Numerical Evidence for the Existence of New Types of Gravity Waves of Permanent Form on Deep Water

Abstract

Numerical results are presented for the shape of finite‐amplitude steady irrotational inviscid gravity waves obtained by solving an integrodifferential equation. It is found that the family of solutions giving the wave as a function of height or equivalent parameter has bifurcation points for h /λ≈0.13, where h is waveheight and λ is wavelength. Two bifurcation points and the branches emanating from them are found specifically, corresponding to a doubling and tripling of the wavelength. Solutions on the new branches are calculated.