Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Abstract

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.

Air entrainment and bubble statistics in breaking waves

“…While LES solves the large scales directly, strong asumptions are needed for the subgrid-scale turbulent bubbly flow closures, e.g. assuming a bubble size distribution (Shi et al 2010;Liang et al 2011Liang et al , 2012Derakhti & Kirby 2014). 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). They are indeed necessary to investigate bubble and spray formation, which are fundamentally three-dimensional processes.…”

Are breaking waves, bores, surges and jumps the same flow?

“…2 approach (Drew, 1983). Two-fluid models are used to model the polydisperse two-fluid bubbly flow based on mixture theory (Carrica et al 1999;Moraga et al, 2008, Shi et al, 2010Ma et al 2011;Derakhti & Kirby, 2014). A first attempt to use a continuum type model for studying bubbly flow under surface breaking waves was made by Shi et al (2010).…”

“…Discrepancies between observations and model behaviour were nevertheless reported. Based on the works of Ma et al (2011), Derakhti and Kirby (2014) used an Eulerian-Eulerian polydisperse two-fluid model in an LES framework. Detailed overviews on methods and models for CFD of multiphase flows can be found in textbooks (Drew and Passman, 1999;Crowe et al 2011).…”

“…The large volumes of air in bubbles rapidly evolve into a distribution of bubble sizes which interacts with liquid turbulence and organised motions. The motion of bubbles relative to the liquid causes velocity fluctuations in the water column and increases the energy of liquid motion at the scales comparable with the bubble diameter (Derakhti and Kirby, 2014). Bubble plume kinematics and dynamics, and the structure of the turbulent bubbly flow under breaking waves constitute critical information to be taken into account for an accurate description of the wave breaking process (Melville 1996).…”