Numerical Model of Internal Solitary Wave Evolution on Impermeable Variable Seabed in A Stratified Two-Layer Fluid System

1.IntroductionIn mathematics and physics,a soliton is a self-reinforcing solitary wave caused by nonlinear ef-fectsinthe medium.Solitons are found in many physical phenomena(Chou and Shih,1996;Chouand Quyang,1999;Chouet al.,2003;Chenet al.,2004;Wang,2004;…     

陡坡上孤立波爬高的数值模拟

波浪爬高是海岸工程中重要的水动力学问题之一,其数值模拟方法通常是通过离散Navier-Stokes方程或Boussinesq方程实现的,其中基于光滑粒子流体动力学方法是近年发展起来的。本文应用该方法模拟相同水深下,不同波高的孤立波在45(°)陡坡上的爬高,模拟结果与理论计算结果及已有物理模型试验结果进行了对比,并模拟出孤立波激散破碎过程及粒子分布和速度场的变化过程。结果表明,对密度近似方程进行重新初始化保持了流场内的质量守恒,同时整个计算域内的压力分布更加规则,说明光滑粒子流体动力学法在波浪爬高计算中的有效性。     

Comparisons of Computational and Experimental Results of Solitary Wave Breaking

- In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume of fluid (VOF) method. The topography used in the experiment consists of three segments. The left segment is a 1:4 slope, the middle segment 1 :SO slope and the right segment a horizontal bed. Both the wave heights and breaking points obtained from numerical simulation and experiments are in good agreement. Numerical results give reasonable pressure distributions of breaking waves on the wall.     

RANS Modeling of Solitary Wave Propagation over A Submerged Rectangular Breakwater

In this paper a series of numerical simulations are performed to investigate the vortex shedding mechanism for a solitary wave propagating over a submerged breakwater by use of Reynolds averaged Navier-Stokes (RANS) model combined with a k-ε model. Flows of different Reynolds numbers up to Re=1.4×105 corresponding to varying incident wave heights are considered in which the characteristic fluid velocity is represented by the maximum horizontal velocity above the submerged breakwater. For the verification of...     

RANS Modeling of Solitary Wave Propagation over A Submerged Rectangular Breakwater

In this paper a series of numerical simulations are performed to investigate the vortex shedding mechanism for a solitary wave propagating over a submerged breakwater by use of Reynolds averaged Navier-Stokes (RANS) model combined with a k-ε model. Flows of different Reynolds numbers up to Re=1.4×105 corresponding to varying incident wave heights are considered in which the characteristic fluid velocity is represented by the maximum horizontal velocity above the submerged breakwater. For the verification of the accuracy of the numerical model, the incident waves and the velocity field in the vicinity of the breakwater are compared with experimental data. The result shows that the model is capable of describing vortex shedding for a solitary wave propagating over a rectangular submerged breakwater. Key features of vortex generation, evolution and dissipation are investigated. It is found that the vortex shedding and their evolution due to separated boundary layer over the breakwater are strongly related to the Reynolds number. A considerable number of vortices and complicated vortex pattern are observed as the Reynolds number increases.     

Laboratory Observations on Internal Solitary Wave Evolution over A Submarine Ridge

Laboratory experiments were conducted in a wave flume on internal solitary wave （ISW） of depression and elevation types propagating over a submarine ridge in semicircular/triangular shape. Tests were arranged in series for combinations of submarine ridges of different heights and ISW of different amplitudes. The resuhant wave motions were found differing from thee of surface gravity waves. In deeper water, where an ISW of depression-type prevailed, the process of wave breaking displayed downward motion with continuous eddy on the front face of the ridge followed by upward motion towards the apex of the obstacle. Experimental results also suggested that blockage parameter ξ could be applied to classify various degrees of ISW-ridge interaction, i.e., ξ 〈 0.5 for weak interaction, 0.5 〈 ξ 〈 0.7 for moderate interaction, and 0.7 〈 ξ for wave breaking.     

Development of A Fully Nonlinear Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in eonjunetion with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method, the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWF are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.     

Numerical modeling of wave runup and forces on an idealized beachfront house

In this paper, a numerical wave model based on the incompressible Reynolds-averaged Navier–Stokes (RANS) and k–ε equations is used to estimate the impact of a solitary wave on an idealized beachfront house located at different elevations on a plane beach. The locations of the free surface are reconstructed by volume of fluid (VOF) method. The model is satisfactorily tested against the experimental data of wave runup, and the analytical solution of wave forces on vertical walls. The time histories of wave profiles, forces, and overturning moments on the idealized house are demonstrated and analyzed. The variations of wave forces and overturning moments with the elevation of the idealized beachfront house are also investigated.     

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two-dimensional Navier-Stokes equations is solved numerically with a finite element method. In order to track the moving non-linear wave surface boundary, the Navier-Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three-step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data.Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder.The effects of the KC number and the cylinder depth on the wave forces are studied.     

南海北部陆坡内孤立波对桩柱作用力的极值推算

内孤立波的发生常伴随着大振幅波动和突发性强流,对桩柱等海中结构物产生强烈破坏作用。基于KdV方程和Morison公式,在忽略高阶模态的情况下,探讨内孤立波对桩柱的单位作用力、总作用力、剪力和弯矩的极值问题,并利用2016-07南海北部陆坡的实测资料对理论结果进行检验。结果表明:1)在内孤立波最大振幅所在的垂向剖面上,上层与下层各存在一个单位作用力极值,且二者方向相反,上层总作用力强于下层,最大剪力和弯矩分别发生于水平流速的转向层和海底;2)各水层中,沿着内孤立波的传播方向,所有作用力的数值均随时间的推移先递增后递减,存在正向或负向的最大值;3)全水层总作用力极值发生在半周期,其值与波动振幅和水平波速有关,其他作用力极值发生于最大振幅时刻之前,作用力极值与振幅和非线性波速正相关,与水平特征宽度负相关;4)单位作用力极值的时间提前量与振幅和水平特征宽度强相关,与非线性波速弱相关。     

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.     

孤立波在岸礁地形上传播与爬坡数值模拟研究

为准确模拟孤立波在岸礁地形上的传播和爬坡,采用基于完全非线性Boussinesq方程开发的Funwave-TVD模型,探究模型的可行性,并利用验证后的模型进一步研究岸礁各地形因素对孤立波爬高的影响。研究结果表明:模型能准确模拟孤立波在岸礁陡变地形上的传播及变形,摩擦系数对礁前陡坡及礁坪上的波浪传播模拟影响不大,但对爬坡预测的敏感性较强;模型空间步长可适当增大,提高计算效率;随着礁坪宽度的增大以及礁后斜坡的变缓,孤立波爬坡高度下降明显,而礁前陡坡坡度变化对孤立波爬坡高度影响不大。     

Numerical simulation of irregular wave overtopping against a smooth sea dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model,a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes.Simulations of fully nonlinear standing wave and regular wave’s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules.To model stationary ergodic stochastic processes,several cases with different random seeds are computed for each specified irregular wave spectrum.It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas,other numerical results and experimental data.     

Experimental and Numerical Study on the Hydrodynamic Characteristics of Solitary Waves Passing Over A Submerged Breakwater

In this study, solitary waves passing over a submerged breakwater are investigated both experimentally and numerically. A total of 9 experimental conditions are carried out, including different incident wave heights and water depths. Numerical simulations are performed using a high-order finite-difference model solving Navier–Stokes (N–S) equations. The predicted water wave elevation, velocity and pressure show good agreement with experimental data, verifying the accuracy and capacity of the numerical model. Furthermore, parametric studies are conducted by numerical modelling to examine the effects of the geometrical features of submerged dike on hydrodynamic characteristics around the breakwater.     

Wave Scattering by Double Slotted Barriers in A Steady Current： Experiments

The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.     

南海北部反气旋涡对内孤立波传播的影响研究

海洋内波具有振幅大、流速强和周期短等特点,可对海上施工和水下作业安全造成严重威胁。南海北部陆坡海域是内孤立波和中尺度涡频发的海域之一,研究中尺度涡对内孤立波传播的影响对深入了解南海北部内孤立波在反气旋涡过境时的传播特征、提高该海域内波预报准确性具有重要意义。基于此,本文利用布放于南海北部东沙群岛西侧陆坡海域的潜标观测数据,针对2017年3月一个反气旋中尺度涡经过潜标站位的过程,探讨了中尺度涡对内孤立波传播的影响。结果表明：①受反气旋涡影响,内孤立波的平均振幅减小28.6%,其主要原因是中尺度涡导致等温线下压,进而对内孤立波的振幅产生抑制作用,其影响过程可用趋浅温跃层理论描述。②反气旋涡影响期间,内孤立波的平均波速由1.26 m/s增大到1.47 m/s,增幅约16.7%,反映了反气旋涡对内孤立波波速的强化作用,这种强化作用主要是由中尺度涡边缘流场引起背景流场变化所致,而中尺度涡引起的温盐场变化对内孤立波波速的影响相对较小。     

Comparative study on the accuracy of solitary wave generations in an ISPH-based numerical wave flume

In the present study, six solitary wave generations by different mathematical approximations are investigated using a piston type wave maker at dimensionless amplitudes ranging from 0.1 to 0.6 and two water depths. Incompressible smoothed particle hydrodynamics is used to simulate solitary wave propagation along the fixed depth channel. The present numerical results are compared with analytical results and experimental data in terms of free surface displacements, fluid particle velocity, phase speed, paddle motion, etc. The present mesh-free numerical results of wave profile variations over time proved that “Rayleigh” has the lowest relative wave height variation. However, its solitary wave has notable phase lead, while “Third order” and “Ninth order” have the least wave lags. Furthermore, the record of present numerical free surface elevation at different distances and the loss of amplitude of the main pulse showed that regarding both of them, “Ninth order” has supremacy over five others. Considering the numerical velocity components of generated solitary wave, “Third order” and “Ninth order” trace analytical results more accurately than other four ones, whereas “Rayleigh” is the most accurate one in predicting the maximum runup. Finally, the paddle motion, its velocity, and displacement, as well as phase speed and outskirts decay coefficient are also compared and discussed intensely.     

Wave Run-up on A Vertical Seawall Protected by An Offshore Submerged Barrier

Submerged barriers are constructed in coastal zones for shoreline or harbor protection or to prevent the beach erosion. In the present study, the wave run-up on a vertical seawall protected by a submerged barrier is analyzed. The physical configurations include a rigid barrier and a long channel of finite depth. For linear water waves, by matching the velocity along the barrier and along the gap, the systems of linear equations about the velocity potentials are obtained. The wave run-up is further analyzed for various settings of barrier height and distance between the barrier and the wall, i.e. the chamber length. For nonlinear waves and random sea waves, a numerical model is extended to investigate the effect parameters of the barrier on the wave run-up against the seawall. Not only the numerical simulations, but also the analytical results illustrate that the wave run-up on the seawall depends very much on the distance between the barrier and the vertical seawall.     

Wave Run-up on A Vertical Seawall Protected by An Offshore Submerged Barrier

Submerged barriers are constructed in coastal zones for shoreline or harbor protection or to prevent the beach erosion. In the present study, the wave run-up on a vertical seawall protected by a submerged barrier is analyzed. The physical configurations include a rigid barrier and a long channel of finite depth. For linear water waves, by matching the velocity along the barrier and along the gap, the systems of linear equations about the velocity potentials are obtained. The wave run-up is further analyzed ...