On modifications of the Zakharov equation for surface gravity waves

Author:

Stiassnie Michael,Shemer Lev

Abstract

The Zakharov integral equation for surface gravity waves is modified to include higher-order (quintet) interactions, for water of constant (finite or infinite) depth. This new equation is used to study some aspects of class I (4-wave) and class II (5-wave) instabilities of a Stokes wave.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference20 articles.

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2. Zakharov, V. E. & Kharitonov, V. G. 1970 Instability of monochromatic waves on the surface of a liquid of arbitrary depth.J. Appl. Mech. Tech. Phys. (Engl. Transl.)11,741–751.

3. Dysthe, K. B. 1980 Note on a modification to the nonlinear Schrödinger equation for application to deep water waves.Proc. R. Soc. Lond. A 369,105–114.

4. Janssen, P. A. E. M. 1983 On a fourth-order envelope equation for deep-water waves.J. Fluid Mech. 126,1–11.

5. Longuet-Higgins, M. S. 1976 On the nonlinear transfer of energy in the peak of a gravity-wave spectrum: a simplified model.Proc. R. Soc. Lond. A 347,311–328.

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