Fully Nonlinear Model for Water Wave Propagation from Deep to Shallow Waters
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 138, Issue 5
Abstract
A set of fully nonlinear Boussinessq-type equations (BTEs) with improved linear and nonlinear dispersive performance is presented. The highest order of the derivatives is three in the equations, and they use the minimum number of unknowns: the free surface elevation and the horizontal velocity at a certain depth. The equations allow reduction of the errors both in linear frequency dispersion and shoaling below 0.30% for , and below 2.2% for , with as the wave number and as the water depth. The weakly nonlinear performance is also improved for . A simple fourth-order explicit numerical scheme is presented to test the linear and nonlinear behavior of the model equations against analytical and experimental results.
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Acknowledgments
The writers received financial support from MICINN Project CTM2010-16915. A. Galan is supported by funding from CSIC through the JAE-Pre Program. G. Simarro is supported by the Spanish government through Ramón y Cajal program. P.L-F. Liu received financial support from the National Science Foundation (NSF). Professor Andrés Encinas’ helpful comments are greatly acknowledged.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 138 • Issue 5 • September 2012
Pages: 362 - 371
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Mar 15, 2011
Accepted: Dec 5, 2011
Published online: Dec 7, 2011
Published in print: Sep 1, 2012
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