| ZHANG Baole,CUI Jifeng,CHEN Xiaogang,ZHANG Wenyu. 2019. The third-order asymptotic solutions in the Lagrangian description for interfacial internal waves in a three layer fluid system. Acta Oceanologica Sinica, 38(7):1－13 |
| The third-order asymptotic solutions in the Lagrangian description for interfacial internal waves in a three layer fluid system |
| 拉格朗日描述下三层流体系统中界面内波的三阶渐近解 |
| Received:July 01, 2018 |
| DOI：10.1007/s13131-019-1453-5 |
| Key words:interfacial internal waves Lagrangian description particle trajectory perturbation method |
| 中文关键词: 界面内波 拉格朗日描述 粒子轨迹 摄动法 |
| 基金项目:The Science Research Project of Inner Mongolia University of Technology under contract No. ZD201613. |
| Author Name | Affiliation | E-mail | | ZHANG Baole | Inner Mongolia University of Technology, Inner Mongolia, Hohhot 010051, China | | | CUI Jifeng | Inner Mongolia University of Technology, Inner Mongolia, Hohhot 010051, China | | | CHEN Xiaogang | Inner Mongolia University of Technology, Inner Mongolia, Hohhot 010051, China | xiaogang_chen@imut.edu.cn | | ZHANG Wenyu | Inner Mongolia University of Technology, Inner Mongolia, Hohhot 010051, China | |
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| Abstract: |
| In this paper, we discuss the interfacial internal waves with a rigid boundary in a three-layer fluid system, where the density of the upper layer fluid is smaller than that of the lower layer. With the Lagrangian matching conditions at the interfaces, the first-order solutions, the second-order solutions and the third-order asymptotic solutions for the interfacial internal waves are obtained in the Lagrangian description using the perturbation method, and the mass transport velocity, the wave frequency, the mean level and the particle trajectory are also given. The results show that the discontinuities across the interfaces appear for the mass transport velocity, wave frequency and mean level, but we find that these discontinuities may disappear if the water depth ratio and the density ratio of the three layer fluids satisfy certain conditions. |
| 中文摘要: |
| 在流体力学中，描述流体运动有Lagrange方法和Euler方法.Euler方法是通过观测通过空间各固定位置点处流体质点的运动行为来描述流体运动规律，而Lagrange方法是跟踪各个流体质点，通过观测它们在时空运动中所走过的路径来描述流体的运动规律.在数学处理上，Euler方法较Lagrange方法简单，但Lagrange方法可以完全描述流体运动的整个流场的所有特性，而Euler方法却无法描述每个流体质点的运动轨迹.本文，我们研究具有刚性边界的三层流体系统中的界面内波，其中上层流体的密度比下层流体的密度大.通过在界面处引入朗格朗日匹配条件并使用微扰法得到了拉格朗日描述下的界面内波的一阶解、二阶解及三阶解，给出了质量输运速度、波频率、平均水平和质点运动轨迹的解.结果表明对于质量输运速度、波频率、平均水平和质点运动轨迹在界面处会有不连续性，但是我们发现在满足一定的三层流体水深比和密度比条件时这种不连续性将会消失. |
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