Application of desingularized approach to water wave propagation over three-dimensional topography

A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data.     

An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion

In the present paper, by introducing the effective wave elevation, we transform the extended ellip- tic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)’s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly vary- ing topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.     

Wave refraction–diffraction effect in the wind wave model WWM

Based on the extended mild-slope equation, the wind wave model (WWM; Hsu et al., 2005) is modified to account for wave refraction, diffraction and reflection for wind waves propagating over a rapidly varying seabed in the presence of current. The combined effect of the higher-order bottom effect terms is incorporated into the wave action balance equation through the correction of the wavenumber and propagation velocities using a refraction–diffraction correction parameter. The relative importance of additional terms including higher-order bottom components, the wave–bottom interaction source term and wave–current interaction that influence the refraction–diffraction correction parameter is discussed. The applicability of the proposed model to calculate a wave transformation over an elliptic shoal, a series of parallel submerged breakwater induced Bragg scattering and wave–current interaction is evaluated. Numerical results show that the present model provides better predictions of the wave amplitude as compared with the phase-decoupled model of Holthuijsen et al. (2003).     

Effects of mesoscale eddies on the internal solitary wave propagation

The mesoscale eddy and internal wave both are phenomena commonly observed in oceans. It is aimed to investigate how the presence of a mesoscale eddy in the ocean affects wave form deformation of the internal solitary wave propagation. An ocean eddy is produced by a quasi-geostrophic model in f-plane, and the one-dimensional nonlinear variable-coefficient extended Korteweg-de Vries (eKdV) equation is used to simulate an internal solitary wave passing through the mesoscale eddy field. The results suggest that the mode structures of the linear internal wave are modified due to the presence of the mesoscale eddy field. A cyclonic eddy and an anticyclonic eddy have different influences on the background environment of the internal solitary wave propagation. The existence of a mesoscale eddy field has almost no prominent impact on the propagation of a smallamplitude internal solitary wave only based on the first mode vertical structure, but the mesoscale eddy background field exerts a considerable influence on the solitary wave propagation if considering high-mode vertical structures. Furthermore, whether an internal solitary wave first passes through anticyclonic eddy or cyclonic eddy, the deformation of wave profiles is different. Many observations of solitary internal waves in the real oceans suggest the formation of the waves. Apart from topography effect, it is shown that the mesoscale eddy background field is also a considerable factor which influences the internal solitary wave propagation and deformation.     

Numerical investigation of the influence of various factors on the propagation and transformation of solitary waves in the sea

For various stratifications and different types of bottom patterns we study the transformations of solitary perturbations of density appearing in the depth of the sea. In the two-dimensional case, under the assumption that the average dynamic characteristics weakly vary in time as compared with the wave characteristics, we deduce the equations for mean currents and waves taking into account vertical and horizontal viscosity and the diffusion of density. Numerical examples show that the stratification, bottom topography, nonlinearity, mean currents, and dissipation strongly affect both the process of splitting of a solitary wave into wave trains and their amplitude and length. The wave currents exhibit the oscillatory (train-like) character. It is emphasized that, in the case of propagation of solitary perturbations of density with dissipation, it is also important to take into account the combined influence of nonlinearity, currents, bottom topography, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Validation of a new generation system for bottom boundary layer beneath solitary wave

Understanding of sea bottom boundary layer characteristics, especially bottom shear stress acting on the sea bed, is an important step needed in sediment transport modeling for practical application purposes. In the present study, a new generation system for bottom boundary layer under solitary wave is proposed. Applicability of this system is examined by comparing measured and numerical solution velocities. Moreover, transitional behavior from laminar to turbulence was investigated. It is concluded that the critical Reynolds number in the experiments shows good agreement with DNS result of Vittori and Blondeaux (2008) and laboratory data of Sumer et al. (2010), indicating validity of the generation system. Since the present generation system enables continuous measurement to obtain ensemble averaged quantities, it can be effectively utilized for future experimental studies on solitary wave boundary layers, including sediment transport experiments with movable bed.     

完全非线性孤立波的直墙反射

报道了应用边界积分方法模拟完全非线性孤立波的传播与直墙反射,给出了波形演变过程。结果表明,本模型对计算孤立波的传播与直墙反射是有效的。三阶Boussinesq方程的孤立波解比低阶方程的孤立波解更接近完全非线性的数值解.当来波波高增大时,孤立波直墙反射的相位滞后变小。若考虑大波高孤立波的直墙反射或波——波相互作用,一阶理论预报的相位滞后往往低估实际情况。     

张力腿平台内孤立波作用特性数值模拟

依据三类内孤立波理论KdV、eK dV和MCC的适用性条件,采用Navier-Stokes方程为流场控制方程,以内孤立波诱导上下层深度平均水平速度作为入口边界条件,建立了两层流体中内孤立波对张力腿平台强非线性作用的数值模拟方法。结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且在内孤立波作用下张力腿平台水平力、垂向力及力矩数值模拟结果与实验结果吻合。研究同时表明,张力腿平台内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;水平力的主要成分为波浪压差力和粘性压差力,粘性压差力与波浪压差力相比较小却不可忽略,流体粘性的影响较小;垂向力中粘性压差力很小,流体粘性影响可以忽略。     

Numerical simulation of solitary wave propagation based on MPS method

The concept of candidate particle set is introduced in the MPS gridless numerical method to generate neighboring particle set matrix, which can reduce the CPU time to 1/11 of that before introduction. The Bi-CGSTAB (bi-conjugate gradient stabilized) algorithm is applied to solving the Poisson pressure equation, by which the solving speed is significantly accelerated. The process of solitary waves propagating over a numerical flume and interacting with a vertical wall is simulated. The simulated results of water surface elevation are in good agreement with the analytical solution as well as the measured data. The predicted maximum values of the run-up of solitary waves with various relative incident wave heights agree well with the measured results.     

南海北部内孤立波数学模型

在二层内潮数学模型的基础上,考虑非静力平衡扰动压力的影响,导出潮频内孤立波产生、传播的数学模型。该模型不受小地形假设的限制,并适用于南海。应用该模型能解释说明产生以下现象的物理机制：潮流流过巴坦-萨布坦海脊时,在一定海洋环境条件下,通过潮流与起伏的底地形相互作用可激发产生潮频内孤立波,并西传至东沙群岛附近的海域。     

南海北部陆架区内孤立波向岸传播过程研究

南海北部是全球海洋中内孤立波最强和最为活跃的海域。然而,内孤立波在传入陆架区后,其形态发生显著变化,其传播演变过程表现出高度的复杂性。本研究综合卫星图像和数值模式手段研究了内孤立波在向岸传播过程中的空间变化特征。可见光卫星图像研究结果显示,南海北部陆架区存在三种形态的内孤立波,分别为第一模态下凹型内孤立波、第一模态上凸型内孤立波和第二模态内孤立波。受水深和层结变化的控制,它们的分布区域显著不同。基于MITgcm的数值模拟研究表明,上凸型内孤立波由第一模态下凹内孤立波经过极性转换过程发展而来,而第二模态内孤立波由第一模态下凹内孤立波与急剧变浅地形相互作用而产生。     

南海北部陆坡海区春末第一模态内孤立波观测及特征分析

为获取南海北部陆坡海区第一模态内孤立波的动力结构及时间变化特征,本文利用该海区1套内孤立波浮标观测数据,对陆坡海区的内孤立波现场观测数据分析,识别判定了2021年5月5日至6月3日共30 d的179次第1模态内孤立波过程,并进行了内孤立波的特征分析。南海北部陆坡海区第1模态内孤立波剖面流场为双层结构,上层主要为西偏北向流动,下层流向与之相背,流速转向发生在100～150 m深度处。内孤立波期间,最大流速多发生于上层,流速为60～120 cm/s,底层流增强,上层流与下层流流向相反。受内潮影响,研究区域内孤立波存在半日和全日2个周期,主要以20～30 min间隔的波列形式向西偏北方向传播。本文关于南海北部陆坡海区第一模态内孤立波的分析研究有助于提升对该海区内孤立波时空变化特征的认识,为工程水下施工提供参考和依据。     

波浪动力因素变化对沙质岸滩演变的影响

通过波浪水槽实验,对海平面变化造成的波浪动力因素改变引起的沙质岸滩形态响应开展机理性研究。实验采用1∶10单一沙质斜坡概化岸滩,利用3种不同实验水深模拟海平面变化,考虑椭圆余弦波、非规则波、规则波和孤立波4种类型波浪作用。实验对波浪在斜坡上的传播变形、破碎、上爬和回落过程的波高及波浪作用后的岸滩地形进行了测量。实验结果表明,椭圆余弦波、规则波和非规则波作用下,平衡岸滩呈现出滩肩形态,孤立波作用下则呈沙坝形态。海平面上升造成波浪动力增强,沙质岸滩平衡剖面形状基本保持不变向岸平移,槽谷、滩肩、沙坝位置以及岸线蚀退距离,均呈现出良好规律性。     

Experimental investigating on the reflected waves from the caisson-type vertical porous seawalls

The hydrodynamic efficiencies of caisson-type vertical porous seawalls used for protecting coastal areas were calculated in this study. Physical models were developed to compare the wave reflection from vertical plane, semi-porous, and porous seawalls caused by both regular and random waves. Tests were carried out for a wide range of wave heights, wave periods, and different water depths (d=0.165, 0.270 and 0.375 m). The performance regarding the reflected waves from porous and semi-porous seawalls showed improvement when compared with those from the plane seawall. The reflection coefficients of the porous and semi-porous seawalls were calculated as 0.6 and 0.75, respectively, while the coefficient for the fully reflecting plane vertical wall was significantly higher (0.9). It was also observed that the reflection coefficient decreases with increase in wave steepness and relative water depth. In addition, the reduction in the reflection coefficient of porous and semi-porous seawalls, as compared to that of a plane seawall, was observed for both regular and random waves. New equations were also proposed to calculate the reflection coefficient of different types of seawalls with the aid of laboratory experiments. By verifying the developed equations using some other experimental data, it was validated that the equations could be used for practical situations. The results of the present study can be applied to optimize the design of vertical seawalls and for coastal protecting schemes.     

Finite element method for strong reflection of water waves

In this study, the propagation of monochromatic water waves over an arbitrarily varying topography is numerically investigated. A finite element model is developed by formulating the diffraction of waves caused by depth changes. Not only the propagating mode but also the evanescent modes are included in the model. The model developed is applied to the study of strong reflection of monochromatic waves over a sinusoidally varying topography. Predicted reflection coefficients are compared with those of available laboratory experiments and the eigenfunction expansion method. A very good agreement is observed.     

孤立波与带窄缝双箱相互作用模拟研究

针对孤立波与带窄缝双箱的作用问题,应用时域高阶边界元方法建立了二维数值水槽。其中,自由水面满足完全非线性运动学和动力学边界条件,对瞬时自由表面流体质点采用混合欧拉-拉格朗日法追踪,采用四阶龙格库塔法对下一时刻的自由水面的速度势和波面升高进行更新。采用加速度势法求解物体湿表面的瞬时波浪力。采用推板方法生成孤立波。通过模拟孤立波在直墙上的爬高以及施加在直墙上的波浪力,并与已发表的实验和数值结果对比,验证本数值模型的准确性。通过数值模拟计算研究了窄缝宽度、方箱尺寸对波浪在箱体迎浪侧爬高,窄缝内波面升高,箱体背浪侧透射波高及箱体受波浪荷载的影响。同时研究了有一定时间间隔的双孤立波与带窄缝双箱系统作用问题。     

Breaking solitary wave evolution over a porous underwater step

Solitary wave evolution over a shelf including porous damping is investigated using Volume-Averaged Reynolds Averaged Navier–Stokes equations. Porous media induced damping is determined based on empirical formulations for relevant parameters, and numerical results are compared with experimental information available in the literature. The aim of this work is to investigate the effect of wave damping on soliton disintegration and evolution along the step for both breaking and non-breaking solitary waves. The influence of several parameters such as geometrical configuration (step height and still water level), porous media properties (porosity and nominal diameter) or solitary wave characteristics (wave height) is analyzed. Numerical simulations show the porous bed induced wave damping is able to modify wave evolution along the step. Step height is observed as a relevant parameter to influence wave evolution. Depth ratio upstream and downstream of the edge appears to be the more relevant parameter in the transmission and reflection coefficients than porosity or the ratio of wave height–water depth. Porous step also modifies the fission and the solitary wave disintegration process although the number of solitons is observed to be the same in both porous and impermeable steps. In the absence of breaking, porous bed triggers a faster fission of the incident wave into a second and a third soliton, and the leading and the second soliton reduces their amplitude while propagating. This decrement is observed to increase with porosity. Moreover, the second soliton is released before on an impermeable step. Breaking process is observed to dominate over the wave dissipation at the porous bottom. Fission is first produced on a porous bed revealing a clear influence of the bottom characteristics on the soliton generation. The amplitude of the second and third solitons is very similar in both impermeable and porous steps but they evolved differently due to the effect of bed damping.     

Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.     

Shoaling Surface Gravity Waves Cause a Force and a Torque on the Bottom

Freely propagating surface gravity waves are observed to slow down and to stop at a beach when the bottom has a relatively gentle upward slope toward the shore and the frequency range of the waves covers the most energetic wind waves (sea and swell). Essentially no wave reflection can be seen and the measured reflected energy is very small compared to that transmitted shoreward. One consequence of this is that the flux of the wave’s linear momentum decreases in the direction of wave propagation, which is equivalent to a time rate of change of the momentum. It takes a force to cause the time rate of change of the momentum. Therefore, the bottom exerts a force on the waves in order to decrease the momentum flux. By Newton’s third law (action equals reaction) the waves then impart an equal but opposite force to the bottom. In shallow (but finite) water depths the wave force per unit bottom area is calculated, for normal angle of incidence to the beach, to be directly proportional to the square of the wave amplitude and to the bottom slope and inversely proportional to the mean depth; it is independent of the wave frequency. Constants of proportionality are: 1/4, the fluid density and the acceleration of gravity. Swell attenuation near coasts and some characteristics of sand movement in the near-shore region are not inconsistent with the algebraic structure of the wave force formula. Since the force has a depth variation which is significantly faster than that of the dimensions of the particle orbits in the vertical direction, the bottom induces a torque on the fluid particles that decreases the angular momentum flux of the waves. By an extension of Newton’s third law, the waves also exert an equal but opposite torque on the bottom. And because the bottom force on the waves exists over a horizontal distance, it does work on the waves and decreases their energy flux. Thus, theoretically, the fluxes of energy, angular and linear momentum are not conserved for shoaling surface gravity waves. Mass flux, associated with the Stokes drift, is assumed to be conserved, and the wave frequency is constant for a steady medium.     

南海北部孤立波对近岸波动的响应

On the basis of the time series observations from a temperature chain and an acoustic Doppler current profiler on the continental shelf of the northern South China Sea, a sequence of internal solitary waves （ISWs） and background waves （BWs, including internal tides and near-inertial waves） on the continental shelf were captured simultaneously after the transit of Typhoon Neast in October 2011. These measurementsprovided a unique opportunity to explore the influence of BWs on the ISWs. The BWs appeared a conversion on the current strength and vertical mode structure during the observational period. The BWs were dominated by weak and mode-one waves before October 2 and then turned to strong and high-mode waves after that time. Meanwhile, the ISWs displayed different wave structures before and after October 2, which was closely related to BWs＇ changes. According to the current profiles of BWs, the high-mode wave structure with strong current could significantly strengthen the vertical shear of ISWs in the near-surface layer and promote the breaking of ISWs, and thus it may play an important role in affecting the background current condition.