海洋环境与人类社会生产生活息息相关。在世界各地的海洋中，由温盐梯度结构形成的密度分层，流动引起密度扰动可以以内波的形式传播。密度分层对物理海洋学以及地球物理、工业和环境应用中若干基本过程的影响成为研究的热点。对分层环境中内波生成演化的研究，有助于推动理解全球洋流的能量级串机制、自然内波与海上结构物或海底地形之间的耦合作用以及海洋中运动物体激发的小尺度内波尾迹。这些内波通常具有规则的模式，其特征研究能够为内波识别与反演提供参考结果与指引。本文围绕海洋环境中内波理论与数值模拟这一关键科学问题，目的在于推进海洋中扰动源激发内波的生成演化机理研究及海洋中关键环境要素的精细刻画模拟。

以海洋大尺度自然内波为研究对象、流固耦合系统为应用背景，引入了弹性恢复力，建立了小尺寸非平坦地形作用下的水弹性内界面波线性和非线性理论模型，实现了基于边界积分法的水弹性内波稳定水跃解数值计算方法，得到了全欧拉方程新的水弹性水跃和陷波解。对比重力界面波，分析了弹性力作用下水跃解形状的变化，以及地形形状、极性对水跃解水动力参数的影响。发现了水跃解和陷波解随刚度参数变化的非唯一性，并确认了基于色散关系对陷波出现的位置、波长进行预测的可行性。结果对于地形影响海洋中结构物载荷的应用具有参考意义。

拓展了水波问题中的非局部表达方法，推导了含大尺寸地形的多层流体系统线性近似下的DtN（Dirichlet-to-Neumann）算子谱空间表达式，实现了真实海洋环境中的多模态内波与大振幅地形相互作用的新数值模拟程序，解除了传统数值计算方法对系统维数、地形尺寸和光滑性的限制。二维线性波爬坡和三维龙勃透镜效应地形算例与理论解对比验证了程序的正确性。基于该数值方法，发现了多模态内波过局部地形时，模态转换现象仅在大斜率地形作用下出现。一模态内波与快速变化地形相互作用典型现象包括Bragg共振、二模态内波的激发、高阶共振及均化效应。最后，实现了真实直布罗陀海峡地形条件下的内波与自由表面波的演化过程数值模拟，推进了对自然内波、表面波在真实海洋地形作用下的演化特征分析与理解。

揭示了海洋环境中水下运动航行体作为扰动源在其近场激发小尺度内波生成、传播机理和内波特征随水动力参数演化规律。发展了适用于任意连续密度分层的内波求解器，结合浸没边界法和大涡模拟，实现了对复杂航行体几何、近场尾流、体效应及尾流效应诱导内波的精细捕捉。应用复杂双向密度分层模型，首次定义并提取了密跃层中的体效应内波尾迹特征量。统计了内波尾迹夹角及波长随弗劳德数和密跃层厚度变化标度率，并形成了特征量随水动力参数演化图谱。

进一步揭示了湍流远尾迹流动结构时空演化机理及湍流效应内波空间传播、尺度变化、水面表征演化规律。在高精度谱方法框架下实现了远场湍流尾迹的长时间演化计算和内波求解。首先，分析了均匀分层环境下湍流尾迹衰减过程、尾迹尺寸及内波水面表征随浮力频率的变化规律。其次通过谱分析，给出了内波空间传播过程中不同潜深位置的尺度、强度演化规律及机理。最后在真实海洋分层环境中，说明了非均匀分层结构导致内波传播具有非对称性，传播方向随浮力频率变化，并证明了扰动所在潜深对流动结构影响微弱，但对内波水面表征强度影响明显。

最后，引入真实海况的风浪因素，初步形成了低航速条件下湍流效应内波尾迹与风浪场的尺度相互作用分析。一方面给出了密度分层环境下风浪背景流场特征随浮力频率变化，另一方面风浪与尾迹耦合数值模拟结果表明湍流尾迹与背景风浪场在低航速大潜深条件下以线性作用为主。基于水面信噪比结果和水下流动统计量分布，讨论了内波识别的潜在可行性。理解体效应和湍流效应尾迹在海洋工程中仍然是一个热门话题，并可以为流场特征、航行体的水动力参数设计以及潜在的内波识别策略提供重要信息。

Oceanic environment is always closely related to production and living of human society. Across the world’s oceans, variation of density caused by thermohaline structure gives rise to density disturbances that can propagate in the form of internal waves. There has been growing interest in the effect of stratification on several essential processes in physical oceanography as well as geophysical, industrial, and environmental applications. Researches on generation and evolution of internal waves in stratified fluid, aiming to understand the global cascade of energy in ocean currents, the interaction between internal waves and offshore facilities or bottom topography and the internal wave wakes excited by moving submerged body, are essential. These internal waves usually show particular patterns, of which the characteristics can be references for detection applications. In this thesis, the key scientific problem of theoretical and numerical studies of internal waves in ocean is considered, aiming to reveal the mechanism of excitation of internal waves due to main perturbation sources and to proceed the fine depiction of key ingredients in oceanic environment.

Large scale internal waves in oceans excited by varying bottom topography with small amplitude are considered. The physical scenario is analogous to applications of systems with elastic body coupled with fluid motion. Linear and weakly nonlinear theories for hydroelastic interfacial waves over small bottom obstacle are established. Besides, boundary integral method is applied to solve the full Euler equation for hydroelastic hydraulic falls and trapped waves. New solutions are found and are compared to the gravity waves. Differences between wave profiles are elaborated as well as the changes in behavior with obstacle size and rigidity parameter. Non-uniqueness for hydroelastic hydraulic fall and trapped wave solutions is presented. The position and wavelength of trapped waves are proved to be predicted by theoretical model. Analysis represents reference for situation where the elastic plate plays a role as an offshore facility, the influence exerted by an obstruction on bottom topography can be important and might need to be considered.

Non-local formulation for water wave problems is extended along with theoretical derivation of Dirichlet-to-Neumann operators in multilayer fluid system with large bottom topography under linear approximation in order to adapt for multimode internal waves interacting with varying bottom in oceanic environment. New numerical method is established, eliminating restrictions on amplitude, smoothness of bottom obstacle and dimension of the system. Simulations of two-dimensional linear wave shoaling and three-dimensional internal waves passing over a Luneberg lens mound are performed and the results are compared with theoretical solutions for validation of algorithm. Based on this numerical method, mode excitation is found to occur while internal waves pass over a locally confined obstacle with large slope. Typical phenomena in evolution of internal waves passing over quickly varying bottom topography including Bragg resonance, mode excitation, high order resonance and homogenization effect are investigated. Finally, internal waves and free surface waves simulated with realistic varying depth in the Strait of Gibraltar are analyzed for understanding their characteristics more profoundly.

Small scale internal wave wakes excited by a moving submerged body in near field are investigated. The mechanisms of generation and propagation of these internal waves as well as the characteristics varying with hydrodynamic parameters are revealed. The solver for arbitrary and continuous density stratification is developed, combining with immersed boundary method and large-eddy simulation, for capturing the complex geometry of submerged body and the internal waves excited by bulk and wake effect. Characteristics of internal wave wakes under bidimensional density stratification are extracted for analysis on the influence of different hydrodynamic parameters to provide a scattergram. Scalings of wake angle and wavelength in function of Froude numbers and thicknesses of pycnocline are given.

Moreover, the time-spatial evolution of turbulent wakes in far field, propagation of internal wakes excited, the variation of dominant scales and the surface manifestation of wakes are investigated based on simulations with high resolution spectral method. The decay of turbulent wake, development of wake sizes and surface manifestation in uniformly stratified flows are firstly analyzed. Then, spectral analysis shows the mechanism of evolution of dominant scale and intensity at different depths for spatial propagation of internal waves. The effect of nonuniform stratification in changing the direction of propagation and generation of asymmetry is illustrated with realistic stratification. The influence of diving depth is also investigated, which is proven to be negligeable on wake structure but evident on surface manifestation.

Finally, the wind and wave effect are introduced in the same numerical frame. Interactions between turbulent wakes and environmental background flow field is studied. On one side, the wind wave turbulent fields in uniformly stratified fluid are proved to be correctly generated and corresponding flow structures are analyzed. On the other side, coupled evolution demonstrates that with low velocity and large diving depth, linear interactions dominate the whole system. The potential application of internal wave wake detection is elaborated based on the result of signal to noise ratio. The motivation for investigating these internal wave wakes is that understanding the bulk flow and turbulent wakes remains a hot topic and a challenging and significant task in ocean engineering. Corresponding researches can provide crucial information about the flow field features, design for the submerged body in terms of hydrodynamic parameters, and potential effective detection strategies.