A high-order nonlinear envelope equation for gravity waves in finite-depth water View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-11

AUTHORS

A. V. Slunyaev

ABSTRACT

A third-order nonlinear envelope equation is derived for surface waves in finite-depth water by assuming small wave steepness, narrow-band spectrum, and small depth as compared to the modulation length. A generalized Dysthe equation is derived for waves in relatively deep water. In the shallow-water limit, one of the nonlinear dispersive terms vanishes. This limit case is compared with the envelope equation for waves described by the Korteweg-de Vries equation. The critical regime of vanishing nonlinearity in the classical nonlinear Schrödinger equation for water waves (when kh ≈ 1.363) is analyzed. It is shown that the modulational instability threshold shifts toward the shallow-water (long-wavelength) limit with increasing wave intensity. More... »

PAGES

926-941

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/1.2149072

DOI

http://dx.doi.org/10.1134/1.2149072

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040636233


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