On a unified breaking onset threshold for gravity waves in deep and intermediate depth water

We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.