关于Boussinesq型水波方程理论和应用研究的综述

孙家文; 房克照; 刘忠波; 范浩煦; 孙昭晨; 王平

doi:10.3969/j.issn.0253-4193.2020.05.001

关于Boussinesq型水波方程理论和应用研究的综述

doi: 10.3969/j.issn.0253-4193.2020.05.001

孙家文^{1, 2, 3,},
房克照³,
刘忠波^2, ,,
范浩煦³,
孙昭晨³,
王平¹

1.
国家海洋环境监测中心国家环境保护海洋生态环境整治修复重点实验室，辽宁大连 116023
2.
大连海事大学交通运输工程学院，辽宁大连 116026
3.
大连理工大学海岸和近海工程国家重点实验室/DUT-UWA海洋工程联合研究中心，辽宁大连 116024

基金项目: 国家自然科学基金项目（51779022，51579034，51809053，51709054）；国家海洋局海域管理技术重点实验室开放基金（201713）；中央高校基本科研业务费（DUT18ZD214）；大连理工大学海岸和近海工程国家重点实验室开放课题基金（LP1915）。

详细信息

作者简介:
孙家文（1983-），男，山东省夏津县人，博士，副研究员，从事海岸水动力学研究。E-mail：jwsun@nmemc.org.cn

通讯作者:
刘忠波（1976-），男，山东省临沭县人，博士，副教授，从事海岸水动力学研究。E-mail：liuzhongbo@dlmu.edu.cn

中图分类号: P731.2
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- 被引次数: 0
出版历程
- 收稿日期: 2019-04-17
- 修回日期: 2019-09-14
- 网络出版日期: 2020-11-18
- 刊出日期: 2020-05-25

A review on the theory and application of Boussinesq-type equations for water waves

Sun Jiawen^{1, 2, 3
,},
Fang Kezhao³,
Liu Zhongbo^{2
, ,},
Fan Haoxu³,
Sun Zhaochen³,
Wang Ping¹

1.
State Environmental Protection Key Laboratory of Marine Ecological Environment Restoration, National Marine Environmental Monitoring Center, Dalian 116023, China
2.
Transportation Engineering College, Dalian Maritime University, Dalian 116026, China
3.
State Key Laboratory of Coastal and Offshore Engineering/DUT-UWA Joint Research Center for Ocean Engineering, Dalian University of Technology, Dalian 116024, China

摘要

摘要:
Boussinesq型方程是研究水波传播与演化问题的重要工具之一，本文就1967-2018年常用的Boussinesq型水波方程从理论推导和数值应用两个方面进行了回顾，以期推动该类方程在海岸(海洋)工程波浪水动力方向的深入研究和应用。此类方程推导主要从欧拉方程或Laplace方程出发。在一定的非线性和缓坡假设等条件下，国内外学者建立了多个Boussinesq型水波方程，并以Stokes波的相关理论为依据，考察了这些方程在相速度、群速度、线性变浅梯度、二阶非线性、三阶非线性、波幅离散、速度沿水深分布以及和（差）频等多方面性能的精度。将Boussinesq型水波方程分为水平二维和三维两大类，并对主要Boussinesq型水波方程的特性进行了评述。进而又对适合渗透地形和存在流体分层情况下的Boussinesq型水波方程进行了简述与评论。最后对这些方程的应用进行了总结与分析。
- Boussinesq型方程 /
- 色散性 /
- 非线性 /
- 变浅性 /
- 应用研究
Abstract:
Boussinesq-type equation is one of the important tools for simulating the propagation and evolution of water waves. The theoretical derivation and numerical application of the Boussinesq-type water wave equation dating back to 1967 are reviewed with the hope of promoting its deep development and application in the fields of coastal and ocean engineering. From the theoretical point of view, the derivation of such equations mainly starts from Euler equations or Laplace equations. Under the conditions of certain nonlinearity and gentle slope assumptions, a variety of Boussinesq-type water wave equations have been proposed worldwide. Through the comparisons with the related theories of Stokes waves, these equations are investigated with respect to phase velocity, group velocity, linear shoaling gradient, second-order nonlinearity, third-order nonlinearity, dispersion characteristics due to amplitude dispersion, velocity distribution along the vertical column, sub- and super harmonics etc. The majority of Boussinesq-type equations in literature for waves are reviewed and grouped into two categories, namely horizontal two-dimensional type and three-dimensional type. The usage of Boussinesq-type equations involved with permeable media and the presence of fluid stratification are also briefly described and commented. Finally, the application of these equations is summarized and analyzed.
- Boussinesq-type equations /
- dispersion /
- nonlinear property /
- linear shoaling property /
- numerical applications

HTML全文

图 1 四层Boussinesq方程的相速度（n代表方程中的最高导数）

Fig. 1 The dimensionless phase celerity of the four-layer Boussinesq equations (n is the highest order of the spatial derivative)

下载: 全尺寸图片幻灯片

表 1 Boussinesq型水波方程的最大适用水深（kh）

Tab. 1 Maximum application water depth of different Boussinesq-type models

参考文献	色散性	二阶非线性	变浅作用	速度分布特征
Peregrine^[2]	0.75	−	−	0.5
Madsen等^[4-5]	3	−	3	−
Nwogu^[6]	3	−	−	1.5
Wei等^[21]	3	1.2	−	1.5
邹志利^[27]	3	0.8	3	−
Gobbi等^[30]	6	3.0	−	4
Madsen等^[40]	25～40	25～40	30	12
Lynett和Liu^[16]	8～10	6	10	6*
Lynett和Liu^[32]	30	−	−	12
Chazel等^[42]	20	−	12	8
Liu和Fang^[44]	53	45	60	23.2
Liu等^[45]**	667～800	300	300	352～423
Liu等^[45]***	7 600	−	−	−
注：是仅针对水平速度，是针对最高空间导数为3的方程，**指最高空间导数为5的方程，-表示原文献没有给出适用范围或不能直接给出。

下载: 导出CSV

参考文献(75)

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