加强的适合复杂地形的水波方程及其一维数值模型验证

刘忠波; 邹志利; 孙昭晨

加强的适合复杂地形的水波方程及其一维数值模型验证

1.
大连海事大学交通工程与物流学院, 辽宁大连 116026
2.
大连理工大学海岸及近海工程国家重点实验室, 辽宁大连 116023

基金项目: 国家自然科学基金资助项目(50479053;10672034)

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出版历程
- 收稿日期: 2007-01-23
- 修回日期: 2007-09-25

Enhanced Boussinesq equations for rapidly varying topographies and their one-dimensional numerical validation

1.
Transportation Engineering and Logistics College, Dalian Maritime University, Dalian 116026, China
2.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China

摘要

摘要: 在他人给出的方程的基础上,通过在其动量方程中引入含4个参数的公式,推导出了加强的适合复杂地形的水波方程,新方程的色散、变浅作用以及非线性均比原来适合复杂地形的方程有了改善:色散关系式与斯托克斯线性波的Padé(4,4)阶展开式一致;变浅作用在相对水深(波数乘水深)不大于6时与解析解符合较好;非线性在相对水深不大于1.05时保持在5%的误差之内.基于该方程,在非交错网格下建立的时间差分格式为混合4阶Adams-Bashforth-Moulton的一维数值模型,并在数值计算中利用了五对角宽带解法.数值模拟了潜堤上波浪传播变形,并将数值计算结果与实验结果进行了对比,验证了该数值模型是合理的.
- 线性色散 /
- 变浅 /
- 非线性 /
- 数值模型
Abstract: On the basis of the equations proposed by another person an enhanced Boussinesq model is derived by introducing additional terms with four parameters.The linear dispersion is accurate to Pad(4,4) expansion of linear Stokes's dispersion,the shoaling is applicable to arelative water depth(wavenumber is multiplied by water depth) not being greater than 6 and nonlinearity is accurate to the relative water depth not being greater than 1.05 within 5% error.Aone-dimensional numerical model is established with a composite fourth-order. A dams-Bashforth-Moult on scheme for time marching in non-staggered grids,and the five-diag onal method is used in the calculations.Numerical simulations are done upon wave propagation over a submerged bar.Numerical results are compared with the experimental data,and the present model is well validated.
- linear dispersion /
- shoaling /
- nonlinearity /
- numerical model

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参考文献(13)

PEREGRINE D H.Long waves on a beach[J].Journal of Fluid Mechanics,1967,27(4):815-827.

MADSEN P A,SφRENSEN O R.A new form of the Boussinesq equations with improved linear dispersion characteristics:Part 2.A slowly-varying bathymetry[J].Coastal Engineering,1992,18:183-204.

NWOGU O.An alternative form of the Boussinesq equations for nearshore wave propagation[J].Journal of Waterway,Port,Coastal and Ocean Engineering,1993,119(6):618-638.

SCHAFFER H A,MADSEN P A.Further enhancements of Boussinesq-type equations[J].Coastal Engineering,1995,26:1-14.

MADSEN P A,SCHAFFER H A.Higher-order Boussinesq-type equations for surface gravity waves:derivation and analysis[J].Philosophicai Transations of Royal Society of London Series A——Mathematical Physical and Engineering Sciences,1998,356:3123-3184.

MADSEN P A,BINGHAM H B,LIU Hua.A new method for fully nonlinear waves from shallow water to deep water[J].Journal of Fluid Mechanics,2002,462:1-30.

邹志利.含强水流高阶Boussinesq水波方程[J].海洋学报,2000,22(4):41-50.

邹志利.适合复杂地形的高阶Boussinesq方程[J].海洋学报,2001,23(1):109-119.

WEI G E,KIRBY J T.A time-dependent numerical code for extended Boussinesq equations[J].Journal of Waterway,Port,Coastal and Ocean Engineering,1995,121:251-261.

GOBBI M F,KIRBY J T.Wave evolution over submerged sills:tests of a high-order Boussinesq model[J].Coastal Engineering,1999,37:57-96.

刘忠波.高阶Boussiensq方程的研究[D].大连:大连理工大学,2006.

KIRBY J T,WEI G E,CHEN Qin,et.al.FUNWAVE 1.0:fully nonlinear Boussinesq wave model.Documentation and User's Manual[M]//Center for Applied Coastal Research,Department of Civil and Environmental Engineering,University of Delaware,1998:80.

LUTH H R,KLOPMAN G,KITOU N.Kinematics of waves breaking partially on an offshore bar,LDV measurements of waves with and without a net onshore current[R]//Report H——1573.Delft Hydraulics,1994:40.

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