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A new approach to high-order Boussinesq models

Published online by Cambridge University Press:  25 November 1999

Y. AGNON ,
P. A. MADSEN  and
H. A. SCHÄFFER
Y. AGNON
Affiliation:
Civil Engineering, Technion, Haifa 32000, Israel
P. A. MADSEN
Affiliation:
Department of Mathematical, Modelling Technical University of Denmark, 2800 Lyngby, Denmark
H. A. SCHÄFFER
Affiliation:
Danish Hydraulic Institute, Agern Alle 5, 2970 Hørsholm, Denmark
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Abstract

An infinite-order, Boussinesq-type differential equation for wave shoaling over variable bathymetry is derived. Defining three scaling parameters – nonlinearity, the dispersion parameter, and the bottom slope – the system is truncated to a finite order. Using Padé approximants the order in the dispersion parameter is effectively doubled. A derivation is made systematic by separately solving the Laplace equation in the undisturbed fluid domain and then addressing the nonlinear free-surface conditions. We show that the nonlinear interactions are faithfully captured. The shoaling and dispersion components are time independent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 399 , 25 November 1999 , pp. 319 - 333
Copyright
© 1999 Cambridge University Press

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