Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

Abstract

The scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier-Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

Air entrainment and bubble statistics in breaking waves

“…Just after the initial entrainment of the cavity, it is connected to the main ambient gas phase by thin filaments of air (b). These filaments of air are commonly observed under breaking waves in surf movies and were recently discussed in detail by Lubin & Glockner (2015). Later on, the cavity starts to collapse, creating both large and small bubbles (c,d).…”

“…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?

“…All authors reported that the energy of the waves was dissipated during the early stages of the breaking events, due to the splash-up kinematics, turbulence generation and air entrainment process. The kinetic energy was found to decay as t -1 , both experimentally (Rapp and Melville, 1990;Melville, 1991, 1992;Melville et al 2002;Drazen et al, 2008) and numerically (Chen et al, 1999;Lubin et al, 2006;Iafrati, 2009Iafrati, , 2011Lakehal andLiovic, 2011, Lubin andGlockner, 2015). The same decay rate was observed for all breaker types (spilling, weak plunging and plunging) (Melville et al 2002, Lubin andGlockner 2015), while similar integral properties in terms void fraction were comparable for different types of breaking waves (Cox and Shin, 2003;Blenkinsopp and Chaplin, 2007).…”

“…What is better characterised however, is the volume of air trapped by the initial contact of the jet with the wave face, which has been numerically simulated, and its shape has been successfully modelled, at least for a limited set of conditions (e.g. Lubin and Glockner 2015). However, the processes that follow the initial contact are only known qualitatively for the majority of the breaking conditions, and thus still require further study in order to acquire improved physical understanding.…”

“…The kinetic energy was found to decay as t -1 , both experimentally (Rapp and Melville, 1990;Melville, 1991, 1992;Melville et al 2002;Drazen et al, 2008) and numerically (Chen et al, 1999;Lubin et al, 2006;Iafrati, 2009Iafrati, , 2011Lakehal andLiovic, 2011, Lubin andGlockner, 2015). The same decay rate was observed for all breaker types (spilling, weak plunging and plunging) (Melville et al 2002, Lubin andGlockner 2015), while similar integral properties in terms void fraction were comparable for different types of breaking waves (Cox and Shin, 2003;Blenkinsopp and Chaplin, 2007). Locations of air entrapment in the roller can be identified at the toe of the advancing roller, and on the whole interface of the roller, where multiple splashes are observed (Miller, 1976;Bonmarin, 1989;Nadaoka et al, 1989;Lin and Hwung, 1992;Rojen and Loewen, 2010;Lim et al, 2015).…”