Evolution of packets of surface gravity waves over smooth topography

E. S. Benilov, J. D. Flanagan, C. P. Howlin

Research output: Contribution to journalArticlepeer-review

Abstract

Weakly nonlinear packets of surface gravity waves over topography are governed by a nonlinear Schrödinger equation with variable coefficients. Using this equation and assuming that the horizontal scale of topography is much larger than the width of the packet, we show that, counter-intuitively, the amplitude of a shoaling packet decays, while its width grows. Such behaviour is a result of the fact that the coefficient of the nonlinear term in the topography-modified Schrödinger equation decreases with depth. Furthermore, there exists a critical depth, hcr, where this coefficient changes sign - if the packet reaches hcr, it disperses.

Original languageEnglish
Pages (from-to)171-181
Number of pages11
JournalJournal of Fluid Mechanics
Volume533
DOIs
Publication statusPublished - 25 Jun 2005

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