保辛水波动力学  

Symplectic Water Wave Dynamics

作　　者：钟万勰[1,2] 吴锋 孙雁[2] 姚征[3] ZHONG Wanxie;WU Feng;SUN Yan;YAO Zheng(Department of Engineering Mechanics,Dalian University of Technology,Dalian,Liaoning 116023,P.R.China;School of Naval Architecture,Ocean ＆ Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,P.R.China;Transportation Engineering College,Dalian Maritime University,Dalian,Liaoning 115025,P.R.China)

机构地区：[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

出　　处：《应用数学和力学》2018年第8期855-874,共20页Applied Mathematics and Mechanics

基　　金：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)~~

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.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.

关 键 词：水波 动力学 位移法 辛 HAMILTON 

分 类 号：O352[理学—流体力学] O353.2[理学—力学]