A boundary layer approach to creeping waves

Research output: Contribution to journalArticle

Abstract

We consider the eigenvalue problem for the Laplace operator in a two dimensional domain exterior to a smooth, closed convex curve C, on which the eigenfunctions are to vanish. Waves whose wavelengths λ are very small may be viewed as particles traveling along specific paths termed rays, along which the waves propagate. Small wavelengths λ correspond to large wavenumbers k=[Formula presented], which are the eigenvalues. Therefore, we restrict attention to the consideration of large eigenvalues. If the amplitude of the eigenfunctions is appreciable only in a thin region attached to the boundary and is negligibly small beyond the layer, they correspond to creeping waves. We employ a boundary layer approach to the problem.

Original languageEnglish (US)
Pages (from-to)320-325
Number of pages6
JournalApplied Mathematics Letters
Volume86
DOIs
StatePublished - Dec 1 2018

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Boundary Layer
Boundary layers
Eigenvalues and eigenfunctions
Eigenfunctions
Wavelength
Convex Curve
Exterior Domain
Closed curve
Largest Eigenvalue
Laplace Operator
Eigenvalue Problem
Half line
Vanish
Eigenvalue
Path

Keywords

  • Wavelengths

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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abstract = "We consider the eigenvalue problem for the Laplace operator in a two dimensional domain exterior to a smooth, closed convex curve C, on which the eigenfunctions are to vanish. Waves whose wavelengths λ are very small may be viewed as particles traveling along specific paths termed rays, along which the waves propagate. Small wavelengths λ correspond to large wavenumbers k=[Formula presented], which are the eigenvalues. Therefore, we restrict attention to the consideration of large eigenvalues. If the amplitude of the eigenfunctions is appreciable only in a thin region attached to the boundary and is negligibly small beyond the layer, they correspond to creeping waves. We employ a boundary layer approach to the problem.",
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A boundary layer approach to creeping waves. / Matkowsky, Bernard J.

In: Applied Mathematics Letters, Vol. 86, 01.12.2018, p. 320-325.

Research output: Contribution to journalArticle

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AB - We consider the eigenvalue problem for the Laplace operator in a two dimensional domain exterior to a smooth, closed convex curve C, on which the eigenfunctions are to vanish. Waves whose wavelengths λ are very small may be viewed as particles traveling along specific paths termed rays, along which the waves propagate. Small wavelengths λ correspond to large wavenumbers k=[Formula presented], which are the eigenvalues. Therefore, we restrict attention to the consideration of large eigenvalues. If the amplitude of the eigenfunctions is appreciable only in a thin region attached to the boundary and is negligibly small beyond the layer, they correspond to creeping waves. We employ a boundary layer approach to the problem.

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