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 language English (US) 320-325 6 Applied Mathematics Letters 86 https://doi.org/10.1016/j.aml.2018.07.011 Published - 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

• Wavelengths

ASJC Scopus subject areas

• Applied Mathematics

Cite this

title = "A boundary layer approach to creeping waves",
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.",
keywords = "Wavelengths",
author = "Matkowsky, {Bernard J}",
year = "2018",
month = "12",
day = "1",
doi = "10.1016/j.aml.2018.07.011",
language = "English (US)",
volume = "86",
pages = "320--325",
journal = "Applied Mathematics Letters",
issn = "0893-9659",
publisher = "Elsevier Limited",

}

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

Research output: Contribution to journalArticle

TY - JOUR

T1 - A boundary layer approach to creeping waves

AU - Matkowsky, Bernard J

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

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.

KW - Wavelengths

UR - http://www.scopus.com/inward/record.url?scp=85050618490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050618490&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2018.07.011

DO - 10.1016/j.aml.2018.07.011

M3 - Article

VL - 86

SP - 320

EP - 325

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -