HIGHER ORDER BOUSSINESQ-TYPE EQUATIONS FOR WATER WAVES ON UNEVEN BOTTOM

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HIGHER ORDER BOUSSINESQ-TYPE EQUATIONS FOR WATER WAVES ON UNEVEN BOTTOM

Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain. The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation. Taking the velocities on half relative water depth as the fundamental unknowns, terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution, with which the problem was closed. With enhancements of the finite order Taylor expansion for the velocity field, the application range of the present model was extended to the slope bottom which is not so mild. For linear properties, some validation computations of linear shoaling and Booij's tests were carried out. The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents. All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.

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作 者: WANG Ben-long LIU Hua  
作者单位:Department of Engineering Mechanics, Shanghai Jiaotong University,Shanghai 200030, P. R. China 
刊 名:应用数学和力学(英文版)  EI SCI
英文刊名:APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION) 
年,卷(期):2005 26(6) 
分类号:O353.2 
关键词:higher order Boussinesq model   wave-current interaction   uneven bottom  
机标关键词:free surfaceexact solutionsurface boundary conditionswater depththeoretical solutionBoussinesq equationsnumerical solutionswave propagationTaylor expansionLaplace equationvelocity fieldtime domainrange of 
基金项目:国家自然科学基金,Special Fund for PhD Program of Education Ministry of China 
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