波浪运动的数学建模  

The Mathematical Model of the Wave Motion of Water Surface

作　　者：王红[1] 李月秋[1] WANG Hong;LI Yue-qiu(Faculty of Science,Qiqihar University,Qiqihar 161006,China)

机构地区：[1]齐齐哈尔大学理学院

出　　处：《数学的实践与认识》2018年第16期215-221,共7页Mathematics in Practice and Theory

基　　金：黑龙江省省属高等学校基本科研业务费科研项目(135209253)

摘　　要：就波浪运动这一常见自然现象,利用流体运动的质量连续性方程和动量守恒定理,建立了波浪运动几种数学模型.并就波浪幅值与波长的比值以及波长与水深的比值不同取值情况进行了分析,讨论了非线性偏微分方程的线性化问题.最后通过数值计算给出了不同深度上的质点运动轨迹以及质点速度沿水深的分布.The water wave is the common natural phenomenon. Several mathematical models of water wave are established by using the continuity equation of fluid and the momentum conservation law in this paper. The linearization of the nonlinear mathematical models is discussed and the numerical analysis is performed for the different cases of the ratio of the amplitude to wavelength and the wavelength to deepness. The motion track and the velocity of water particle at different deel^ness are shown ~rar^h~r^ll.,

关 键 词：波浪运动 速度分布 波浪面 质点运动轨迹 不可压流 

分 类 号：O353.2[理学—流体力学]