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

TL;DR

This paper explores the energetic conditions leading to wave breaking, focusing on the normalized energy flux parameter $B$, and finds that its rate of change correlates with crest energy growth, enhancing understanding of wave breaking onset.

Contribution

It provides a theoretical explanation linking the energy flux parameter $B$ to crest energy growth, building on previous empirical and numerical validations.

Findings

The rate of change of $B$ correlates with crest energy convergence.

A threshold value of $B_{th} \\approx 0.85$ predicts breaking onset.

Results are validated across various wave configurations.

Abstract

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