陆架陆坡区内孤立波的演化：理论分析与数值实验研究
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摘要
海洋内波是发生在密度稳定层化的海水内部的一种波动,其最大振幅出现在海洋内部,波动频率介于惯性频率和Brunt-V?is?l?之间。经常观测到的一种特殊的内波就是内孤立波或者称为内孤立子,是一种自然界中常见的振幅大,周期短的非线性波,是单个的、孤立的波结构,其传播是单方向的,且速度、波形在传播过程中基本保持不变。内孤立波的研究对海洋声学,海洋资源开发,海洋生态环境保护,海洋军事和海洋工程等方面都具有重要影响。观测表明内孤立波是海洋中普遍存在的一种波动,尤其是在陆架陆坡区,潮流与变化的底地形的作用是这一波动的主要源。
南海东北部是内孤立波的频发地带,这里既有吕宋海峡处生成的振幅达100多米,波峰线长达200千米以上的强非线性内孤立波,也有陆架陆坡区局地生成振幅可达几米到几十米的小振幅内孤立波波列。本文结合ASIAEX实验期间南海东北部陆架陆坡区内孤立波的观测资料,以理论与数值实验手段分析研究了内孤立波在变化地形上的传播演化特征,主要可以分为三个方面。
首先,回顾了内孤立波研究中弱非线性KdV理论的发展及慢变孤立子理论在内孤立波演化中的应用,研究了内孤立波的分裂特征。基于摄动方法,导出了连续分层条件下的变系数KP方程,这一方程可以描述内孤立波的水平二维特性。
其次,开发完成了一个用于分层流数值模拟的非静力近似海洋数值模式,基于这一模式,首次研究了南海东北部陆架陆坡区内孤立波(波列)的局地生成,结果表明,潮流与陆架波折处的相互作用可以激发生成振幅达几米到十几米的向岸传播的内孤立波波列,跃层位置及潮流强度是控制内孤立波生成强弱的主要因素。结合ASIAEX期间观测到的南海东北部陆架陆坡区的内孤立波演化特征,数值模拟了这一海区大振幅内孤立波在向岸传播演化过程中的运动学及动力学特征。研究了内孤立波在传播演化过程中的极性转化特征,采用经验正交函数(EOF)法分析了这一过程中模态演化特征,定量的分析了非静力压强效应。受地形效应的影响,内孤立波可能发生极性转换或强烈的破碎过程,这些过程往往伴随着高模态组分的生成。
最后,介绍了新近开发的用于分层流及内波实验的粒子图像速度场仪(PIV)系统,实验研究了不同极性及振幅下内孤立波在斜坡地形上的破碎演化特征。重点分析了内孤立波在爬坡破碎过程中所引起的复杂流场结构。在实验的基础上,借助于前文开发的非静力近似数值模式,数值模拟了下凹型内孤立波在斜坡地形上的翻转破碎特征。揭示了内孤立波在斜坡地形上翻转破碎过程中,多个涡旋结构的形成及发展。
Internal waves are generated by disturbances to a stratified ocean at frequencies between the inertial and the buoyancy frequency. A primary source is the oscillating barotropic tidal flow over varying topography, which gives rise to the disturbance of the pycnocline. Under certain circumstances, this disturbance can transform into a set of high frequency, non-linear internal waves. This thesis mainly focuses on the evolution of internal solitary wave (hearafter“ISW”), which is a special kind internal wave. Internal solitary waves (hereafter“ISWs”) are typically observed as propagating in packets with the longer and larger amplitude waves leading, indicating that both nonlinear and dispersive (nonhydrostatic) effects may play a significant role in the evolution process. As ISWs propagate in the ocean, they carry considerable momentum and energy, resulting in significant transient hydrodynamic loading on any offshore structures, undersea navigation vehicles and subsurface storage facilities that they may encounter
In the Northern South China Sea (SCS), ISW has been found to be active and frequently happened phenomenon. Observations have revealed the existence of large amplitude ISWs with amplitude more than 100m and wave crest more than 200km, which propagated out from the Luzon Straits and disappeared on the continental shelf in the Northern South China Sea. Combined with the in situ observation data on ISWs during ASIAEX, this thesis studied the evolution characteristics of ISW on variable topography, and can be resolved into three aspects.
First, the weakly nonlinear variable coefficients KdV theory for ISWs was reviewed and the application of the slowly varying solitary wave theory was discussed, the fission characteristic of ISW was studied numerically. Even further, the two dimensional KP equation for ISWs in continuously stratified fluid was derived, which can be used for the simulation of the two dimensional characteristics of ISW
Second, a nonhydrostatic numerical model for density stratified flow was developed. With this model, we studied the local generation of ISW trains around the continental shelf break; it revealed that the interaction of barotropic tide with the continental shelf break can promote the generation of ISW trains with amplitude of several meters propagating towards the continental shelf. The pycnocline depth and the intensity of the tidal current were two main factors controlling the generation process. After that, we numerically studied the evolution characteristics of large amplitude ISWs on the continental shelf. The simulation captured the depression to elevation conversion the large amplitude ISWs, the effect of topography on the ISW propagation. The nonhydrostatic pressure was quantified. Empirical Orthogonal Function (EOF) method was employed on the analysis of the mode evolution characteristics during this whole process. Results revealed the generation of higher mode during the interaction of the first mode ISW with the shelf break.
Finally, we report the recently developed PIV (Particle Image Velocity) systems for the laboratory experiment on density stratified flow and internal wave research. Experiments were carried out on the run-up of ISW on a slope. Different polarity ISW with different amplitude has been considered. The main focus is on the complex velocity and vorticity field during the strong breaking process, development of vortices structure were analyzed. Furthermore, a typical numerical experiment has been accomplished, results were compared with the laboratory experiment, numerical results provided a clearer picture on the whole breaking process, and revealed the strong mixing process during the ISW run-up and breaking process.
南海东北部是内孤立波的频发地带,这里既有吕宋海峡处生成的振幅达100多米,波峰线长达200千米以上的强非线性内孤立波,也有陆架陆坡区局地生成振幅可达几米到几十米的小振幅内孤立波波列。本文结合ASIAEX实验期间南海东北部陆架陆坡区内孤立波的观测资料,以理论与数值实验手段分析研究了内孤立波在变化地形上的传播演化特征,主要可以分为三个方面。
首先,回顾了内孤立波研究中弱非线性KdV理论的发展及慢变孤立子理论在内孤立波演化中的应用,研究了内孤立波的分裂特征。基于摄动方法,导出了连续分层条件下的变系数KP方程,这一方程可以描述内孤立波的水平二维特性。
其次,开发完成了一个用于分层流数值模拟的非静力近似海洋数值模式,基于这一模式,首次研究了南海东北部陆架陆坡区内孤立波(波列)的局地生成,结果表明,潮流与陆架波折处的相互作用可以激发生成振幅达几米到十几米的向岸传播的内孤立波波列,跃层位置及潮流强度是控制内孤立波生成强弱的主要因素。结合ASIAEX期间观测到的南海东北部陆架陆坡区的内孤立波演化特征,数值模拟了这一海区大振幅内孤立波在向岸传播演化过程中的运动学及动力学特征。研究了内孤立波在传播演化过程中的极性转化特征,采用经验正交函数(EOF)法分析了这一过程中模态演化特征,定量的分析了非静力压强效应。受地形效应的影响,内孤立波可能发生极性转换或强烈的破碎过程,这些过程往往伴随着高模态组分的生成。
最后,介绍了新近开发的用于分层流及内波实验的粒子图像速度场仪(PIV)系统,实验研究了不同极性及振幅下内孤立波在斜坡地形上的破碎演化特征。重点分析了内孤立波在爬坡破碎过程中所引起的复杂流场结构。在实验的基础上,借助于前文开发的非静力近似数值模式,数值模拟了下凹型内孤立波在斜坡地形上的翻转破碎特征。揭示了内孤立波在斜坡地形上翻转破碎过程中,多个涡旋结构的形成及发展。
Internal waves are generated by disturbances to a stratified ocean at frequencies between the inertial and the buoyancy frequency. A primary source is the oscillating barotropic tidal flow over varying topography, which gives rise to the disturbance of the pycnocline. Under certain circumstances, this disturbance can transform into a set of high frequency, non-linear internal waves. This thesis mainly focuses on the evolution of internal solitary wave (hearafter“ISW”), which is a special kind internal wave. Internal solitary waves (hereafter“ISWs”) are typically observed as propagating in packets with the longer and larger amplitude waves leading, indicating that both nonlinear and dispersive (nonhydrostatic) effects may play a significant role in the evolution process. As ISWs propagate in the ocean, they carry considerable momentum and energy, resulting in significant transient hydrodynamic loading on any offshore structures, undersea navigation vehicles and subsurface storage facilities that they may encounter
In the Northern South China Sea (SCS), ISW has been found to be active and frequently happened phenomenon. Observations have revealed the existence of large amplitude ISWs with amplitude more than 100m and wave crest more than 200km, which propagated out from the Luzon Straits and disappeared on the continental shelf in the Northern South China Sea. Combined with the in situ observation data on ISWs during ASIAEX, this thesis studied the evolution characteristics of ISW on variable topography, and can be resolved into three aspects.
First, the weakly nonlinear variable coefficients KdV theory for ISWs was reviewed and the application of the slowly varying solitary wave theory was discussed, the fission characteristic of ISW was studied numerically. Even further, the two dimensional KP equation for ISWs in continuously stratified fluid was derived, which can be used for the simulation of the two dimensional characteristics of ISW
Second, a nonhydrostatic numerical model for density stratified flow was developed. With this model, we studied the local generation of ISW trains around the continental shelf break; it revealed that the interaction of barotropic tide with the continental shelf break can promote the generation of ISW trains with amplitude of several meters propagating towards the continental shelf. The pycnocline depth and the intensity of the tidal current were two main factors controlling the generation process. After that, we numerically studied the evolution characteristics of large amplitude ISWs on the continental shelf. The simulation captured the depression to elevation conversion the large amplitude ISWs, the effect of topography on the ISW propagation. The nonhydrostatic pressure was quantified. Empirical Orthogonal Function (EOF) method was employed on the analysis of the mode evolution characteristics during this whole process. Results revealed the generation of higher mode during the interaction of the first mode ISW with the shelf break.
Finally, we report the recently developed PIV (Particle Image Velocity) systems for the laboratory experiment on density stratified flow and internal wave research. Experiments were carried out on the run-up of ISW on a slope. Different polarity ISW with different amplitude has been considered. The main focus is on the complex velocity and vorticity field during the strong breaking process, development of vortices structure were analyzed. Furthermore, a typical numerical experiment has been accomplished, results were compared with the laboratory experiment, numerical results provided a clearer picture on the whole breaking process, and revealed the strong mixing process during the ISW run-up and breaking process.
引文
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