An energetic signature for breaking inception in surface gravity waves

Abstract

A dynamical understanding of the physical process of surface gravity wave breaking remains an unresolved problem in fluid dynamics. Conceptually, breaking can be described by inception and onset, where breaking inception is the initiation of unknown irreversible processes within a wave crest that precede the visible manifestation of breaking onset. In the search for an energetic indicator of breaking inception, we use an ensemble of non-breaking and breaking crests evolving within unsteady wave packets simulated in a numerical wave tank to investigate the evolution of each term in the kinetic energy balance equation. We observe that breaking onset is preceded by around one quarter of a wave period by a rapid increase in the rate of convergence of kinetic energy that triggers an irreversible acceleration of the kinetic energy growth rate. This energetic signature, which is present only for crests that subsequently break, arises when the kinetic energy growth rate exceeds a critical threshold. At this point the additional kinetic energy convergence cannot be offset by converting excess kinetic energy to potential energy or by dissipation through friction. Our results suggest that the ratio of the leading terms of the kinetic energy balance equation at the time of this energetic signature is proportional to the strength of the breaking crest. Hence this energetic inception point both predicts the occurrence of breaking onset and indicates the strength of the breaking event.

The influence of spectral bandwidth and shape on deep-water wave breaking onset

“…The times at which are similar to the times at which in figure 10 of Boettger et al. (2023). Thus, there may be a link between a surface-slope-based and an energy-based signature of breaking inception.…”

“…Similarity in the crest shape of breaking waves may be linked to a kinematic description of breaking (and, thus, to a given value of or (Boettger et al. 2023)) which, alongside the robustness and generality of a slope-based threshold, should be examined further.…”

“…In a recent paper, Boettger et al. (2023) examined the flux of the maximum kinetic energy at the crest of breaking and non-breaking waves, and found that breaking occurred when for 2-D chirped wave packets on intermediate and deep water (). This threshold occurs approximately 0.25 periods prior to and may potentially be an indication of irreversible breaking inception, which precedes breaking onset.…”

“…In experiments performed using clean water, Diorio, Liu & Duncan (2009) observed PCW formation on spilling breaking waves that were generated by dispersive focusing with characteristic wavelengths as large as m. Boettger et al. (2023) performed computational fluid dynamics (CFD) simulations of 2-D breaking waves, concluding that the effects of surface tension were negligible on the energetics of breaking onset and that small amounts of viscous dissipation occurred at the wave crest ( m, ). The studies we have referenced above examine a mixture of breaking and non-breaking waves.…”