Liquid–bubble interaction, especially in complex two-phase bubbly flow under breaking waves, is still poorly understood. In the present study, we perform a large-eddy simulation using a Navier–Stokes solver extended to incorporate entrained bubble populations, using an Eulerian–Eulerian formulation for a polydisperse bubble phase. The volume-of-fluid method is used for free-surface tracking. We consider an isolated unsteady deep water breaking event generated by a focused wavepacket. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. The model is shown to predict free-surface evolution, mean and turbulent velocities, and integral properties of the entrained dispersed bubbles fairly well. We investigate turbulence modulation by dispersed bubbles as well as shear- and bubble-induced dissipation, in both spilling and plunging breakers. We find that the total bubble-induced dissipation accounts for more than 50 % of the total dissipation in the breaking region. The average dissipation rate per unit length of breaking crest is usually written as $b{\it\rho}g^{-1}c_{b}^{5}$, where ${\it\rho}$ is the water density, $g$ is the gravitational acceleration and $c_{b}$ is the phase speed of the breaking wave. The breaking parameter, $b$, has been poorly constrained by experiments and field measurements. We examine the time-dependent evolution of $b$ for both constant-steepness and constant-amplitude wavepackets. A scaling law for the averaged breaking parameter is obtained. The exact two-phase transport equation for turbulent kinetic energy (TKE) is compared with the conventional single-phase transport equation, and it is found that the former overpredicts the total subgrid-scale dissipation and turbulence production by mean shear during active breaking. All of the simulations are also repeated without the inclusion of a dispersed bubble phase, and it is shown that the integrated TKE in the breaking region is damped by the dispersed bubbles by approximately 20 % for a large plunging breaker to 50 % for spilling breakers. In the plunging breakers, the TKE is damped slightly or even enhanced during the initial stage of active breaking.

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.

Breaking waves on the ocean surface transfer energy and momentum into currents and turbulence. What is less well understood, however, is the associated total loss of wave energy and momentum flux. Further, finding a robust and universal diagnostic parameter that determines the onset of breaking and its strength is still an open question. Derakhti & Kirby (J. Fluid Mech., vol. 761, 2014, pp. 464-506) have recently studied bubble entrainment and turbulence modulation by dispersed bubbles in isolated unsteady breaking waves using large-eddy simulation. In this paper, a new diagnostic parameter ξ (t) is defined based on that originally proposed by Song & Banner (J. Phys. Oceanogr., vol. 32, 2002, pp. 2541-2558, and it is shown that using a threshold value of ξ th = 0.05, the new dynamic criteria is capable of detecting single and multiple breaking events in the considered packets. In addition, the spatial variation of the total energy and momentum flux in intermediate-and deep-water unsteady breaking waves generated by dispersive focusing is investigated. The accuracy of estimating these integral measures based on free surface measurements and using a characteristic wave group velocity is addressed. It is found that the new diagnostic parameter just before breaking, ξ b , has a strong linear correlation with the commonly used breaking strength parameter b, suggesting that ξ b can be used to parameterize the averaged breaking-induced dissipation rate and its associated energy flux loss. It is found that the global wave packet time and length scales based on the spectrally weighted packet frequency proposed by Tian et al. (J. Fluid Mech., vol. 655, 2010, pp. 217-257), are the reasonable estimations of the time and length scales of the carrier wave in the packet close to the focal/break point. A global wave steepness, S s , is defined based on these spectrally weighted scales, and its spatial variation across the breaking region is examined. It is shown that the corresponding values of S s far upstream of breaking, S s0 , have a strong linear correlation with respect to b for the considered focused wave packets. The linear relation, however, cannot provide accurate estimations of b in the range b < 5 × 10 −3 . A new scaling law given by b = 0.3(S s0 − 0.07) 5/2 , which is consistent with inertial wave dissipation scaling of Drazen et al. (J. Fluid Mech., vol. 611, 2008, pp. 307-332), is shown to be capable of providing accurate estimates of b in the full range of breaking intensities, where the scatter of data in the new formulation is significantly decreased compared with that proposed by Romero et al. (J. Furthermore, we examine nonlinear interactions of different components in a focused wave packet, noting interactive effect on a characteristic wave group velocity in both † Email address for correspondence: derakhti@udel.edu 554 M. Derakhti and J. T. Kirby non-breaking and breaking packets. Phase locking between spectral components is observed in the breaking region as well, and subsequently illustrated by calcula...

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 $b$ 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.

This study investigates short‐crested waves in the surf zone by using the mesh‐free Smoothed Particle Hydrodynamics model, GPUSPH. The short‐crested waves are created by generating intersecting wave trains in a numerical wave basin with a beach. We first validate the numerical model for short‐crested waves by comparison with large‐scale laboratory measurements. Then short‐crested wave breaking over a planar beach is studied comprehensively. We observe rip currents as discussed in Dalrymple (1975) and undertow created by synchronous intersecting waves. The wave breaking of the short‐crested wavefield created by the nonlinear superposition of intersecting waves and wave‐current interaction result in the formation of isolated breakers at the ends of breaking wave crests. Wave amplitude diffraction at these isolated breakers gives rise to an increase in the alongshore wave number in the inner surf zone. Moreover, 3‐D vortices and multiple circulation cells with a rotation frequency much lower than the incident wave frequency are observed across the outer surf zone to the beach. Finally, we investigate vertical vorticity generation under short‐crested wave breaking and find that breaking of short‐crested waves generates vorticity as pointed out by Peregrine (1998). Vorticity generation is not only observed under short‐crested waves with a limited number of wave components but also under directional wave spectra.