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We revisit the classical but as yet unresolved problem of predicting the strength of breaking 2-D and 3-D gravity water waves, as quantified by the amount of wave energy dissipated per breaking event. Following Duncan ( J. Fluid Mech. , vol. 126, 1983, pp. 507–520), the wave energy dissipation rate per unit length of breaking crest may be related to the fifth moment of the wave speed and the non-dimensional breaking strength parameter $$b$$ . We use a finite-volume Navier–Stokes solver with large-eddy simulation resolution and volume-of-fluid surface reconstruction (Derakhti & Kirby, J. Fluid Mech. , vol. 761, 2014 a , pp. 464–506; J. Fluid Mech. , vol. 790, 2016, pp. 553–581) to simulate nonlinear wave evolution, with a strong focus on breaking onset and postbreaking behaviour for representative cases of wave packets with breaking due to dispersive focusing and modulational instability. The present study uses these results to investigate the relationship between the breaking strength parameter $$b$$ and the breaking onset parameter $$B$$ proposed recently by Barthelemy et al. ( J. Fluid Mech. , vol. 841, 2018, pp. 463–488). The latter, formed from the local energy flux normalized by the local energy density and the local crest speed, simplifies, on the wave surface, to the ratio of fluid speed to crest speed. Following a wave crest, when $$B$$ exceeds a generic threshold value at the wave crest (Barthelemy et al. 2018), breaking is imminent. We find a robust relationship between the breaking strength parameter $$b$$ and the rate of change of breaking onset parameter $$\text{d}B/\text{d}t$$ at the wave crest, as it transitions through the generic breaking onset threshold ( $$B\sim 0.85$$ ), scaled by the local period of the breaking wave. This result significantly refines previous efforts to express $$b$$ in terms of a wave packet steepness parameter, which is difficult to define robustly and which does not provide a generically accurate forecast of the energy dissipated by breaking.more » « less
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Derakhti, Morteza; Kirby, James T.; Banner, Michael L.; Grilli, Stephan T.; Thomson, Jim (, Journal of Geophysical Research: Oceans)Abstract We investigate the validity and robustness of the Barthelemy et al. (2018,https://doi.org/10.1017/jfm.2018.93) wave‐breaking onset prediction framework for surface gravity water waves in arbitrary water depth, including shallow water breaking over varying bathymetry. We show that the Barthelemy et al. (2018) breaking onset criterion, which they validated for deep and intermediate water depths, also segregates breaking crests from nonbreaking crests in shallow water, with subsequent breaking always following the exceedance of their proposed generic breaking threshold. We consider a number of representative wave types, including regular, irregular, solitary, and focused waves, shoaling over idealized bed topographies including an idealized bar geometry and a mildly to steeply sloping planar beach. Our results show that the new breaking onset criterion is capable of detecting single and multiple breaking events in time and space in arbitrary water depth. Further, we show that the new generic criterion provides improved skill for signaling imminent breaking onset, relative to the available kinematic or geometric breaking onset criteria in the literature. In particular, the new criterion is suitable for use in wave‐resolving models that cannot intrinsically detect the onset of wave breaking.more » « less
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