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Capillary effects on wave breaking

Published online by Cambridge University Press:  25 March 2015

Luc Deike ,
Stephane Popinet  and
W. Kendall Melville
Luc Deike*
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA National Institute for Water and Atmospheric Research, P.O. Box 14901, Kilbirnie, Wellington 6003, New Zealand
Stephane Popinet
Affiliation:
National Institute for Water and Atmospheric Research, P.O. Box 14901, Kilbirnie, Wellington 6003, New Zealand Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d’Alembert, F-75005 Paris, France
W. Kendall Melville
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number, $\mathit{Bo}$, and the initial wave steepness, ${\it\epsilon}$, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of $({\it\epsilon},\mathit{Bo})$ is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness ${\it\epsilon}_{c}$ defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as ${\it\epsilon}\sim (1+\mathit{Bo})^{-1/3}$. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter $b$ is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Waves/Free-surface Flows: Wave breaking Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 541 - 569
Copyright
© 2015 Cambridge University Press 

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