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

Published online by Cambridge University Press:  16 February 2015

P. Lubin  and
S. Glockner
P. Lubin*
Affiliation:
I2M, CNRS UMR 5295, Université de Bordeaux, 16 Avenue Pey-Berland, 33607 Pessac, France
S. Glockner
Affiliation:
I2M, CNRS UMR 5295, Université de Bordeaux, 16 Avenue Pey-Berland, 33607 Pessac, France
*
†Email address for correspondence: p.lubin@i2m.u-bordeaux1.fr
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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.

JFM classification

Waves/Free-surface Flows: Wave breaking Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 364 - 393
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Copyright
© 2015 Cambridge University Press 

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Lubin and Glockner supplementary movie

The generation and evolution of aerated vortex filaments is visualized using the phase function isosurface C = 0.5, to characterize the free-surface, and isocontours of the axial vorticity calculated in an axis x' tilted 50° from the horizontal axis x (ωx'=700 s-1 in red and ωx'=-1000 s-1 in orange). Shown is a 3D strip extracted from the whole numerical domain. The frame rate is 10 fps.

Download Lubin and Glockner supplementary movie(Video)
Video 9.8 MB

Lubin and Glockner supplementary movie

The generation and evolution of aerated vortex filaments is visualized using the phase function isosurface C = 0.5, to characterize the free-surface, and isocontours of the axial vorticity calculated in an axis x' tilted 50° from the horizontal axis x (ωx'=700 s-1 in red and ωx'=-1000 s-1 in orange). Shown is a 3D strip extracted from the whole numerical domain. The frame rate is 10 fps.

Download Lubin and Glockner supplementary movie(Video)
Video 19 MB

Lubin and Glockner supplementary movie

The generation and evolution of aerated vortex filaments are visualized using the phase function isosurface C = 0.5, to characterize the free-surface, and the Line Integral Convolution (LIC) calculated in the 2D plane (xz), to display the evolution of the flow. The celerity of the initial wave is subtracted to the longitudinal velocity component to be in a frame-of-reference moving with the wave. In the top right corner, movie 1 is inserted, showing the evolution of the vorticity at the same sampling time. The frame rate is 10 fps.

Download Lubin and Glockner supplementary movie(Video)
Video 9.1 MB

Lubin and Glockner supplementary movie

The generation and evolution of aerated vortex filaments are visualized using the phase function isosurface C = 0.5, to characterize the free-surface, and the Line Integral Convolution (LIC) calculated in the 2D plane (xz), to display the evolution of the flow. The celerity of the initial wave is subtracted to the longitudinal velocity component to be in a frame-of-reference moving with the wave. In the top right corner, movie 1 is inserted, showing the evolution of the vorticity at the same sampling time. The frame rate is 10 fps.

Download Lubin and Glockner supplementary movie(Video)
Video 9.9 MB

Lubin and Glockner supplementary movie

The evolution of the coherent vortex filaments underneath the breaking wave is visualized using the Q-criterion (green isosurface Q=1), to identify the vortex envelopes, and the blue phase function isosurface C=0.5, showing the air entrainment. Shown is a 3D view under the breaking wave, between t=0.1156 s and 0.2676 s. The frame rate is 15 fps.

Download Lubin and Glockner supplementary movie(Video)
Video 10.1 MB

Lubin and Glockner supplementary movie

The evolution of the coherent vortex filaments underneath the breaking wave is visualized using the Q-criterion (green isosurface Q=1), to identify the vortex envelopes, and the blue phase function isosurface C=0.5, showing the air entrainment. Shown is a 3D view under the breaking wave, between t=0.1156 s and 0.2676 s. The frame rate is 15 fps.

Download Lubin and Glockner supplementary movie(Video)
Video 21 MB