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Mathematical Problems in Engineering
Volume 2013, Article ID 160749, 11 pages
http://dx.doi.org/10.1155/2013/160749
Research Article

Alternative Forms of Enhanced Boussinesq Equations with Improved Nonlinearity

1State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
2National Marine Environment Monitoring Center, State Oceanic Administration, Dalian 116023, China
3Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province, Changsha 41004, China
4Civil Engineering Department, University of Dundee, Dundee DD1 4HN, UK

Received 15 October 2012; Revised 1 March 2013; Accepted 9 March 2013

Academic Editor: Shihua Li

Copyright © 2013 Kezhao Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose alternative forms of the Boussinesq equations which extend the equations of Madsen and Schäffer by introducing extra nonlinear terms during enhancement. Theoretical analysis shows that nonlinear characteristics are considerably improved. A numerical implementation of one-dimensional equations is described. Three tests involving strongly nonlinear evolution, namely, regular waves propagating over an elevated bar feature in a tank with an otherwise constant depth, wave group transformation over constant water depth, and nonlinear shoaling of unsteady waves over a sloping beach, are simulated by the model. The model is found to be effective.