Long nonlinear waves in resonance with topography

Jongho Choi; Paul A. Milewski

doi:10.1111/1467-9590.00229

Long nonlinear waves in resonance with topography

Jongho Choi
, Paul A. Milewski

Eberly College of Science

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The evolution of periodic long surface waves over a periodic bottom topography resonant with the waves is studied. Coupled Korteweg-de Vries equations are derived and describe the evolution in terms of interaction between right- and left-traveling waves. The coupling arises from the cumulative effect of wave scattering. We discuss the various conserved quantities of the system and compute solutions for the initial value problem and for the time-periodic problem of fluid "sloshing̊ in a tank. Some three-dimensional extensions are discussed.

Original language	English (US)
Pages (from-to)	21-47
Number of pages	27
Journal	Studies in Applied Mathematics
Volume	110
Issue number	1
DOIs	https://doi.org/10.1111/1467-9590.00229
State	Published - Jan 2003

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1111/1467-9590.00229

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title = "Long nonlinear waves in resonance with topography",

abstract = "The evolution of periodic long surface waves over a periodic bottom topography resonant with the waves is studied. Coupled Korteweg-de Vries equations are derived and describe the evolution in terms of interaction between right- and left-traveling waves. The coupling arises from the cumulative effect of wave scattering. We discuss the various conserved quantities of the system and compute solutions for the initial value problem and for the time-periodic problem of fluid {"}sloshing̊ in a tank. Some three-dimensional extensions are discussed.",

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AB - The evolution of periodic long surface waves over a periodic bottom topography resonant with the waves is studied. Coupled Korteweg-de Vries equations are derived and describe the evolution in terms of interaction between right- and left-traveling waves. The coupling arises from the cumulative effect of wave scattering. We discuss the various conserved quantities of the system and compute solutions for the initial value problem and for the time-periodic problem of fluid "sloshing̊ in a tank. Some three-dimensional extensions are discussed.

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Long nonlinear waves in resonance with topography

Abstract

All Science Journal Classification (ASJC) codes

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