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Existence of edge waves along three-dimensional periodic structures

Published online by Cambridge University Press:  06 July 2010

SERGEY A. NAZAROV  and
JUHA H. VIDEMAN
SERGEY A. NAZAROV
Affiliation:
Institute of Mechanical Engineering Problems, Russian Academy of Sciences, VO, Bol'shoi pr., 61, 199178 St. Petersburg, Russia
JUHA H. VIDEMAN*
Affiliation:
CEMAT/Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
*
†Email address for correspondence: videman@math.ist.utl.pt
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Abstract

Existence of edge waves travelling along three-dimensional periodic structures is considered within the linear water-wave theory. A condition ensuring the existence is derived by analysing the spectrum of a suitably defined trace operator. The sufficient condition is a simple inequality comparing a weighted volume integral, taken over the submerged part of an element in the infinite array of identical obstacles, to the area of the free surface pierced by the obstacle. Various examples are given, and the results are extended to edge waves along periodic coastlines and over a periodically varying ocean floor.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 659 , 25 September 2010 , pp. 225 - 246
Copyright
Copyright © Cambridge University Press 2010

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