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On a unified breaking onset threshold for gravity waves in deep and intermediate depth water

Published online by Cambridge University Press:  23 February 2018

X. Barthelemy*
Affiliation:
School of Mathematics and Statistics, UNSW Sydney, NSW 2052, Australia Water Research Laboratory, School of Civil and Environmental Engineering, UNSW Sydney, 110 King Street, Manly Vale, NSW 2093, Australia
M. L. Banner
Affiliation:
School of Mathematics and Statistics, UNSW Sydney, NSW 2052, Australia
W. L. Peirson
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, UNSW Sydney, 110 King Street, Manly Vale, NSW 2093, Australia
F. Fedele
Affiliation:
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
M. Allis
Affiliation:
National Institute of Water and Atmospheric Research, Hamilton 3216, New Zealand
F. Dias
Affiliation:
School of Mathematics and Statistics, University College Dublin, Ireland
*
Email address for correspondence: x.barthelemy@unsw.edu.au

Abstract

We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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