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On step approximations for water-wave problems

Published online by Cambridge University Press:  26 April 2006

D. V. Evans and
C. M. Linton
D. V. Evans
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
C. M. Linton
Affiliation:
Department of Mathematical Sciences, Loughborough University of Technology, Leicestershire, LE11 3TU, UK
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Abstract

The scattering of water waves by a varying bottom topography is considered using two-dimensional linear water-wave theory. A new approach is adopted in which the problem is first transformed into a uniform strip resulting in a variable free-surface boundary condition. This is then approximated by a finite number of sections on which the free-surface boundary condition is assumed to be constant. A transition matrix theory is developed which is used to relate the wave amplitudes at ±∞. The method is checked against examples for which the solution is known, or which can be computed by alternative means. Results show that the method provides a simple accurate technique for scattering problems of this type.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994, pp. 229 - 249
Copyright
© 1994 Cambridge University Press

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