Predicting the Onset and Strength of Breaking of Surface Gravity Waves from Deep to Shallow Water

The problem of predicting both the location and form (or strength) of breaking remains an open problem for surface gravity water waves in all depths from the deep ocean to the nearshore. Recently, Barthelemy et al (2018) have shown, based on numerical experiments with a BEM model, that the onset of breaking is guaranteed for wave crests passing a threshold value of the canonical ratio B = U/C, where U is the horizontal fluid velocity at the crest in the direction of crest propagation, and C is the translation speed of the crest. Barthelemy et al (2018) find that the threshold value is close to B=0.85, which is suggested as a precursor to breaking occurring before the classic B = 1. This threshold has been validated for intermediate depth and deep water waves using LES/VOF calculations (Derakhti et al, 2018) and laboratory experiments (Saket et al, 2017). During their study, Derakhti et al (2018) showed that the dissipation rate in individual breaking events can be predicted by the rate of change dB/dt at the time of passage through the breaking onset threshold, thus providing a prediction of whitecap dissipation based on local properties of highest wave crests. In the present study, we turn to the case of depth-limited breaking in shallow water. We establish the consistency between BEM and LES/VOF computations for shoaling solitary waves, and then establish that the threshold value B=0.85 also holds in shallow water and thus is robust for all water depths. We then examine the problem of predicting the initial rate of energy dissipation (and thus breaker type) based on the approach of Derakhti et al (2018). Preliminary results indicate that a robust estimate of energy dissipation rate may also be made in shallow water, providing a means for describing breaking that does not depend on parameters involving beach slope. Analysis of the scaling parameter b in the Duncan/Phillips formulation extends the framework of Drazen et al (2008), replacing dependence on wave slope S with dependence on a wave Froude number F = ga/c^2, which is asymptotic to S in deep water and to a/h in shallow water. Implications for the specification of breaking criteria in phase resolved wave models are discussed.