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New solutions for the propagation of long water waves over variable depth

Published online by Cambridge University Press:  26 April 2006

Yinglong Zhang  and
Songping Zhu
Yinglong Zhang
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, NSW 2500, Australia
Songping Zhu
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, NSW 2500, Australia
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Abstract

Based on the linearized long-wave equation, two new analytical solutions are obtained respectively for the propagation of long surface gravity waves around a conical island and over a paraboloidal shoal. Having been intensively studied during the last two decades, these two problems have practical significance and are physically revealing for wave propagation over variable water depth. The newly derived analytical solutions are compared with several previously obtained numerical solutions and the accuracy of those numerical solutions is discussed. The analytical method has the potential to be used to find solutions for wave propagation over more natural bottom topographies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994 , pp. 391 - 406
Copyright
© 1994 Cambridge University Press

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