保辛水波动力学

钟万勰; 吴锋; 孙雁; 姚征

doi:10.21656/1000-0887.390062

保辛水波动力学

doi: 10.21656/1000-0887.390062

钟万勰^1,2,
吴锋¹,
孙雁²,
姚征³

¹大连理工大学工程力学系, 辽宁大连 116023;²上海交通大学船舶海洋与建筑工程学院, 上海 200240;³大连海事大学交通运输工程学院, 辽宁大连 116026

基金项目: 国家自然科学基金（11472076;51609034;51278298）;中央高校基本科研业务费（DUT17RC(3)069）

详细信息

作者简介:
钟万勰（1934—），男，教授，中科院院士（通讯作者. E-mail: zwoffice@dlut.edu.cn）；吴锋（1985—），男，副教授（E-mail: vonwu@dlut.edu.cn）；孙雁（1965—）,女，副教授(E-mail: sunyan@sjtu.edu.cn)；姚征（1978—），男，副教授（E-mail: yaozheng@dlmu.edu.cn）.

中图分类号: O352;O353.2
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- 被引次数: 0
出版历程
- 收稿日期: 2018-02-09
- 修回日期: 2018-04-11
- 刊出日期: 2018-08-15

Symplectic Water Wave Dynamics

¹Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China;²School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;³Transportation Engineering College, Dalian Maritime University, Dalian, Liaoning 116026, P.R.China

Funds: The National Natural Science Foundation of China（11472076;51609034;51278298）

摘要

摘要: 初步介绍了基于位移表示的水波动力学理论，给出了线性水波、浅水波的位移周期行波解.提出保辛摄动法，计算一般水深周期行波解，并通过数值算例验证了算法的正确性.该研究注重水波的动力学属性，可以直接给出质点粒子的轨迹，模拟出水面尖锐的周期行波解.
- 水波 /
- 动力学 /
- 位移法 /
- 辛 /
- Hamilton
Abstract: Here, an elementary introduction to the displacement method-based water wave dynamics theory was presented. The periodic travelling wave solutions of the linear water waves and shallow water waves were given. The symplectic perturbation method was proposed to analyze the periodic travelling wave solution for the water system with a general depth. Numerical tests were given to demonstrate the correctness of the proposed method. The present research emphasizes the dynamics property of water waves. By means of the proposed theory, the particle trajectory can be obtained directly, and the periodic travelling wave with sharp surface can be simulated.
- water wave /
- dynamics /
- displacement method /
- symplectic /
- Hamilton

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参考文献(23)

[1]	梅强中. 水波动力学[M]. 北京: 科学出版社, 1984.(MEI Qiangzhong. Water Wave Dynamics [M]. Beijing: Science Press, 1984.(in Chinese))
[2]	钟万勰, 姚征. 位移法浅水孤立波[J]. 大连理工大学学报, 2006,46(1): 151-156.(ZHONG Wanxie, YAO Zheng. Shallow water solitary waves based on displacement method[J]. Journal of Dalian University of Technology,2006,46(1): 151-156.(in Chinese))
[3]	钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHONG Wanxie. Symplectic Solution Methodologyin Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
[4]	钟万勰, 陈晓辉. 浅水波的位移法求解[J]. 水动力学研究与进展, 2006,21(4): 486-493.(ZHONG Wanxie, CHEN Xiaohui. Solving shallow water waves with the displacement method[J]. Journal of Hydrodynamics,2006,21(4): 486-493.(in Chinese))
[5]	钟万勰, 吴锋. 力-功-能-辛-离散: 祖冲之方法论[M]. 大连: 大连理工大学出版社, 2016.(ZHONG Wanxie, WU Feng. Force-Work-Energy-Symplecticity-Discretization: ZU Chongzhi’s Methodology [M]. Dalian: Dalian University of Technology Press, 2016.(in Chinese))
[6]	吴锋, 钟万勰. 浅水问题的约束Hamilton变分原理及祖冲之类保辛算法[J]. 应用数学和力学, 2016,37(1): 1-13.(WU Feng, ZHONG Wanxie. The constrained Hamilton variational principle for shallow water problems and the Zu-type symplectic algorithm[J]. Applied Mathematics and Mechanics,2016,37(1): 1-13.(in Chinese))
[7]	吴锋. 基于位移的水波数值模拟: 辛方法[M]. 大连: 大连理工大学, 2017.(WU Feng. Numerical Modeling of Water Waves Based on Displacement: Symplectic Method [M]. Dalian: Dalian University of Technology Press, 2017.(in Chinese))
[8]	WEYL H. The Classical Groups: Their Invariants and Representations [M]. Princeton, New Jersey: Princeton University Press, 1939.
[9]	冯康, 秦孟兆. 哈密尔顿系统的辛几何算法[M]. 杭州: 浙江科学技术出版社, 2004.(FENG Kang, QIN Mengzhao. Symplectic Geometric Algorithms for Hamiltonian Systems [M]. Hangzhou: Zhejiang Science and Technology Press, 2004.(in Chinese))
[10]	吴云岗, 陶明德. 水波动力学基础[M]. 上海: 复旦大学出版社, 2011.(WU Yungang, TAO Mingde. The Foundation of Hydrodynamic [M]. Shanghai: Fudan University Press, 2011.(in Chinese))
[11]	钟万勰, 吴锋, 孙雁. 浅水机械激波[J]. 应用数学和力学, 2017,38(8): 845-852.(ZHONG Wanxie, WU Feng, SUN Yan. Shallow water mechanical shock wave[J]. Applied Mathematics and Mechanics,2017,38(8): 845-852.(in Chinese))
[12]	STOKER J J. Water Waves: the Mathematical Theory With Applications [M]. New York: Interscience Publishers Ltd, 1957.
[13]	吴锋, 孙雁, 姚征, 等. 椭圆余弦波的位移法分析[J]. 计算机辅助工程, 2018,27(2): 1-5.(WU Feng, SUN Yan, YAO Zheng, et al. Analysis on cnoidal wave using the displacement method[J]. Computer Aided Engineering,2018,27(2): 1-5.(in Chinese))
[14]	ADRIAN C. Nonlinear Water Waves With Applications to Wave-Current Interactions and Tsunamis [M]. New York: Society for Industrial & Applied Mathematics, 2011.
[15]	CONSTANTIN A. The trajectories of particles in Stokes waves[J]. Inventiones Mathematicae,2006,166(3): 523-535.
[16]	CONSTANTIN A, ESCHER J. Particle trajectories in solitary water waves[J]. Bulletin of the American Mathematical Society,2007,44(3): 423-431.
[17]	吴锋, 钟万勰. 浅水动边界问题的位移法模拟[J]. 计算机辅助工程, 2016,25(2): 5-13.(WU Feng, ZHONG Wanxie. Simulation on moving boundaries of shallow water using displacement method[J]. Computer Aided Engineering,2016,25(2): 5-13.(in Chinese))
[18]	姚征, 钟万勰. 位移法浅水波方程解及其特性[J]. 计算机辅助工程, 2016,25(2): 21-25.(YAO Zheng, ZHONG Wanxie. Solutions and characteristics of shallow water equation based on displacement method[J]. Computer Aided Engineering,2016,25(2): 21-25.(in Chinese))
[19]	吴锋, 钟万勰. 不平水底浅水波问题的位移法[J]. 水动力学研究与进展, 2016,31(5): 549-555.(WU Feng, ZHONG Wanxie. Displacement method for the shallow water wave problems with uneven bottoms[J]. Chinese Journal of Hydrodynamics,2016,31(5): 549-555.(in Chinese))
[20]	WU Feng, ZHONG Wanxie. On displacement shallow water wave equation and symplectic solution[J]. Computer Methods in Applied Mechanics and Engineering,2017,318: 431-455.
[21]	WU F, YAO Z, ZHONG W. Fully nonlinear (2+1)-dimensional displacement shallow water wave equation[J]. Chinese Physics B,2017,26(5): 253-258.
[22]	WU F, ZHONG W. A shallow water equation based on displacement and pressure and its numerical solution[J]. Environmental Fluid Mechanics,2017,17(5): 1-28.
[23]	吴锋, 钟万勰. 水波的界带有限元[J]. 应用数学和力学, 2015,36(12): 1219-1227.(WU Feng, ZHONG Wanxie. Simulation of water waves based on the inter-belt finite element method[J]. Applied Mathematics and Mechanics,2015,36(12): 1219-1227.(in Chinese))