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

TitleFocusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model
Publication TypeJournal Article
Year of Publication2019
AuthorsPizzo N., Melville W.K
Date Published2019/08
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000472630900001
Keywordscompact equation; energy-dissipation; evolution; finite-amplitude; generation; instabilities; mechanics; modulation; momentum flux; physics; stability; surface gravity waves; threshold; wave breaking

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 Schrodinger 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.

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