Laboratory experiments on depression interfacial solitary waves over a trapezoidal obstacle with horizontal plateau

While shoaling from deep water in a stratified ocean, an internal wave may encounter different types of submarine topography. As it travels, the wave may generate vortex motion on a slope, turbulent mixing between the upper and bottom layer, and even waveform inversion on the plateau of a slope-shelf feature. Although many oceanographers have believed that the inversion from depression to elevation may commence at the turning point where the upper and low layer are equal in depth, this phenomenon has not been fully verified in field observations or numerical schemes. In order to clarify this unique phenomenon, a series of laboratory experiments were conducted on the evolution of an interfacial solitary wave of depression across a slope followed by a horizontal plateau on slope-shelf obstacle. Experimental results indicate the length of the plateau may become a proxy to determine whether the inverted waveform could maintain its strength or be weakened swiftly, which could inflict direct impact on the ecology of the local oceanic environment. Comparison on the internal flow field is also presented in this paper to illustrate the process of waveform inversion as an internal wave propagating over a trapezoidal, triangular ridge and uniform long slope, respectively.     

内孤立波与平顶海山作用的能量耗散实验研究

内波破碎引起的能量耗散和混合是海洋内部的重要物理过程。通过在二维内波水槽进行实验室实验,分析内波与地形的作用,探究内孤立波与平顶海山地形作用时波要素、能量以及湍耗散率的时空变化。本实验利用重力塌陷法在两层流体中制造第一模态内孤立波,通过粒子图像测速技术(particle image velocimetry, PIV)获得内孤立波与地形作用时的流场结构,定量分析整个作用过程。结果表明,地形会改变波形甚至引起破碎,内波与地形作用时,振幅和能量密度会在内孤立波爬坡时迅速增大,在地形前缘产生强烈能量耗散。入射波的能量与塌陷高度呈二次函数关系,透射波能量随地形升高减小,反射波能量随地形升高增大。地形前缘局地湍耗散率极值时间序列在部分实验中呈双峰结构,对应内孤立波界面处剪切加强引起湍流耗散和波后缘翻转破碎。破碎引起的地形前缘区域平均湍耗散率量级在10~(-5)m~2/s~3,局地湍耗散率极值与入射波振幅呈指数关系,所有实验中局地湍耗散率的最大值接近10~(-3) m~2/s~3量级。     

潜堤上破碎波浪传播变形的数值模型及其验证

为模拟潜堤上破碎波浪传播时产生能量的耗散这一特性,在改进的具有四阶色散的Boussinesq水波方程中中入二阶紊动粘性项,建立了考虑波浪破碎的水波数学模型.在非交错网格下建立了有限差分数值模型,并利用三阶Adams-Bash forth格式预报、四阶Adams-Mouton格式校正对数值模型进行求解.通过数值试验,模拟...     

Numerical study on the characteristics of flow field and wave propagation near submerged breakwater on slope

In this study,characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical twodimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propa-gates over breakwater. When wave crest propagates over breakwater,the anticlockwise vortex may generate. On the contrary,when wave hollow propagates over breakwater,the clockwise vortex may generate. Meanwhile,the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy,turbulent dissi-pation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.     

Turbulence and energy dissipations of surf-zone spilling breakers

A laboratory study on the turbulence and wave energy dissipations of spilling breakers in a surf zone is presented. Instantaneous velocity fields of propagating breaking waves on a 1/20 slope were measured using Particle Image Velocimetry (PIV). Due to the large region of the evolving wave breaking generated turbulent flow, seven PIV fields of view (FOVs) were mosaicked to form a continuous flow field in the surf zone. Mean and turbulence quantities were extracted by ensemble averaging 25 repeated instantaneous measurements at each FOV. New results for distribution and evolution of turbulent kinetic energy, mean flow energy, and total energy across the surf zone were obtained from analyzing the data. The turbulence dissipation rate was estimated based on several different approaches. It was found that the vertical distribution of the turbulence dissipation rate decays exponentially from the crest level to the bottom. The resulting energy budget and energy flux were also calculated. The calculated total energy dissipation rate was compared to that based on a bore approximation. It was found that the ratio of turbulence dissipation rate to total energy dissipation rate was about 0.01 in the outer surf zone and increased to about 0.1 after the breaking waves transformed into developed turbulent bores in the inner surf zone.     

Modelling of the upper turbulent layer in the ocean

A differential model of the upper turbulent layer in the ocean is considered. A closed system of equations includes equations of motion, balance, and dissipation of kinetic turbulence energy. Boundary conditions at the surface are determined using a solution of the atmospheric problem taking into account the interaction between the two media. The formulated algorithm allows for a relationship between turbulent energy dissipation and flux and the parameters of wind disturbance. The vertical profiles of turbulence and drift current characteristics are presented as well as parameters of the ocean-atmosphere interaction for various values of impulse jump within the limits of the wave layer with waves collapsing and not collapsing.UDK 551.456.152     

A nearshore wave breaking model

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一种近岸区波浪破碎模型

从波浪破碎的能量关系入手,以紊流能量方程为基础,考虑破碎区内单个波在不同破碎阶段所提供的紊动能量强度的变化过程,提出了一种波浪破碎模式.通过将这一模型引入Boussinesq方程中,初步建立了一种近岸区波浪变形数学模型,并用波浪水槽实验资料对模型模拟波高和平均水位的情况进行了初步验证,得到了良好的结果.     

Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part I. Solitary waves

Interactions between a solitary wave and a submerged rectangular obstacle are investigated both experimentally and numerically. The Particle Image Velocimetry (PIV) technique is used to measure the velocity field in the vicinity of the obstacle. The generation and evolution of vortices due to flow separation at the corners of the obstacle are recorded and analyzed. It is found that although the size of the vortex at the weatherside of the obstacle is smaller than that at the leeside, the turbulence intensity is, however, stronger. A numerical model, based on the Reynolds Averaged Navier–Stokes (RANS) equations with a k–ϵ turbulence model, is first verified with the measurements. Overall, the agreement between the numerical results and laboratory velocity measurements is good. Using the RANS model, a series of additional numerical experiments with different wave heights and different heights of the rectangular obstacle are then performed to test the importance of the energy dissipation due to the generation of vortices. The corresponding wave transmission coefficient, the wave reflection coefficient and the energy dissipation coefficient are calculated and compared with solutions based on the potential flow theory. As the height of the obstacle increases to D/h=0.7, the energy dissipation inside the vortices can reach nearly 15% of the incoming wave energy.     

Reynolds stress and TKE production in an estuary with a tidal bore

We report new measurements of the turbulent properties of the flow in a tidally energetic estuarine channel of almost uniform cross-section. A high-frequency (1.2 MHz), bottom-mounted Acoustic Doppler Current Profiler (ADCP) has been used to observe the velocity field at a sampling rate of 10 Hz in parallel with measurements of the surface elevation by tide gauges. Our data have been analysed using the Variance Method to determine turbulent kinetic energy (TKE), shear stress and TKE production over the tidal cycle with a time resolution of 60 s. During the highly energetic but brief flood period, when the surface axial velocity reaches 2 m s⁻¹, we observed large values of stress (>2 Pa) and shear production (5 W m⁻³). TKE is also input through the release of energy in the bore itself which results in a brief but intense injection of energy at the bore front with large transient TKE levels (100 J m⁻³). Subsequent input by shear production maintains TKE levels which are generally lower (20 J m⁻³) than the strong peak associated with the bore for the rest of the flood. On the ebb, the flow is relatively tranquil with maximum speeds 0.5 m s⁻¹ and peak TKE production rates of 0.1 W m⁻³.The flow and elevation data have also been used to estimate the energy fluxes into and out of the estuary. Short (1 h), intense energy inputs (8 MW at springs) on the flood flow are largely balanced by longer, less intense seaward energy flow on the ebb. The net energy input is found to be 0.1 MW at springs which is consistent with estimates of upstream dissipation. Peak dissipation in the bore itself may exceed the mean energy input but it is active only for a small fraction of the tidal cycle and its average contribution does not exceed 12% of total dissipation.     

Numerical study of turbulence and wave damping induced by vegetation canopies

Vegetation canopies control mean and turbulent flow structure as well as surface wave processes in coastal regions. A non-hydrostatic RANS model based on NHWAVE (Ma et al., 2012) is developed to study turbulent mixing, surface wave attenuation and nearshore circulation induced by vegetation. A nonlinear k − ϵ model accounting for vegetation-induced turbulence production is implemented to study turbulent flow within the vegetation field. The model is calibrated and validated using experimental data from vegetated open channel flow, as well as nonbreaking and breaking random wave propagation in vegetation fields. It is found that the drag-related coefficients in the k − ϵ model C_fk and C_fϵ can greatly affect turbulent flow structure, but seldom change the wave attenuation rate. The bulk drag coefficient C_D is the major parameter controlling surface wave damping by vegetation canopies. Using the empirical formula of Mendez and Losada (2004), the present model provides accurate predictions of vegetation-induced wave energy dissipation. Wave propagation through a finite patch of vegetation in the surf zone is investigated as well. It is found that the presence of a finite patch of vegetation may generate strong pressure-driven nearshore currents, with an onshore mean flow in the unvegetated zone and an offshore return flow in the vegetated zone.     

Propagation of solitary waves over a submerged permeable breakwater

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique is employed to measure instantaneous free surface displacements and velocity fields in the vicinity of a porous dike. The porous medium, consisting of uniform glass spheres, is mounted on the seafloor. Due to the limited size of each field of view (FOV) for high spatial resolution purposes, four FOVs are set in order to form a continuous flow field around the structure. Quantitative mean properties are obtained by ensemble averaging 30 repeated instantaneous measurements. The Reynolds decomposition method is then adopted to separate the velocity fluctuations for each trial to estimate the turbulent kinetic energy. In addition, a highly accurate two-dimensional model with the volume of fluid interface tracking technique is used to simulate an idealized volume-averaged porous medium. The model is based on the Volume-Averaged Reynolds Averaged Navier–Stokes equations coupled with the non-linear k–ε turbulence closure solver. Comparisons are performed between measurements and numerical results for the time histories of the free surface elevation recorded by wave gauges and the spatial distributions of free surface displacement with the corresponding velocity and turbulent kinetic energy around the permeable object imaged by the PIV system. Fairly good agreements are obtained. It is found that the measured and modeled turbulent intensities on the weather side are much larger than those on the lee side of the object, and that the magnitude of the turbulent intensity increases with increasing wave height of a solitary wave at a constant water depth. The verified numerical model is then used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.     

An experimental study of stratified mixing caused by internal solitary waves in a two-layered fluid system over variable seabed topography

Stratified mixing is observed in a wave flume on an internal solitary wave (ISW) of depression or elevation type propagating over a submarine ridge. The submarine ridges, which comprise the seabed topography, are either semicircular or triangular. Tests are performed in a series of combinations of submarine ridges with different heights and ISW in different amplitudes within a two-layer fluid system. When the thickness of the top layer is less than that of the lower layer (i.e., H₁<H₂), a depression-type ISW may produce a strong hydraulic jump with downwards motion and continuous eddy diffusion. During diffusion, the leading profile of the ISW transforms a wrapped vortex on the front face of the ridge, and a vortex separation at the apex of the ridge. Meanwhile, an elevation-type ISW causes a vortex in the lee of a submarine ridge, which resembles a surface solitary wave in terms of wave transmission process. The degree of wave-obstacle interaction is determined by energy loss, which is induced by submarine ridge blockage. The experiment results suggest that degree of blocking can be applied to classify various degrees of ISW-obstacle encounter in the stratified two-layer fluid system.     

海岸破波带内水底悬沙浓度形成机理实验研究

通过大尺度水槽波浪引起泥沙悬移的动床模型实验,研究了沙坝海岸破波带内水底悬沙浓度形成机理,通过比较时间平均水底悬沙浓度与时间平均水底波浪水质点动能或时间平均水底湍动能之间的相关性,论证了利用时间平均湍动能比利用时间平均波浪水质点动能计算时间平均水底悬沙浓度更为适用,并提出了以上时间平均水底悬沙浓度与水底湍动能之间的关系也可以用来近似表达时间变化的水底悬沙浓度与时间变化的水底湍动能之间的关系。研究针对规则波、波群和不规则波3种波浪形态进行,并分别对破波带内的爬坡区、内破波区和沙坝区3个区域实验结果进行讨论。     

夏季长江口及其邻近海域湍流特征分析

利用2019年7月在长江口科学考察实验研究夏季航段(NORC2019-03-02)中获得的MSS90L湍流剖面仪的直接观测数据,本文计算并分析了该断面的湍动能耗散率ε和垂向湍扩散系数K_Z的分布情况。湍动能耗散率的大小为1.72×10?10～2.95×10?5 W/kg;垂向湍扩散系数的大小为3.24×10?7～4.55×10?2 m2/s。湍动能耗散率和垂向湍扩散系数的分布相似,均为上层最强,底层次之,中层最弱。上层由于风应力的作用,使得湍动能耗散率和垂向湍扩散系数较大;温跃层处层化较强,抑制了湍动能的耗散和垂向上的湍混合。盐度锋面的次级环流会促使低盐水团脱离,锋面引起的垂向环流会加强海洋的湍混合。低盐水团与外界的能量交换较少,湍动能耗散率较弱。长江口海区存在明显的上升流和下降流,它们是由锋面的次级环流产生的;上升流和下降流的存在促进湍动能的耗散与湍混合。     

Numerical study on vertical structures of undertow inside and outside the surf zone

Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and t...     

Hydrodynamic characteristics of semi-immersed breakwater with an attached porous plate

In the present study, wave interaction with a fixed, partially immersed breakwater of box type with a plate attached (impermeable-permeable) at the front part of the structure is investigated numerically and experimentally. The large scale laboratory experiments on the interaction of regular waves with the special breakwater were conducted in the wave flume of Laboratori d’Enginyeria Marνtima (LIM) at Universitat Politecnica de Catalunya (UPC) in Barcelona. Experimental results are compared with numerical results obtained with the use of the Cornell breaking Wave and Structures (COBRAS) wave model. The effects of an impermeable as well as a permeable plate attached to the bottom of the breakwater on its hydrodynamic characteristics (wave transmission, reflection, dissipation, velocity and turbulence kinetic energy) are investigated. Computed velocities and turbulence kinetic energy in the vicinity of the structure indicate the effects of the breakwater with the attached (impermeable/permeable) plate on the flow pattern and the turbulence structure. The attached impermeable plate at the front part of the breakwater enhances significantly the efficiency of the structure in attenuating the incident waves. The permeable plate reduces the efficiency of the structure since wave energy is transmitted through the porous body of the plate. Based on the hydrodynamic characteristics it is inferred that the breakwater with an impermeable plate attached to its bottom is more efficient. The comparison of horizontal and vertical forces acting on the breakwater for all cases examined reveals that plate porosity influences slightly vertical force and severely horizontal force acting on the structure, reducing maximum values in both cases.     

孤立波与升沉水平板相互作用数值模拟研究

合理的刚度和潜深设计可以使升沉水平板获得优异的消浪性能。基于考虑流体黏性的二维不可压缩Navier-Stokes方程,以高阶紧致插值CIP(constrained interpolation profile)方法求解方程对流项,采用VOF(volume of fluid)方法重构自由液面,构建二维数值波浪水槽。采用试验数据验证模型后,研究孤立波与升沉水平板相互作用,分析相对刚度K*、相对潜深d/h、相对波高H/h对于升沉板的消浪性能和运动响应的影响,揭示升沉板对孤立波的消浪机理。研究表明:在孤立波通过时,升沉板会经历一个先上升后下降的运动,随后非线性自由振动,板下方水体近似均匀流动,且水流的垂向流动与板的垂荡方向一致;升沉板主要通过不对称涡旋脱落、浅水变形、波浪反射与辐射波转化等方式消耗孤立波能量;一定条件下,采用最优相对刚度K*=4.0和最优相对潜深d/h=0.52可以取得良好的消浪效果,此时透射系数最小,同时升沉板的运动响应在合理的范围内。     

欧拉模型模拟波浪的抑制数值耗散效应的一种简单方法

数值波浪水槽是研究波浪及波浪与结构相互作用的常用工具，可在真实尺度下产生波浪，并提供流场的详细数据。然而，大部分数值波浪水槽都存在数值耗散和数值色散问题，数值耗散使波能缓慢消散，数值弥散在波传播过程中使波频移。本文在有限差分法（FDM）求解欧拉方程的基础上，提出了一种抑制数值耗散效应的简单方法，考虑阻尼项的影响，对波的传播解进行了解析求解。该方法的主要思想是在动量方程中附加一个源项，其强度由数值阻尼效应的强度决定。本文通过对规则线性波、Stokes波和不规则波的数值模拟，验证了该方法的有效性。结果表明，本文方法可有效减小数值波浪水槽中存在的数值耗散现象。     

A numerical model for wave motions and turbulence flows in front of a composite breakwater

A mathematical model based on the Volume-Averaged/Reynolds Averaged Navier-Stokes (VARANS) equations is developed to describe surface wave motions in the vicinity of a coastal structure, which could be either a rigid solid structure or a permeable structure or a combination of both. In the VARANS equations, the volume-averaged Reynolds stress is modeled by adopting the nonlinear eddy viscosity assumption. The model equations for the volume-averaged turbulent kinetic energy and its dissipation rate are derived by taking the volume-average of the standard k−ϵ equations. Because of the volume-averaging process, the effects of the small-scale turbulence in porous media are introduced. The performance of the model is checked by comparing numerical solutions with the experimental data related to a composite breakwater reported by Sakakiyama and Liu [Coast. Eng. 121 (2001) 117].