance. We also compute Wilton ripples in which the leading term has a (1:2) harmonic resonance, the triad ripple configuration. Global branches of waves are computed, terminating in three types of self-intersecting waves.