A new definition of the kinematic breaking onset criterion validated with solitary and quasi-regular waves in shallow water

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). Although the relationship u c provides a solid physical background to establish the onset of wave breaking, this approach has never been applied to spectral wave models because it requires phaseresolving the wave field.…”

“…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)).…”

Wave Breaking in Undular Bores with Shear Flows

“…The constant vorticity is = −0.2213 and the bore strength is 0.307 criterion has been shown to pinpoint the commencement of wave breaking in various situations. In particular, the criterion was shown to perform well in deep water in [29,49], and in shallow water both on flat bathymetry [25] and on a sloping beach [27,50]. In some situations where the kinematic breaking criterion performs poorly, the problem can be ascribed to the difficulty of accurately finding the phase velocity of the waves from measurements [45], and the directionality of the waves in threedimensional situations [53].…”

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

“…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 (Barthelemy et al, 2018;Derakhti et al, 2020;Saket et al, 2017;Varing et al, 2020), it was not used by any of the approaches mentioned above. This study provides a new promising wave breaking model by revisiting Rices ' (1944) and Longuet-Higgins' (1957) statistical descriptions of Gaussian processes (i.e., for linear waves) to obtain the theoretical joint probability density between c and u (p(c, u)).…”