A boundary layer approach to creeping waves

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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.

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

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Keywords

  • Wavelengths

ASJC Scopus subject areas

  • Applied Mathematics

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