Boussinesq Model for Weakly Nonlinear Fully Dispersive Water Waves
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 135, Issue 5
Abstract
In the present work a new Boussinesq dispersive wave propagation model is proposed. The model is based on a system of equations expressed in terms of the free-surface elevation and the depth-averaged horizontal velocities. The approach is developed for fully dispersive and weakly nonlinear irregular waves propagating over any constant water depth in two horizontal dimensions, but it can also be applied in mildly sloping beaches with considerable accuracy. The model in its two-dimensional formulation involves in total five terms in each momentum equation, including the classical shallow water terms and only one frequency dispersion term. The latter is expressed through convolution integrals, which are estimated using appropriate impulse functions. The formulation is fully explicit in space and thus no inversion is required for the numerical solution. The model is applied to simulate the propagation of regular and irregular waves using a simple explicit scheme of finite differences. Numerical integration of a convolution integral is also required. The results of the simulations are compared with experimental data, as well as with linear and nonlinear wave theory. The comparisons show that the method is capable of simulating weakly nonlinear dispersive wave propagation over finite constant or slowly diminishing water depth in a satisfactory way.
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Acknowledgments
A part of this work was carried out by one of us (T.V.K.) within the framework of the project “Environmental Design of Coastal Protection Works using Advanced Numerical Models,” funded by the University of the Aegean’s Research Committee.
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Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 135 • Issue 5 • September 2009
Pages: 187 - 199
Copyright
© 2009 ASCE.
History
Received: Jan 23, 2007
Accepted: Mar 17, 2009
Published online: Aug 14, 2009
Published in print: Sep 2009
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