A Unified Breaking Onset Criterion for Surface Gravity Water Waves in Arbitrary Depth

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.

Low-order Boussinesq models based on coordinate series expansions

“…Physical velocities expressed at fixed z elevations would be found by determining the σ value at the desired z and local values of h(x) and η(x, t), after which the horizontal velocity in physical coordinates is given by u = u α + ∇φ 2 σ (z) 2 + 2σφ 2 ∇σ . On the other hand, the model described here provides a natural setting for determining quantities at the free surface, as in, for example, the determination of wave breaking criteria based on values of the horizontal particle velocity at the free surface (Barthelemy et al 2018;Derakhti et al 2020). We conclude that trough instability is not an intrinsic feature of FNBTE and can be eliminated by derivations that produce equations with total layer depth as the only measure of layer thickness in dispersive term coefficients.…”

A New Probabilistic Wave Breaking Model for Dominant Wind-sea Waves Based on the Gaussian

“…For the data investigated here, such underestimation did not result in a high mean absolute error (MAE) and, in fact, our model had one of the lowest MAE. Recent results of Barthelemy et al (2018), Derakhti et al (2020) and Varing et al (2020) showed that waves with horizontal fluid velocity that exceeds 0.85 times the phase velocity will inevitably break. These results suggest that the breaking threshold derived from Cokelet (1977) in Section 2.3 could be reduced by ≈15%.…”

“…Recently, Barthelemy et al (2018) found and Derakhti et al (2020) confirmed via numerical simulations that waves will inevitably start to break shortly after u c exceeds 0.85 in deep and shallow water. Further numerical simulations showed that wave breaking occurs when the maximum orbital velocity (u max ) equals c somewhere along the wave profile and not necessarily at the wave crest (Varing et al, 2020).…”

“…However, Phillips' (1985) framework remains controversial, particularly regarding its practical application, given that different interpretations of his concepts can generate differences of several orders of magnitude in the calculations of Λ(c)dc and its moments (Banner et al, 2014). For a detailed review of commonly used parametric wave breaking models please refer to Appendix A. Interestingly, while the ratio between the horizontal orbital velocity at the crest (u) to wave phase speed (c) appears the most reliable parameter to determine wave breaking occurrence (Saket et al, 2017;Barthelemy et al, 2018;Derakhti et al, 2020;Varing et al, 2020), it was not used by any of the approaches mentioned above. This paper provides a new promising wave breaking model by revisiting Rice (1944) and Longuet-Higgins (1957) statistical descriptions of Gaussian processes (that is, for linear waves) to obtain the theoretical joint probability density between c and u (p(c, u)).…”

A New Probabilistic Wave Breaking Model for Dominant Wind‐Sea Waves Based on the Gaussian Field Theory

“…For the data investigated here, such underestimation did not result in a high MAE and, in fact, our model had one of the lowest MAE. Recent results of Barthelemy et al (2018), Derakhti et al (2020), andVaring et al (2020) showed that waves with the horizontal fluid velocity that exceeds 0.85 times the phase velocity will inevitably break. These results suggest that the breaking threshold derived from Cokelet (1977) in Section 2.3 could be reduced by ≈15%.…”