Linear three-dimensional instabilities of nonlinear two-dimensional uniform gravitycapillary waves are studied using numerical methods. The eigenvalue system for the stability problem is generated using a Galerkin method and differs in detail from techniques used to study the stability of pure gravity waves (McLean 1982) and pure capillary waves (Chen & Saffman 1985). It is found that instabili...

We thank the anonymous referee #1 for the positive and constructive remarks. Just like the referee, we struggled to improve and simplify the presentation of the technical results. In section 2 we tried to illustrate in a simple way the role of coherence by considering the (weak) pseudo-maximal signals. Then, to justify the use of the wavelet transform, we showed how the coherence of phase infor...

[1] We report on near-bottom waves of elevation with amplitude nearly half the 25 m water column, very steep, and propagating into a sheared turbulent waveguide. The waves contained trapped cores transporting parcels of water shoreward. These large waves depart strongly from weakly-nonlinear and weakly-nonhydrostatic conditions and challenge established paradigms. They can also represent an imp...

In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in the conformal variables [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical experim...