Envelope solitary waves and their reflection and transmission due to impurities in a granular material

A nonlinear Schrodinger equation in one-dimensional bead chain is first obtained and an envelope solitary wave of the system is verified numerically in this system. The reflection and the transmission of an incident envelope solitary wave due to impurities has also been investigated. It is found that the magnitudes of both the reflection and the transmission not only depend on the characters of impurity materials, the wave number, the incident wave amplitude, but also on the impurity number. This can be used to detect the character and the number of the impurity materials in the bead chain by measuring the reflection and the transmission of an incident pulse.

Particle-in-Cell Simulation of the Reflection of a Korteweg-de Vries Solitary Wave and an Envelope Solitary Wave at a Solid Boundary

Reflections of a Korteweg-de Vries （KdV） solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method. Defining the phase shift of the reflected solitary wave, we notice that there is a phase shift of the reflected KdV solitary wave, while there is no phase shift for an envelope solitary wave. It is also noted that the reflection of a KdV solitary wave at a solid boundary is equivalent to the head-on collision between two identical amplitude solitary waves.

Numerical Simulation of Solitary Wave Forces on A Vertical Cylinder on A Slope Beach

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves.Based on the Reynolds-averaged Navier-Stokes equations and the k-ε turbulence model,wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations.The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy.Then,the wave forces and characteristics around the cylinder are studied,including the velocity field,wave surface elevation and pressure.The effects of relative wave height,Keulegan-Carpenter(KC)number and cylinder locations on the wave forces are also discussed.The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number.Before the wave force peaks,the growth rate of the wave force shows an increasing trend as the cylinder moves onshore.The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region.As the cylinder moves onshore,the wave force on the cylinder initially increases and then decreases.For the cases considered here,the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline.Furthermore,the fluid velocity peaks when the maximum wave force appears at the same location.

Experimental, Numerical and Simplified Theoretical Model Study for Internal Solitary Wave Load on FPSO with Emphasis on Scale Effect

Scale effect of ISWs loads on Floating Production Storage and Offloading(FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depthaveraged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model.The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension.Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.

A numerical study of generation and propagation of type-a and type-b internal solitary waves in the northern South China Sea

Numerical simulations based on a high-resolution three-dimensional MIT general circulation model(MITgcm)using realistic topography and tidal forcing are conducted to investigate the generation and propagation of the so-called type-a waves(large-amplitude rank-ordered wave packets)and type-b waves(isolated wave packets)in the northern South China Sea.At first,we summarized and analyzed the generation and propagation characteristics of these waves.Then,energy budget at the Luzon Strait is calculated.Energy generation has three local maxima every day,of which the largest one corresponds to the emergence of the type-a wave.Energy flux at the west boundary of the Luzon Strait shows two local maxima each day.The larger one is consistent with the generation of the type-a wave and the smaller one is in correspondence with the generation of the type-b wave.Sensitivity experiments are designed to explore the role of the east and west ridge of the Luzon Strait on the generation and propagation of the type-a and type-b waves.It is found that the east ridge is indispensable on the generation of the type-a wave while the west ridge has little contribution.The west ridge diminishes the type-a waves'amplitude but hardly changes their propagation speed.The type-b waves also come from perturbation signals which originate from the east ridge and are enhanced in amplitude and reduced in propagation speed by the west ridge.

On the Generation and Evolution of Internal Solitary Waves in the Andaman Sea

Internal solitary waves(ISWs)are ubiquitous in the Andaman Sea,as revealed by synthetic aperture radar images;however,their generation mechanisms and corresponding influencing factors remain unknown.Based on a nonhydrostatic two-dimensional model,the generation of ISW packets along the transect of a channel lying between Batti Malv Island and Car Nicobar Island is investigated.Moreover,the influences of topographic characteristics,seasonal stratifications,and tidal forcings are analyzed through a series of sensitivity runs.The simulation results indicate that bidirectional rank-ordered ISW packets are generated by the nonlinear steepening of internal tides.An east-west ISW asymmetry is observed,which is attributed to distinct topographic characteristics.The surrounding sills can also generate internal wave beams,which modulate the intensity of ISWs.However,the topographic structure of the west flank of the ridge mainly contributes to the suppression of westward ISWs,which decreases the modulating effect of internal wave beams.During the spring tide,the generation of ISWs is enhanced.During the neap tide,ISWs are weak,and the east-west ISW asymmetry is less obvious.Moreover,seasonal stratification only has a minor effect on the generation and evolution of ISWs.

Numerical Simulation and Physical Simulation of Sea Wave Groups

Based on field wave data, an empirical formula of wave envelope spectrum is given in this paper. Then the methods of both numerical and physical simulation of sea wave groups with the given spectrum and groupiness parameters are suggested.

Particle trajectories under interactions between solitary waves and a linear shear current

This paper is concerned with particle trajectories beneath solitary waves when a linear shear current exists.The fluid is assumed to be incompressible and inviscid,lying on a flat bed.Classical asymptotic expansion is used to obtain a Korteweg-de Vries(Kd V)equation,then a forth-order Runge-Kutta method is applied to get the approximate particle trajectories.On the other hand,our particular attention is paid to the direct numerical simulation(DNS)to the original Euler equations.A conformal map is used to solve the nonlinear boundary value problem.Highaccuracy numerical solutions are then obtained through the fast Fourier transform(FFT)and compared with the asymptotic solutions,which shows a good agreement when wave amplitude is small.Further,it also yields that there are different types of particle trajectories.Most surprisingly,periodic motion of particles could exist under solitary waves,which is due to the wave-current interaction.

A Numerical Study on the Mechanisms Producing Forces on Cylinders Interacting with Stratified Shear Environments

A three dimensional(3D)numerical wave flume is used to investigate carefully the ISWs(Internal solitary wave)forces acting on cylinders interacting with a stratified shear environment.Using the Large-Eddy Simulation(LES)approach and analyzing the distribution of shear stress and pressure along the surface of the cylinder,the differential pressure resistance and the viscous force are obtained.The method of multiple linear regression analysis is adopted and a comprehensive influence coefficient is determined accordingly to account for the dimensionless forces acting on the cylinder.Results show that the differential pressure resistance on a square cylinder is 1.5 times higher than that on a circular cylinder in the upper layer,while the differential pressure resistance on a square cylinder is 3.5 times larger than that on a circular cylinder in the lower layer.The viscous force is 1–2 orders of magnitude smaller than the differential pressure resistance,which means that the viscous force could be ignored.The comprehensive influence coefficient shows positive correlation with the relative wave height and negative correlation with upper and lower water depth ratio.

内波环境下水下滑翔机流场与载荷特性分析

为保障水下滑翔机的作业安全,本文采用k-Epsilon湍流模型,结合自定义场函数建立了密度分层流体中水下滑翔机的流场与载荷特性分析的CFD模型。结果表明:水下滑翔机在工作时不能忽略内波的影响。当滑翔机经过内孤立波时,滑翔机所处的流场流速会增大,涡量也会明显增大;当滑翔机接近交界面时,滑翔机受到的升力和俯仰力矩变化趋势增大,远离交界面时,阻力会逐渐增大;当滑翔机的俯仰角增大时,其受到的阻力幅值会减小,升力幅值变化较小,俯仰力矩的幅值增大。本文揭示了内波环境下水下滑翔机的流场与载荷特性,对经典式水下滑翔机的设计以及作业时遭遇内孤立波的水动力响应预测具有重要的理论和工程意义。

两相流模型在南海内孤立波与沙波相互作用中的应用

为研究内孤立波与沙波的相互作用,本文对基于OpenFOAM的SedWaveFoam求解器进行改进,建立了内孤立波-泥沙运动欧拉两相流模型。在利用试验资料对模型进行验证的基础上,在南海北部典型代表性条件下,模拟分析了500 m水深位置沙波床面上内孤立波作用下的水动力变化和泥沙运动。结果表明,内孤立波逐渐离开沙波时,海底沙波背流面处出现与内孤立波背景流速反向的流速,在内孤立波导致的流场作用下,沙波床面上的泥沙悬起并运动到床面以上的水体中。振幅100 m的内孤立波可以导致床面以上14 m高的位置处出现约0.07 kg/m3的悬沙浓度。

海底物体运动生成内波问题研究

为研究物体在海底运动产生大幅内孤立波问题,本文基于商业软件STAR-CCM+,选用无粘模型,求解欧拉方程,采用流体体积法监测内波界面,对网格、时间步长开展收敛性分析,得到STAR-CCM+计算的内波波面空间分布收敛结果与全非线性势流模型结果高度吻合。研究了物体形状对于生成内波的影响,对比了上下层液体密度比分别为0.787和0.95时,刚盖假设与自由表面这2种不同边界条件下的内波波面空间分布结果,研究表明:当上下层液体的密度比不接近1时,必须考虑自由面效应对内波波幅和波速的影响。

风对孤立波海堤越浪特性影响的数值模拟研究

海堤在保护沿海城镇免受极端波浪破坏方面具有重要作用。该文基于二维不可压缩两相流数值模型,系统研究了向岸风对孤立波海堤越浪特性的影响。通过数值计算结果与实验数据的对比,验证了该数值模型的可靠性,并重点讨论了向岸风风速、入射波高、堤顶超高、岸滩坡度和海堤坡度等因素对孤立波海堤越浪水动力过程的影响。研究表明:随着向岸风风速、入射波高的增大以及堤顶超高的减小,孤立波的最大越浪量、最大爬高以及沿程最大水位高程逐渐增大;随着岸滩坡度和海堤坡度的增大,孤立波的最大越浪量分别增大和减小,最大爬高逐渐增大。向岸风会影响孤立波海堤越浪的水动力特性,增大孤立波的波陡以及波峰传播速度,使波浪提前破碎;相比无风情况,最大越浪量、最大爬高、最大水动力荷载以及沿程最大水位高程均有所增大。研究结果可为海岸工程的设计提供参考。

内孤立波对海洋结构物与潜体作用机制综述

内孤立波是密度分层水体中产生并传播的一种特殊波动。在这一过程中,如果遇到地形变化复杂的浅海区域,内孤立波会因地形的影响而表现出变形、失稳和破碎,并在海底附近区域产生强烈的紊动混合和能量耗散。其可使海洋结构发生移位或扭曲,也可削弱潜艇的运动稳定性而失去控制。这一系列过程的动态特性一直是国内外学者的研究焦点。该文从物理试验、数值模拟2方面总结海洋内孤立波常见的研究方法,并归纳海洋结构物和潜体在分层强剪切环境下受到内波的作用特性,这对掌握内孤立波特性以及探索海洋资源和海洋工程建设具有一定的工程意义。

On the generation and propagation of internal solitary waves in the southern Andaman Sea:A numerical study

Numerous internal solitary waves(ISWs)have been observed in the southern Andaman Sea.In this study,the twodimensional Massachusetts Institute of Technology general circulation model is applied to investigate the dynamics of ISWs and explore the effects of the bottom topography and tidal forcing on the generation and propagation of ISWs in the southern Andaman Sea.The results show that the large-amplitude depression ISWs are mainly generated via the oscillating tidal flow over the sill of the Great Channel,and the generation of ISWs is subject to the lee wave regime.The Dreadnought Bank cannot generate ISWs itself;however,it can enhance the amplitudes of eastward-propagating ISWs generated from sill A,owing to constructive interference of internal tide generation between the sill of the Great Channel and the Dreadnought Bank.The eastward-propagating ISWs generated by the eastern shallow sill near the continental shelf can propagate to the shelf,where they evolve into elevation waves because of the shallow water.Sensitivity runs show that both the semidiurnal and diurnal tides over the sill of the Great Channel can generate ISWs in this area.However,the ISWs generated by diurnal tides are much weaker than those generated by semidiurnal tides.Mixed tidal forcing has no significant effect on the generation of ISWs.

内孤立波过陆架陆坡地形的数值模拟研究

内波是海洋中普遍存在的波动形式。内孤立波是典型的非线性内波,多发于陆架边缘海,如南海等海域,对陆架海域有重要影响。本文针对内孤立波在陆架地形上的传播问题,先基于弱非线性与全非线性数值模型,模拟了不同振幅、地形高度条件下内孤立波的演化的过程,探讨了动力系数对内孤立波演化过程的影响,对比了两模型的模拟结果在内孤立波演化过程、能量分配以及能量耗散的差异,后分析了南海的动力系数分布特征。结果表明,在内孤立波不发生破碎的情况下,弱非线性模型与全非线性模拟结果相近。当发生破碎过程时,弱非线性模型可准确模拟头波,但无法通过强非线性的破碎过程耗散能量,只能以裂变的方式辐射能量。在弱非线性模型中,随地形高度增加,频散系数减小到零,平方非线性系数由负转正,立方非线性系数绝对值增大一个量级,并主导陆架地形上内孤立波的演化过程。通过对比南海夏季与冬季非线性内波动力系数空间分布,发现内孤立波在传播过程由于夏季平方非线性效应、立方非线性效应与频散效应较强的影响,其在夏季更易发生陡化与裂变,波列发生频率高。

内波作用下水下航行体水动力载荷及运动特性研究

中国南海区域海洋内波出现频率较多。海洋内波携带着巨大能量,对于水下航行体的安全航行具有非常大的威胁。为了研究内波对水下航行体的水动力性能影响,该文基于RANS方法和KdV理论建立了分层流中的内孤立波与水下航行体相互作用的数值模拟方法。在对约束模型数值模拟分析的基础上,采用DFBI方法结合重叠网格技术,开展了内孤立波作用下水下航行体自由运动的数值模拟。分析表明,内孤立波与航行体相遇,会使得其周围流场变得异常复杂,从而引起突变的流体动力和运动,对此时的航行安全性应给予极大重视。

波群的数值模拟和物理模拟

基于现场实测资料，给出了一个波包谱的经验公式；在此基础上建议了波群的数值模拟和物理模拟方法，可按指定的波谱和波群特征参数，数值模拟和在实验水槽中制造出所要求的波群，得到了满意的结果．

内孤立波环境下圆柱和方柱受力特征——Ⅱ.数值模拟

柱体受内波作用力的数值模拟大多针对圆柱展开,方柱在内波环境下受力特性研究较少。借助三维数值波浪水槽,采用大涡模拟(LES)技术研究了内孤立波的产生、传播及其对不同形状柱体的受力特性。对比分析了内孤立波波幅对圆柱和方柱受力的影响规律。研究表明,在分层流环境下,随着内孤立波波幅的增大,圆柱和方柱所受的水平作用力均增大;相同波幅情况下,无论在上层或下层水体,方柱表面的压力分布更不均匀,迎流面与背流面的压差更大,从而导致方柱相较于圆柱会受到更大的水平作用力。

S波包络时间差影响因素的数值分析

介质非均匀性可引起高频S波包络的展宽.S波包络展宽是定量研究岩石圈中随机速度非均匀性的有力工具.S波的初至与其均方根包络最大振幅的一半之间的时间延迟定义为S波包络时间差,该时间的大小可反映介质非均匀性强弱.采用有限差分算法模拟了2DvonKrmn型随机介质中S波包络的展宽现象,统计分析了影响S波包络时间差的主要因素.结果表明,随机介质中S波传播的距离、随机介质速度扰动率及S波频率均可对S波包络时间差产生影响.相比较而言,速度扰动率对S波包络时间差影响程度最大,S波传播距离次之,S波频率影响程度最小.