一种适用于非均匀地形的高阶Boussinesq水波模型

王本龙; 刘桦

一种适用于非均匀地形的高阶Boussinesq水波模型

王本龙,
刘桦

上海交通大学工程力学系,上海 200240

基金项目: 国家自然科学基金资助项目(10172058);教育部博士点研究基金资助项目(2000024817)

详细信息

作者简介:
王本龙(1977- ),男,黑龙江人,博士研究生;刘桦(联系人.Tel/Fax:+86-21-62933021;E-mail:hliu@sjtu.edu.cn).

中图分类号: O353.2
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- 文章访问数: 2908
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出版历程
- 收稿日期: 2003-07-21
- 修回日期: 2004-12-03
- 刊出日期: 2005-06-15

Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom

Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, P. R. China

摘要

摘要: 推导了适用于变地形情况的高阶Boussinesq波浪模型．该模型采用自由表面边界条件作为时间步进方程，利用势函数满足的Laplace方程的解析解形式建立了自由表面边界速度和底面边界速度之间的关系，使得问题封闭．以0.5倍相对水深处的速度为基本未知量，在对Laplace方程解析解进行级数求逆时保留水深梯度的高阶项，改进了速度场的Taylor展开式．对于线性特性，进行了线性浅化和Booij反射的验证性计算．为了检验有背景流动情况下拓展的Boussinesq模型的性态，对波-流相互作用问题进行了数值模拟．数值计算结果与现有理论解或其他完全势流的数值解吻合良好，表明该模型的应用范围可以扩展到含有非均匀变化地形的问题．
- 高阶Boussinesq方程 /
- 波流相互作用 /
- 变地形
Abstract: 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 not so mild slope bottom.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.
- higher order Boussinesq model /
- wave-current interaction /
- uneven bottom

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参考文献(12)

[1]	Madsen P A,Schffer H A.Higher-order Boussinesq-type equations for surface gravity waves: derivation and analysis[J].Phil Trans Roy Soc,London A,1998,(356)：3123—3184.
[2]	Gobbi M F,Kirby J T,Wei G.A fully nonlinear Boussinesq model for surface wave—Ⅱ:Extension to O(kh)4[J].J Fluid Mech,2000,(405)：181—210.
[3]	HONG Guang-wen.Higher order model of nonlinear and dispersive wave in water of varying depth with arbitrary sloping bottom[J].China Ocean Engineering,1997,11(3):243—260.
[4]	邹志利.含强水流高阶Boussinesq水波方程[J].海洋学报,2000,22(4)：41—50.
[5]	CHEN Qin,Madsen P A,Basco D R.Current effects on nonlinear interactions of shallow-water waves[J].Journal of Waterway, Port, Coastal, and Ocean Engineering,1999,125(4)：176—186. doi: 10.1061/(ASCE)0733-950X(1999)125:4(176)
[6]	Kristensen M K.Boussinesq equations and wave-current interaction[D].Master's thesis.International Research Center for Computed Hydrodynamics (ICCH) at Danish Hydraulic Institute,Denmark and ISVA,Technical University of Denmark,1995,130—142.
[7]	Madsen P A,Bingham H B,Liu H.A new Boussinesq method for fully nonlinear waves from shallow to deep water[J].J Fluid Mech,2002,(462)：1—30.
[8]	Wu T Y.A unified theory for modeling water waves[A].In:Advances in Applied Mechanics[C].Boston:Academic Press,2000,37:1—88.
[9]	Booij N.A note on the accuracy of the mild-slope equation[J].Coastal Engineering,1983,7(2)：191—203. doi: 10.1016/0378-3839(83)90017-0
[10]	Suh K D,Lee C,Park W S.Time-dependent equations for wave propagation on rapidly varying topography[J].Coastal Engineering,1997,32(2/3)：91—117. doi: 10.1016/S0378-3839(97)81745-0
[11]	Chen Q,Madsen P A.Schffer H A,et al.Wave-current interaction based on an enhanced Boussinesq approach[J].Coastal Engineering,1998,33(1)：11—39. doi: 10.1016/S0378-3839(97)00034-3
[12]	Agnon Y,Madsen P A,Schffer H A.A new approach to high order Boussinesq models[J].J Fluid Mech,1999,(399)：319—333.

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一种适用于非均匀地形的高阶Boussinesq水波模型

作者简介:
王本龙(1977- ),男,黑龙江人,博士研究生;刘桦(联系人.Tel/Fax:+86-21-62933021;E-mail:hliu@sjtu.edu.cn).

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Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom

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留言板

一种适用于非均匀地形的高阶Boussinesq水波模型

作者简介: 王本龙(1977- ),男,黑龙江人,博士研究生;刘桦(联系人.Tel/Fax:+86-21-62933021;E-mail:hliu@sjtu.edu.cn).

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出版历程

Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom

计量

出版历程

目录

作者简介:
王本龙(1977- ),男,黑龙江人,博士研究生;刘桦(联系人.Tel/Fax:+86-21-62933021;E-mail:hliu@sjtu.edu.cn).