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.

We examine how Eulerian statistics of wave breaking and associated turbulence dissipation rates in a field of intermittent events compare with those obtained from sparse Lagrangian sampling by surface following drifters. We use a polydisperse two-fluid model with large-eddy simulation (LES) resolution and volume-of-fluid surface reconstruction (VOF) to simulate the generation and evolution of turbulence and bubbles beneath short-crested wave breaking events in deep water. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. Eulerian statistics are obtained from the numerical results, which are available on a fixed grid. Next, we sample the LES/VOF model results with a large number of virtual surface-following drifters that are initially distributed in the numerical domain, regularly or irregularly, before each breaking event. Time-averaged Lagrangian statistics are obtained using the time series sampled by the virtual drifters. We show that convergence of statistics occurs for signals that have minimum length of approximately 1000–3000 wave periods with randomly spaced observations in time and space relative to three-dimensional breaking events. We further show important effects of (i) extent of measurements over depth and (ii) obscuration of velocity measurements due to entrained bubbles, which are the two typical challenges in most of the available in situ observations of upper ocean wave breaking turbulence. An empirical correction factor is developed and applied to the previous observations of Thomson et al. Applying the new correction factor to the observations noticeably improves the inferred energy balance of wind input rates and turbulence dissipation rates. Finally, both our simulation results and the corrected observations suggested that the total wave breaking dissipation rates have a nearly linear relation with active whitecap coverage.

We present a systematic study of the influence on tsunami waves generated by the uplift of a rectangular plug, of the rise time of the deformation, and of its topographic details (e.g., the presence of a sill). We are motivated by the fact that most simulation codes use an instantaneous deformation of a flat ocean floor as an initial condition of the problem, although Hammack (1973, http://resolver.caltech.edu/CaltechAUTHORS:HAMjfm73) performed pioneering laboratory studies as well as analytical computations featuring variable rise times. Here, we consider three 2‐D source shapes, including a flat seafloor, a simple elevated piston, and additional trapezoidal sill on top of it, all with variable rise times, and simulate the resulting waves using the fully nonlinear smooth particle hydrodynamic model graphics processing unit smooth particle hydrodynamic. We validate our results against Hammack's (1973) laboratory measurements and analytical results. We find that a relatively large sill, with height and width of more than half of the local depth and width of the source, has a profound effect on the spatiotemporal structure of the generated free surface wavefield. Specifically, we show that the maximum water surface elevation over the source region is not always the same as the bottom displacement, as assumed in most tsunami propagation models. Next, we obtain simple scaling relationships to predict the maximum height of the generated tsunami over and outside the source, based on the geometry of the sill and the nondimensional bed rise time. Last, we show that inertial effects may lead to an initial free surface displacement over the generation region greater than the maximum vertical displacement of the displaced seabed.

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, 2014a, 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 and the breaking onset parameter 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 dB/dt at the wave crest, as it transitions through the generic breaking onset threshold (B ~ 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.