On the energetics of breaking inception and onset in surface gravity\n waves

Accurate prediction of the onset and strength of breaking surface gravity\nwaves is a long-standing problem of significant theoretical and applied\ninterest. Recently, Barth\\'el\\'emy et al (https://doi.org/10.1017/jfm.2018.93)\nexamined the energetics of focusing wave groups in deep and intermediate depth\nwater and found that breaking and non-breaking regimes were clearly separated\nby the normalised energy flux, $B$, near the crest tip. Furthermore, the\ntransition of $B$ through a generic breaking threshold value $B_\\mathrm{th}\n\\approx 0.85$ was found to precede visible breaking onset by up to one fifth of\na wave period. This remarkable generic threshold for breaking inception has\nsince been validated numerically for 2D and 3D domains and for shallow and\nshoaling water waves; however, there is presently no theoretical explanation\nfor its efficacy as a predictor for breaking. This study investigates the\ncorrespondence between the parameter $B$ and the crest energy growth rate\nfollowing the evolving crest for breaking and non-breaking waves in a numerical\nwave tank using a range of wave packet configurations. Our results indicate\nthat the time rate of change of the $B$ is strongly correlated with the energy\ndensity convergence rate at the evolving wave crest. These findings further\nadvance present understanding of the elusive process of wave breaking.\n