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Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model

Published online by Cambridge University Press:  24 June 2019

Nick Pizzo Open the ORCID record for Nick Pizzo [Opens in a new window]  and
W. Kendall Melville
Nick Pizzo*
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92037, USA
W. Kendall Melville
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92037, USA
*
†Email address for correspondence: npizzo@ucsd.edu
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Abstract

Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrödinger equation of Dysthe (Proc. R. Soc. Lond. A, vol. 369 (1736), 1979, pp. 105–114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of $\unicode[STIX]{x1D716}$ and $\unicode[STIX]{x1D6E5}$, for $\unicode[STIX]{x1D716}$ the linear prediction of the maximum slope at focusing and $\unicode[STIX]{x1D6E5}$ the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of $\unicode[STIX]{x1D716}-\unicode[STIX]{x1D6E5}$ phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air–sea interaction processes is discussed.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 238 - 259
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Copyright
© 2019 Cambridge University Press 

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