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

Citation:
Pizzo, N, Melville WK.  2019.  Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model. Journal of Fluid Mechanics. 873:238-259.

Date Published:

2019/08

Keywords:

compact equation, energy-dissipation, evolution, finite-amplitude, generation, instabilities, mechanics, modulation, momentum flux, physics, stability, surface gravity waves, threshold, wave breaking

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 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.

Notes:

n/a

Website

DOI:

10.1017/jfm.2019.428

Scripps Publication ID:

Pii s0022112019004282