Unveiling three-dimensional sea surface signatures caused by internal solitary waves:insights from the surface water ocean topography mission

Internal solitary waves(ISW),characterized by large amplitude and long propagation distance,are widespread in global oceans.While remote sensing images have played an essential role in studying ISWs,they mainly exploit two-dimensional image information.However,with the launch of the surface water ocean topography(SWOT)satellite on December 16,2022,a unique opportunity has emerged to capture wide-swath three-dimensional ISW-induced sea surface information.In this study,we examine ISWs in the Andaman Sea using data from the Ka-band Radar Interferometer(KaRIN),a crucial sensor onboard SWOT.KaRIN not only provides backscattering satellite images but also employs synthetic aperture interferometry techniques to retrieve wide-swath two-dimensional sea surface height measurements.Our observations in the Andaman Sea revealed the presence of ISWs characterized by dark-bright strips and surface elevation solitons.The surface soliton has an amplitude of 0.32 m,resulting in an estimation of ISW amplitude of approximately 60 m.In contrast to traditional two-dimensional satellite images or nadir-looking altimetry data,the SWOT mission’s capability to capture threedimensional sea surface information represents a significant advancement.This breakthrough holds substantial promise for ISW studies,particularly in the context of ISW amplitude inversion.

Study of the ability of SWOT to detect sea surface height changes caused by internal solitary waves

Surface Water and Ocean Topography(SWOT)is a next-generation radar altimeter that offers high resolution,wide swath,imaging capabilities.It has provided free public data worldwide since December 2023.This paper aims to preliminarily analyze the detection capabilities of the Ka-band radar interferometer(KaRIn)and Nadir altimeter(NALT),which are carried out by SWOT for internal solitary waves(ISWs),and to gather other remote sensing images to validate SWOT observations.KaRIn effectively detects ISW surface features and generates surface height variation maps reflecting the modulations induced by ISWs.However,its swath width does not completely cover the entire wave packet,and the resolution of L2/L3 level products(about 2 km)cannot be used to identify ISWs with smaller wavelengths.Additionally,significant wave height(SWH)images exhibit blocky structures that are not suitable for ISW studies;sea surface height anomaly(SSHA)images display systematic leftright banding.We optimize this imbalance using detrending methods;however,more precise treatment should commence with L1-level data.Quantitative analysis based on L3-level SSHA data indicates that the average SSHA variation induced by ISWs ranges from 10 cm to 20 cm.NALTs disturbed by ISWs record unusually elevated SWH and SSHA values,rendering the data unsuitable for analysis and necessitating targeted corrections in future retracking algorithms.For the normalized radar cross section,Ku-band and four-parameter maximum likelihood estimation retracking demonstrated greater sensitivity to minor changes in the sea surface,making them more suitable for ISW detection.In conclusion,SWOT demonstrates outstanding capabilities in ISW detection,significantly advancing research on the modulation of the sea surface by ISWs and remote sensing imaging mechanisms.

Dynamic Responses of Top Tensioned Riser Under Combined Excitation of Internal Solitary Wave, Surface Wave and Vessel Motion

An investigation on the dynamic response of a top tensioned riser （TTR） under combined excitation of internal solitary wave, surface wave and vessel motion is presented in this paper. The riser is idealized as a tensioned slender beam with dynamic boundary conditions. The KdV-mKdV equation is chosen to simulate the internal solitary wave, and the vessel motion is analysed by using the method proposed by Sexton. Using finite element method, the governing equation is solved in time domain with Newmark-13 method. The computation programs for solving the differential equations in time domain are compiled and numerical results are obtained, including dimensionless displacement and stress. The action of internal solitary wave on the riser is like a slow powerful impact, and is much larger than those of surface wave and vessel motion. When the riser is under combined excitation, it vibrates at frequencies of both surface wave and vessel motion, and the vibration is dominated by internal solitary wave. As the internal solitary wave crest passes by the centre of the riser, the maximum displacement and stress along the riser occur. Compared to the lower part, the displacement and stress of the riser in the upper part are much larger.

MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS

A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid(VOF) method was used to reconstruct the free surface. The model was verified by experimental data. Then the model was used to simulate solitary wave interaction with submerged, alternative submerged and emerged semi-circular breakwaters. The process of velocity field, pressure field and the wave surface near the breakwaters was obtained. It is found that when the semi-circular breakwater is submerged, a large vortex will be generated at the bottom of the lee side wall of the breakwater; when the still water depth is equal to the radius of the semi-circular breakwater, a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting, but the velocity near the bottom of the lee side wall of the breakwater is always relatively small. When the semi-circular breakwater is emerged, and solitary wave cannot overtop it, the solitary wave surface will run up and down secondarily during reflecting from the breakwater. It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.

NON-PROPAGATING SOLITARY SURFACE WAVE IN AN ANNULAR TROUGH

The nonlinear equation governing the nonpropagating solitary surface wave and its single solitary wave solution were derived by the method of multiple scales.The results obtained were compared with that in rectangular trough.

Numerical Simulation of Spatial Lag Between Wave Breaking Point and Location of Maximum Wave-Induced Current

A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point. The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direc- tion. The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress. An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy. The wave driver model is a phase-averaged wave model based on the wave action balance equation. Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach am used to evaluate the model＇s performance. The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.

An Improved Nearshore Wave Breaking Model Based on the Fully Nonlinear Boussinesq Equations

This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.

Multi-lens stereo reconstruction of wave surface in a wave basin

A new method is developed to measure the wave surface elevation in a wave basin.A thin film of tiny granules floating on the free surface ensures the formation of the dot grid pattern on the wave surface.The dot grid pattern is generated by a high-brightness projector.The granule film has little influence on the wave propagation in a wave basin.The measuring system is validated by the experiments of the propagation of solitary wave in water of uniform depth.It turns out that the time series of the surface elevation measured by the multi-lens stereo reconstruction method agree well with that measured by wave gauges.The errors of the measuring system are discussed.This work sheds a light on measuring the local wave field with high precision and efficiency in laboratory.

内孤立波对同反向传播的表面波的调制特征研究

当内孤立波在海洋内部传播时,会引起表层水体的辐聚辐散,从而对海表波浪进行调制作用。本文使用计算流体力学(Computational fluid dynamics,CFD)技术,针对内孤立波对表面波的调制问题进行数值模拟研究。建立两层模型,模拟了表面波在同反向传播的情况下,不同振幅内孤立波对不同波长表面波的调制过程。基于表面波的波长和波高这两个基本特征,发现内孤立波引起的表层水平流速变化会调制表面波的波高,相同方向传播时,表面波波高会在最大水平流速附近处减小,而相反传播时会增大。同时内孤立波引起的水体辐聚辐散(水平流速梯度)的分布会调制表面波的波长特征,表面波波长会在流场辐散的区域变长,在流场辐聚的区域变短。表面波受调制作用变化的强弱与内孤立波振幅、表面波初始波长相关。内孤立波振幅的增加会加强调制作用,使得表面波波高与波长的变化程度更显著。表面波初始波长增加会减弱调制作用。本研究着重分析了内孤立波对表面波的调制作用,得到了内孤立波引起的上层水体流动和受调制的表面波具体的对应关系与变化规律,有助于更好地理解内孤立波对表面波调制的水动力过程,对于解读内波成像的过程有重要意义。

Three-dimensional numerical modeling of nearshore circulation

A three-dimensional nearshore circulation model was developed by coupling CH3D, a three-dimensional hydrodynamic model and REF/DIF, a nearshore wave transformation model. The model solves the three-dimensional wave-averaged equations of motion. Wave-induced effects on circulation were introduced in the form of radiation stresses, wave-induced mass transport, wave-induced enhancement of bottom friction and wave-induced turbulent mixing. Effects of breaking waves were considered following Svendsen (1984a and 1984b) and Stive and Wind (1986). The model was successfully tested against the analytical solution of longshore currents by Longuet and Higgins (1970). The model successfully simulated the undertow as observed in a laboratory experiment by Stive and Wind (1982). In addition, the model was applied to a physical model by Mory and Hamm (1997) and successfully reproduced the eddy behind a detached breakwater as well as the longshore current on the open beach and the contiguous eddy in the open area of the wave tank. While the qualitative agreement between model results and experimental observations was very good, the quantitative agreement needs to be further improved. Albeit difficult to explain every discrepancy between the model results and observations, in general, sources of errors are attributed to the lack of understanding and comprehensive description of following processes: (1)the horizontal and vertical distribution of radiation stress, especially for breaking waves;(2)the detailed structure of turbulence;(3)Wave-current interaction (not included at this moment); and (4)the wave-current boundary layer and the resulting bottom shear stress.

内孤立波中潜水器纵向运动特性数值仿真研究

海洋中内孤立波会诱发突变的环状剪切流,导致潜水器产生大幅度的垂向掉深和俯仰运动,给潜水器航行安全和作业性能带来威胁。本文基于CFD的速度入口造波法和重叠网格技术,建立内孤立波中潜水器运动响应预报方法,通过与分层流水池试验结果对比,证明该方法可准确模拟内孤立波中潜水器大振幅运动;通过对处于分层界面的无动力悬浮潜水器在内孤立波中的运动过程模拟分析,揭示内孤立波中潜水器掉深及俯仰运动产生机理,同时探究分层厚度比、波幅、潜深等参数对无动力悬浮潜水器纵向运动的影响规律。结果表明:潜水器在内孤立波中的掉深和俯仰运动幅值是由内孤立波波幅和最大波倾角决定;波幅、分层厚度比、潜深等因素对潜水器纵向运动特性有较大影响。

一种改进的近岸波浪破碎数值模型

提出一种基于完全非线性Boussinesq方程的改进波浪破碎模型,用于模拟近岸浅水波浪破碎。模型借助水滚的概念,提出一种确定k方程紊动模式中紊动源项的计算公式,通过解k方程计算Boussinesq方程中的涡黏系数,实现对破碎波的模拟。岸边界采用窄缝法,使得模型可用于波浪爬坡的计算。用实验室实测波高和增减水资料对模型进行了验证,得到了一致的结果。紊动源、紊动动能以及紊动耗散率的计算结果表明:①在破波点处紊动源项值最大,随着波浪向岸边传播,逐渐减小;②破波点处,水平方向的对流和扩散在紊动能量输移中发挥重要作用;③岸边附近紊动源与紊动耗散接近平衡。

非均匀海流、表面波与内孤立波共同作用下钻井隔水管准静态分析

针对我国南海内孤立波活动频繁的实际情况,建立了非均匀海流、表面波和内孤立波联合作用下钻井隔水管的准静态分析模型,并分别采用Airy线性波理论和两层流的Kd V理论计算表面波和下凹型内孤立波的速度和加速度,利用有限差分离散和LU分解法求解钻井隔水管的静态微分方程。方法验证结果表明,本文方法与其他文献结果吻合较好,具有较高的可靠性。实例分析结果表明,表面波和内孤立波分别在相位角为12°和0°时对隔水管的准静态性能影响最大;内孤立波使上层流体中隔水管的横向偏移、弯矩、Von Mises应力大幅增加;在内孤立波波谷对应深度附近,隔水管弯矩呈"台阶状"突变,剪力呈"尖峰状"突变;内孤立波振幅越大、上下两层海水密度差越大,内孤立波对隔水管受力与变形的影响越剧烈。建议加强我国南海各油气区内海洋内孤立波的监测和预测,更好地指导海上钻井隔水管安全作业。

近岸波生流运动三维数值模拟及验证

开发建立了近岸波生流运动三维数值计算模式。模式中,引入了三维时均剩余动量、破波表面水滚、波浪水平与垂向紊动作为主要驱动力,同时考虑了波流共同作用的底部剪切力。推导了可综合反映底坡、能量传递率和密度影响的水滚能量传输方程;将Larson-Kraus的二维波浪水平紊动系数表达式拓展至三维。采用大量实测数据和文献资料测试验证了所建模式,表明所建模式可有效模拟波浪增减水、底部离岸流、沿岸流、裂流、堤后环流等不同维度的波生流现象。此外,研究也表明破波水滚效应可解释波生流峰值向岸推移的物理现象,从而在模拟中不能忽略;破波带内沿岸流速垂向较为均匀的现象与波浪附加垂向紊动有关。

用NS方程模型模拟孤立波在各种防波堤堤前的爬高

本文以Navier Stokes方程为控制方程,用k ε模型来封闭湍流模型,采用VOF方法来跟踪波动自由表面,建立了二维垂向数学模型。并用解析解和实验数据对模型进行了验证。利用此数学模型模拟了在水位较浅,不发生越浪的情况下,孤立波在直立堤、斜坡堤、半圆型防波堤堤前爬高的过程,并对波面、速度场和压强场进行了比较。

拉伸状态下LDPE/SiO_2改性材料的空间电荷特性研究

为深入研究低密度聚乙烯(low-density polyethylene,LDPE)/Si O_2改性材料内部空间电荷的运动特性,利用纳米粒径分别为15和50 nm的Si O_2纳米粒子制备了质量分数为5%的LDPE/Si O_2改性材料,同时制备了拉伸率为10%的样品,利用电声脉冲(pulsed electroacoustic apparatus,PEA)法装置测量了每种样品的空间电荷分布。结果表明:添加Si O_2纳米粒子后,材料中靠近电极处的空间电荷累积由异极性电荷转变为同极性电荷;拉伸后,所有材料内部的空间电荷累积量均出现了增加,并且当拉伸率为10%,质量分数为5%时,LDPE/Si O_2改性材料内部出现了空间电荷大量累积的现象,在材料中心位置处形成了两个不同极性的空间电荷包,15nm粒径改性材料的空间电荷包远小于50nm粒径的改性材料。文中从弧波理论、电荷在改性材料中的受力以及具有不同介电常数材料表面电荷的累积等方面对LDPE/Si O_2改性材料内部的空间电荷包现象进行了详细解释,为深入理解空间电荷在改性材料中的运动特性和分布特性提供参考。

用时变雷诺方程模型模拟孤立波与半圆型防波堤的相互作用

以时变雷诺方程为控制方程,用k＿ε模型封闭该方程,采用体积函数(VOF)方法来跟踪波动自由表面,建立了二维垂向波浪数学模型,并用已有的实验资料进行了验证· 随后用该模型模拟了半圆型防波堤与孤立波在淹没、平顶水位、完全露顶且不越浪3种典型工况下的相互作用过程· 得到了半圆堤附近的流场、压强场和波面的变形过程· 结果表明,在淹没状态下,半圆堤背浪面的底部会产生涡旋;平顶水位时,由于越浪的冲击作用,在半圆堤的背浪面将逐渐形成一对较大的涡旋,而半圆堤背浪面的底部,速度始终相对较小;而在露顶不越浪时。

MCC-FS内孤立波模型算法及速度场研究

针对浅水模式下的两层流体间大幅内孤立波问题,本文给出了MCC-FS模型的速度场结果,并使用物理实验结果进行验证。采用考虑自由面效应的MCC-FS模型开展了研究,并针对MCC-FS模型,提出了一种稳定、高效的算法。使用中心差分法对一阶和二阶导数进行空间离散,使用牛顿迭代法对MCC-FS模型4个方程进行直接求解。研究表明:通过该算法可同时求得内波波形、自由表面波波形以及上、下层平均速度。

波浪在浅水中运动及破碎的数值研究

在一维的 Boussinesq方程中引入表面翻滚的概念 ,通过附加迁移动量项来考虑浅水中的波浪运动以及破碎情况 ,建立数学模型。利用此数学模型对 Airy波和孤立波在浅水中运动以及破碎情况进行模拟 ,得出的结果与 Schoiffer和 Goda的结果比较 ,吻合良好。

任意拉格朗日欧拉有限元法中的自由面网格追踪分析(英文)

本文对任意拉格朗日欧拉有限元法中的自由面网格追踪问题进行了分析。在任意拉格朗日欧拉坐标系下,用非定常不可压的N avier-Stokes 方程来描述粘性带自由面流体的运动,在时间的数值积分中采用了速度修正分步法。文中提出了四种不同的自由面网格追踪方法,并对用各种方法得到的数值结果进行比较,得到了较优的追踪方法。为了验证方法的有效性,对孤立波传播进行了详细的分析。