地转对海洋内波的影响研究
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摘要
海洋内波是发生在密度层结海洋中一种常见的海洋波动现象,其最大振幅出现在海洋内部。研究海洋内波不仅对了解内波相关现象有着重要意义,而且还有助于了解内波在海洋内部质量、动量、能量等交换过程、海洋内部混合、环境和气候变化中的作用,加深对内波与其它多尺度海洋波动间的相互作用(例如:内波-表面波、内波-流、内波-涡等等)的理解。另外,研究海洋内波对海洋工程和海洋军事等也具有重要的指导意义。
本文在非传统近似(即,包含地转水平分量在内的完整地转效应)条件下,用WKB方法得到了密度连续分层海洋内波的一组WKB近似解。为了检验所得到的WKB近似解的有效性,WKB解各垂向速度模态与直接数值计算结果进行了详细比对。结果表明,当浮频率N(z)是关于深度z的慢变函数时,文中得到的WKB近似解与数值结果符合良好。另外,讨论了在背景流场存在时地转效应对内波的影响。研究还表明:地转水平分量一般是不能忽略的。因此,在海洋内波理论研究中保留地转水平分量对研究内波的生成、演变及消衰是非常必要的。
界面波是内波的一种特殊情况,界面波通常借助于由两层具有不同密度流体所构建的模型来进行研究。虽然现有的研究从各个不同方面阐述了两层流体界面波的特性,但他们均忽略了地转对其的影响。然而,当考虑表面波或内波对大尺度环流的影响时,地转的影响是不能忽略的。为此,本文将孙孚等(2003)在地转条件下导出的表面波解及其波生切应力推广到两层流体,研究了地转对两层流体界面波解及波生切应力的影响。
Ocean internal waves is a kind of waves occurred in continuous density- stratified ocean, the largest amplitude of the fluctuations occurred in the interior of the ocean. Investigation on them is very important not only on studying the phenomena related to themselves but also is helpful for us to understand the interactions of internal waves on the exchange process of mass, momentum, energy, environmental and climate change in the ocean. Furthermore, the understanding for internal waves’behaviours will increase the knowledge about the interactions between internal waves and many other multi-scale ocean processes (for example: internal waves-surface waves, internal waves–current, internal waves-eddy, etc, especially the contribution for large scale movements). In addition, it has great significance guidance to the marine engineering and marine military and so on.
In this thesis, a kind of WKB approximate solutions is derived by using WKB method for the internal waves in continuous density-stratified ocean under the‘non-traditional approximation’that is to include a complete effect of the earth’rotation. The vertical velocity modes obtained from the WKB approximate solutions are compared with the numerical result in detail in order to test the validity of WKB approximate solutions. The study shows that the WKB approximate solutions proposed are consistent with the numerical results for the buoyancy frequency N(z) varies gradually with the ocean depth z. Furthermore, the effects of the earth’rotation on the internal waves are studied in the present of background current. The results indicate that the horizantal component of the earth’rotation can not be ignored generally. Therefore, it is very important to retain the horizantal component of the earth’rotation in the studying on internal wave about its generation, evolution and dissipation.
The interface wave is a special case of internal wave, it is usually studied by using the model with two-layers fluid with different density. Although the existing investigations described the basic behaviours of the interfacial waves from different aspects, there appear to be no one taking into account of the influence of the earth rotation on the interfacial waves. However, this influence could not be neglected when we study the wave-induced stress and its driven effect on currents of the earth’s rotation, at least for surface waves. In this thesis, the results of Sun et al. (2003) for surface waves were extended to a more general case of two-layer fluid with a top free surface and a flat bottom, the solutions were deduced from the general form of linear fluid dynamic equations with the f-plane approximation for geostrophic small amplitude surface waves and interfacial waves, and wave-induced tangential stress were obtained based on the solutions presented. The results obtained here have potential important applications for understanding the behaviours of the interfacial waves, the interaction between the surface wave and the interfacial wave, ocean dynamics and in ocean engineering.
本文在非传统近似(即,包含地转水平分量在内的完整地转效应)条件下,用WKB方法得到了密度连续分层海洋内波的一组WKB近似解。为了检验所得到的WKB近似解的有效性,WKB解各垂向速度模态与直接数值计算结果进行了详细比对。结果表明,当浮频率N(z)是关于深度z的慢变函数时,文中得到的WKB近似解与数值结果符合良好。另外,讨论了在背景流场存在时地转效应对内波的影响。研究还表明:地转水平分量一般是不能忽略的。因此,在海洋内波理论研究中保留地转水平分量对研究内波的生成、演变及消衰是非常必要的。
界面波是内波的一种特殊情况,界面波通常借助于由两层具有不同密度流体所构建的模型来进行研究。虽然现有的研究从各个不同方面阐述了两层流体界面波的特性,但他们均忽略了地转对其的影响。然而,当考虑表面波或内波对大尺度环流的影响时,地转的影响是不能忽略的。为此,本文将孙孚等(2003)在地转条件下导出的表面波解及其波生切应力推广到两层流体,研究了地转对两层流体界面波解及波生切应力的影响。
Ocean internal waves is a kind of waves occurred in continuous density- stratified ocean, the largest amplitude of the fluctuations occurred in the interior of the ocean. Investigation on them is very important not only on studying the phenomena related to themselves but also is helpful for us to understand the interactions of internal waves on the exchange process of mass, momentum, energy, environmental and climate change in the ocean. Furthermore, the understanding for internal waves’behaviours will increase the knowledge about the interactions between internal waves and many other multi-scale ocean processes (for example: internal waves-surface waves, internal waves–current, internal waves-eddy, etc, especially the contribution for large scale movements). In addition, it has great significance guidance to the marine engineering and marine military and so on.
In this thesis, a kind of WKB approximate solutions is derived by using WKB method for the internal waves in continuous density-stratified ocean under the‘non-traditional approximation’that is to include a complete effect of the earth’rotation. The vertical velocity modes obtained from the WKB approximate solutions are compared with the numerical result in detail in order to test the validity of WKB approximate solutions. The study shows that the WKB approximate solutions proposed are consistent with the numerical results for the buoyancy frequency N(z) varies gradually with the ocean depth z. Furthermore, the effects of the earth’rotation on the internal waves are studied in the present of background current. The results indicate that the horizantal component of the earth’rotation can not be ignored generally. Therefore, it is very important to retain the horizantal component of the earth’rotation in the studying on internal wave about its generation, evolution and dissipation.
The interface wave is a special case of internal wave, it is usually studied by using the model with two-layers fluid with different density. Although the existing investigations described the basic behaviours of the interfacial waves from different aspects, there appear to be no one taking into account of the influence of the earth rotation on the interfacial waves. However, this influence could not be neglected when we study the wave-induced stress and its driven effect on currents of the earth’s rotation, at least for surface waves. In this thesis, the results of Sun et al. (2003) for surface waves were extended to a more general case of two-layer fluid with a top free surface and a flat bottom, the solutions were deduced from the general form of linear fluid dynamic equations with the f-plane approximation for geostrophic small amplitude surface waves and interfacial waves, and wave-induced tangential stress were obtained based on the solutions presented. The results obtained here have potential important applications for understanding the behaviours of the interfacial waves, the interaction between the surface wave and the interfacial wave, ocean dynamics and in ocean engineering.
引文
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