A numerical study of breaking waves

Song, Chiyoon; Sirviente, A. I.

doi:10.1063/1.1738417

Cited by 39 publications

(40 citation statements)

References 57 publications

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“…wave focusing, modulation instability), and the Stokes waves used here have a breaking threshold higher than the one observed in laboratory experiments using focusing wave packet. Second, the low values of the entrained air in the DNS for small slopes can also be related to the relatively short wavelength of our breaking wave, λ = 0.24, and the influence of surface tension in the shape of the breaking wave, which reduces the amount of entrained air, as discussed in Song & Sirviente (2004); Liu & Duncan (2003; Kiger & Duncan (2012).…”

Section: Volume Scaling Of the Dns And Available Experimental Datamentioning

confidence: 95%

“…In contrast, DNS is an appealing tool since no parametrizations are used to solve the multi-phase flow. The DNS has been limited to two-dimensional evolution of periodic unstable waves with relatively small wavelengths, providing numerical data on wave dissipation and the splashing processes (Chen et al 1999;Song & Sirviente 2004;Iafrati 2011;Deike et al 2015). Three dimensional simulations of breaking waves have recently become available, both DNS (Fuster et al 2009) and LES (Derakhti & Kirby 2014;Lubin & Glockner 2015).…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Air entrainment and bubble statistics in breaking waves

2016

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We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. The air-entrainment properties and bubble-size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N (r, t) = B(V 0 /2π)(ε(t − ∆τ )/W g)r −10/3 r −2/3 m during the active breaking stages, where ε(t − ∆τ ) is the time dependent turbulent dissipation rate, with ∆τ the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r m the maximum bubble radius, g gravity, V 0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described bȳ N (r) = B(1/2π)( l L c /W gρ)r −10/3 r −2/3 m , where l is the wave dissipation rate per unit length of breaking crest, ρ the water density and L c the length of breaking crest. Finally, the averaged total volume of entrained air,V , per breaking event can be simply related to l byV = B( l L c /W gρ), which leads to a relationship to a characteristic slope, S, of V ∝ S 5/2 . We propose a phenomenological turbulent bubble break-up model, based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

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Section: Volume Scaling Of the Dns And Available Experimental Datamentioning

confidence: 95%

Section: Numerical Simulationsmentioning

confidence: 99%

Air entrainment and bubble statistics in breaking waves

2016

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“…As summarized by Perlin et al (2012), most of the numerical simulations for deep water breaking waves are limited to the evolution of a periodic unstable wave train with relatively low-Reynolds numbers (∼ 10 4 ) and short wave lengths (< 0.3m) (Chen et al 1999, Song & Sirviente 2004, Lubin et al 2006, Iafrati 2009, 2011, Lubin & Glockner 2013. This artificial way of leading a wave train to breaking has an advantage in that it represents a more compact computational problem.…”

Section: Introductionmentioning

confidence: 99%

Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Derakhti

Kirby

2014

J. Fluid Mech.

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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.

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“…Periodic boundary conditions are used in the x-and y-directions. We note here that the use of the periodic boundary condition is a common practice in simulations of breaking waves [58][59][60][61][62][63][64], because the non-periodic condition would substantially increase the computational cost. The no-slip condition is imposed at the bottom.…”

Section: Introductionmentioning

confidence: 99%

“…The initial flow field is fully-developed wind turbulence over prescribed steep waves. Following the practice of many previous two-fluid numerical simulations of wave breaking [58][59][60][61][62][63][64], the initial wave geometry is given by the analytical solution of the third-order Stokes wave as:…”

Section: Introductionmentioning

confidence: 99%

Numerical Study on the Generation and Transport of Spume Droplets in Wind over Breaking Waves

et al. 2017

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Sea spray droplets play an important role in the momentum, heat and mass transfer in the marine atmospheric boundary layer. We have developed a new direct numerical simulation method to study the generation and transport mechanisms of spume droplets by wind blowing over breaking waves, with the wave breaking process taken into account explicitly. In this new computational framework, the air and water are simulated as a coherent system on fixed Eulerian grid with the density and viscosity varying with the fluid phase. The air-water interface is captured accurately using a coupled level-set and volume-of-fluid method. The trajectories of sea spray droplets are tracked using a Lagrangian particle-tracking method. The generation of droplets is captured by comparing the fluid particle velocity of water and the phase speed of the wave surface. From the simulation data, we obtain for the first time a detailed description of the instantaneous distribution of droplets at different stages of wave breaking. Furthermore, the time histories of the droplet number and its generation and disappearance rates are analyzed. Simulation cases with different parameters are performed to study the effects of wave age and wave steepness. The flow and droplet fields obtained from simulation provided a detailed physical picture of the problem of interest. It is found that plunging breakers generate more droplets than spilling breakers. Droplets are generated near the wave crest at young and intermediate wave ages, but at old wave ages, droplets are generated both near and behind the wave crest. It is also elucidated that the large-scale spanwise vortex induced by the wave plunging event plays an important role in suspending droplets. Our simulation result of the vertical profile of sea spray concentration is consistent with laboratory measurement reported in the literature.

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A numerical study of breaking waves

Cited by 39 publications

References 57 publications

Air entrainment and bubble statistics in breaking waves

Air entrainment and bubble statistics in breaking waves

Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Numerical Study on the Generation and Transport of Spume Droplets in Wind over Breaking Waves

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