Cyclic gravity waves in deep water

Model Equations for Gravity-capillary Waves in Deep Water

The Euler equations for water waves in any depth have been shown to have solitary wave solutions when the effect of surface tension is included. This paper proposes three quadratic model equations for these types of waves in infinite depth with a two-dimensional fluid domain. One model is derived directly from the Euler equations. Two further simpler models are proposed, both having the full gr...

Traveling Waves in Deep Water with Gravity and Surface Tension

This paper is concerned with the simulation of periodic traveling deep-water freesurface water waves under the influence of gravity and surface tension in two and three dimensions. A variety of techniques is utilized, including the numerical simulation of a weakly nonlinear model, explicit solutions of low-order perturbation theories, and the direct numerical simulation of the full water wave e...

Spectral Stability of Deep Two-Dimensional Gravity-Capillary Water Waves

In this contribution we study the spectral stability problem for periodic traveling gravity-capillary waves on a two-dimensional fluid of infinite depth. We use a perturbative approach that computes the spectrum of the linearized water wave operator as an analytic function of the wave amplitude/slope. We extend the highly accurate method of Transformed Field Expansions to address surface tensio...

Long wavelength bifurcation of gravity waves on deep water

Conditions are found for the appearance of non-uniform progressive waves of permanent form from a long-wave modulation of a finite-amplitude Stokes wave on deep water. The waveheight at which the modulated waves can occur is a very slowly decreasing function of the modulation wavelength for values up to 150 times the original wavelength. Some qualitative remarks are made about the problem of de...

A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory