非线性海洋内波的理论、模型与计算

王展; 朱玉可

doi:10.6052/0459-1879-19-326

非线性海洋内波的理论、模型与计算

doi: 10.6052/0459-1879-19-326

王展^*†2), ,,
朱玉可^**

^*中国科学院力学研究所, 北京 100190
^†中国科学院大学工程科学学院, 北京 100049
^**浙江大学数学科学学院, 杭州 310027

基金项目: 1) 国家自然科学基金资助项目(11772341);国家自然科学基金资助项目(11911530171)

详细信息

通讯作者:
王展

中图分类号: O352
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出版历程
- 收稿日期: 2019-10-25
- 刊出日期: 2019-11-18

THEORY, MODELLING AND COMPUTATION OF NONLINEAR OCEAN INTERNAL WAVES

Wang Zhan^{*†2)
, ,},
Zhu Yuke^**

^*Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
^†School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
^**School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

摘要

摘要: 海水因盐度与温度的垂向差异造成密度层结现象, 进而由于海洋系统的内部扰动(如海潮流过局部隆起的海底地形)与外部扰动(如死水现象)造成等密面的波动, 这一现象称为“内波”. 内波在全球范围内大量存在, 尤其是在海峡入海口等密度层结现象较为明显和稳定的区域会有内波频繁活动. 海洋通常呈现“三明治”状的结构: 密度相对稳定的混合层与深水层, 以及位于中间密度连续过渡的密跃层. 密跃层的整体脉动对于海洋工程和海洋生态环境有重大的影响; 而密跃层内部的波动对于潜艇的非声探测(反过来说, 对于潜艇的隐身作战)具有潜在的应用价值. 而造成这些重大影响的根源在于内波在水平和垂直方向都具备传播能力, 这是有别于海洋表面波浪的关键之处.本文针对两类海洋密度模型-连续分层模型与间断分层模型, 从理论研究、数值模拟、实验室机理实验等方面论述了研究海洋内波的各类非线性模型(包括弱非线性的Korteweg-de Vries方程、Benjamin-Ono方程, Kadomtsev-Petviashvili方程等著名模型以及强非线性Miyata-Choi-Camassa方程、非线性势流理论、带密度变化的不可压缩Navier-Stokes方程等), 讨论各自的适用范围, 并借此探讨内波在海洋质量动量能量输运中所起的至关重要的作用.
- 海洋内波 /
- 间断分层模型 /
- 连续分层模型 /
- 非线性波 /
- 边界积分法 /
- Boussinesq方程 /
- 高阶算法
Abstract: Salinity and temperature variations in the vertical direction lead to density stratification in oceans, and the fluctuation of isopycnal surfaces resulting from internal perturbations (such as stratified shear flow over a bottom topography) or external disturbances (such as the dead water phenomenon) is called the internal wave. Internal waves are ubiquitous in the ocean and usually arise in the situation when the density stratification is obvious and stable such as at the mouth of strait. Oceans are usually characterized by a sandwich-like structure: a mixing layer and a deep-water layer featuring an almost uniform density, and a transition layer in the middle with continuous density variation. Fluctuations of the transition layer have great impact on ocean engineering and ocean ecology, while waves inside the transition layer has potential applications in the non-acoustic detection of submarines (conversely, in the stealth operation of submarines). The main reason for these important influences lies in the ability of internal waves to propagate in both horizontal and vertical directions, which is the essential difference from that of ocean surface waves. In the current paper, two types of ocean density models, continuously stratified models and discontinuous layered models, are thoroughly discussed. Various nonlinear models used to study ocean internal waves (including celebrated weakly nonlinear models, such as the Korteweg-de Vries equation, the Benjamin-Ono equation, and the Kadomtsev-Petviashvili equation, and strongly nonlinear models, such as the Miyata-Choi-Camassa equation, the fully nonlinear potential theory, and the incompressible Navier-Stokes equation with density variations), as well as their respective scope of application, are reviewed from the aspects of theoretical analyses, numerical simulations, and laboratory experiments. Particular attention is paid to the important role of internal waves in transferring mass, momentum and energy in oceans.
- internal ocean wave /
- layered model /
- continuously stratified model /
- nonlinear wave /
- boundary integral method /
- Boussinesq equations /
- high-order numerical scheme

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