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一种改善了非线性和色散性的Boussinesq方程模型

张殿新 陶建华

张殿新, 陶建华. 一种改善了非线性和色散性的Boussinesq方程模型[J]. 应用数学和力学, 2008, 29(7): 813-824.
引用本文: 张殿新, 陶建华. 一种改善了非线性和色散性的Boussinesq方程模型[J]. 应用数学和力学, 2008, 29(7): 813-824.
ZHANG Dian-xin, TAO Jian-hua. A Boussinesq Model With Improved Nonlinearity and Dispersion[J]. Applied Mathematics and Mechanics, 2008, 29(7): 813-824.
Citation: ZHANG Dian-xin, TAO Jian-hua. A Boussinesq Model With Improved Nonlinearity and Dispersion[J]. Applied Mathematics and Mechanics, 2008, 29(7): 813-824.

一种改善了非线性和色散性的Boussinesq方程模型

基金项目: 国家自然科学基金资助项目(50509018)
详细信息
    作者简介:

    张殿新(1980- ),女,天津人,博士生(联系人.Tel:+86-22-27890726;E-mail:dianxinz@ho-maail.com);陶建华,教授(Tel:+86-22-27404403;E-mail:jhtao@tju.edu.cn).

  • 中图分类号: O353.2

A Boussinesq Model With Improved Nonlinearity and Dispersion

  • 摘要: 推导了一种在不平底上的新的Boussinesq方程.在不增加方程的最高导数项的阶数的情况下提高了模型方程的非线性.为了提高模型的色散性,引入长波近似,通过调节待定系数来使模型的色散性达到Padé(2,2).对模型方程进行了非线性、线性色散性和线性浅化性分析,分析表明此模型在非线性、色散性和浅化性上都有所提高.将计算结果与实验数据做了比较,结果显示模型更好的符合了实验数据.
  • [1] Boussinesq M J. Théorie des ondes et des ramous qui se propagent le long d’un canal rectangularies horizontal, en communiquant au liquide contenudans ce canal des vitesses sensiblement pareilles de la surface au fond[J].Journal de Mathematique Pures et Apppliquées,Deuxieme Série,1872,17(1):55-108.
    [2] Peregrine D H. Long waves on a beach[J].J Fluid Mech,1967,27(7): 815-827. doi: 10.1017/S0022112067002605
    [3] Madsen P A, Sorensen 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(4/3):183-204. doi: 10.1016/0378-3839(92)90019-Q
    [4] Nwogu O. Alternative form of Boussinesq equations for nearshore wave propagation[J].Journal of Waterway, Port, Coastal and Ocean Engineering,1993,119(6):618-638. doi: 10.1061/(ASCE)0733-950X(1993)119:6(618)
    [5] Wei G, Kirby J T, Grilli S T,et al.A fully nonlinear Boussinesq model for surface waves—Part 1: Highly nonlinear unsteady waves[J].J Fluid Mech,1995,294(13):71-92. doi: 10.1017/S0022112095002813
    [6] Agnon B Y, Madsen P A,Schffer H A.A new approach to high-order Boussinesq models[J].J Fluid Mech,1999,399(22): 319-333. doi: 10.1017/S0022112099006394
    [7] Gobbi M F, Kirby J T, Wei G. A fully nonlinear Boussinesq model for surface waves—Part 2:Extension to O((kh)4)[J].J Fluid Mech,2000,405(4):181-210. doi: 10.1017/S0022112099007247
    [8] Madsen P A, Bingham B B,LIU Hua.A new Boussinesq method for fully nonlinear waves from shallow to deep water[J].J Fluid Mech,2002,462(13):1-30.
    [9] Madsen P A, Fuhrman D R,WANG Ben-long.A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry[J].Coastal Engineering,2006,53(5/6):487-504. doi: 10.1016/j.coastaleng.2005.11.002
    [10] 陶建华.水波的数值模拟[M].天津:天津大学出版社,2005,108.
    [11] Gobbi M F, Kirby J T. A fourth order Boussinesq-type wave model[A].In:Billy L,Ed.Proceedings of the 25th international Conference on Coastal Engineering[C].New York:ASCE.1997,1(1):1116-1129.
    [12] Schffer H A, Madsen P A.Further enhancements of Boussinesq-type equations[J].Coastal Engineering,1995,26(1/2):1-14. doi: 10.1016/0378-3839(95)00017-2
    [13] Madsen P A, Schffer H A.Higher order Boussinesq-type equations for surface gravity waves-Derivation and analysis[J].Phil Trans R Soc Lond A,1998,356(12):1-59.
    [14] Abbott M B, McCowan A D, Warren I R.Accuracy of short wave numerical models[J].J Hydraul Eng,1984,110(10):1287-1301. doi: 10.1061/(ASCE)0733-9429(1984)110:10(1287)
    [15] Drago M. Mathematical models for propagation of sea waves in the surf zone[D].Ph D Thesis. Italian: University of Bologna, 1991, 135.
    [16] Dean R G, Sharma J N. Simulation of wave systems due to nonlinear directional spectra[J].Proc Internat Symp Hydrodynamics in Ocean Engng,1981,2(1):1211-1222.
    [17] Beji S, Battjes J A.Experimental investigations of wave propagation over a bar[J].Coastal Engineering,1993,19(1/2):151-162. doi: 10.1016/0378-3839(93)90022-Z
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出版历程
  • 收稿日期:  2008-03-19
  • 修回日期:  2008-05-15
  • 刊出日期:  2008-07-15

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