Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.     

斜向入射波与反射波的分离

提出了一种分离斜向入射波和反射波的方法,波浪可以是规则波、不规则波,波向可以任意.在一定的限制条件下,采用两点浪高仪的波浪信号就可将斜向入射波和反射波分离.     

斜向不规则波入、反射波分离的实验研究

斜向入射的不规则波在海岸结构物前发生反射形成入、反射波共存的波浪场,对这种物理场的入、反射波的分离是海岸工程研究的一个重要课题.改进了一种可用于斜向入射的不规则波分离的两点法,使得测波阵列的两波高仪可布置在结构物前任何方向上.将此方法应用于三维波浪水池的物理模型试验研究,试验了不同的两波高仪的组合、不同的基床高度、不同的入射方向和不同的波浪要素等各种条件对分离结果的影响,结果表明,各种情况在满足非奇异条件下可得到较好的分离结果.该方法计算简便,可以给出较准确的反射系数和入、反射波的频谱.     

Separation of obliquely incident and reflected irregular waves by the Morlet wavelet transform

An existing 2D time-domain method for separating irregular incident and reflected waves by wavelet transform [Ma et al., 2010. A new method for separation of 2D incident and reflected waves by the Morlet wavelet transform. Coastal Eng., 57(6):597–603] is extended to account for obliquely incident irregular waves propagating over sloping bottoms. The linear shoaling and refraction coefficients are adopted to determine the amplitude and phase changes of waves. The optimal central frequency of the Morlet wavelet is determined by the minimum Shannon wavelet entropy. Numerical tests show that the present method can accurately separate waves over horizontal depths. For waves at sloping bottoms, however, the separation errors increase as bottom slope increases and are significant for waves with incident angle larger than π/3.     

波流作用下海底边界层沉积物再悬浮与影响因素研究

海底沉积物再悬浮及其分布取决于海洋水动力、沉积物类型与床面形态之间复杂的相互作用,准确地理解和确定沉积物再悬浮过程对于沉积物输运的研究具有重要的意义。本文在祥云湾海洋牧场典型海域开展现场原位观测,获取研究区波浪、海流及悬浮沉积物浓度数据;分析了波、流作用下海底边界层悬浮沉积物垂向分布特征,并探究了海洋水动力和床面形态对悬浮沉积物垂向分布的影响。结果表明,研究区波流之间的相互作用不显著,沉积物再悬浮受控于风暴浪作用,风暴浪作用下底床切应力可以达到沉积物临界切应力的10～15倍,沉积物的再悬浮滞后于风暴浪作用2～3 h。在波浪荷载微小的情况下,悬浮沉积物垂向分布呈现"I"型,波浪荷载下,悬浮沉积物垂向分布呈现幂指函数分布,表现为"L"型;床面形态随波、流作用而演化,影响沉积物的再悬浮过程,u_?w/u_?c=1.00可作为波浪和海流起主导控制作用的床面形态的判别依据,纯波浪荷载作用下的u_?w/u_?c显著高于波浪主控作用下,但二者之间的界线随着波浪荷载的增加而升高。     

锁相波浪场入、反射波方向谱及反射系数估算

通过数模波浪和物模实验，比较分析了估算多向不规则入射波与反射波相互叠加的锁相波浪场方向分布和反射系数方向分布的改进的贝叶斯估计法MBDM和扩展的最大似然法MMLM的性能。数模试验检验了不同波浪条件、不同波浪测量系统和结构物的不同反射特性等情况下的估算结果，同时还比较了两种分析方法的计算速度和稳定性，结果显示，对于波浪的方向分布估计，MBDM优于MMLM，对于反射系数的方向分布估计以及计算速度和稳定性，MMLM优于MBDM。     

A method to determine the incident wave boundary conditions and its application

When studying the harbor water tranquility, cases are often confronted as that the verification point is not located on the generation line or that the angle between the generation line and the isobath is so large that the differences of the wave climates along the generation line can not be ignored. For these cases, the incident boundary conditions are difficult to evaluate. In order to solve this problem, a combined wave model is developed in the present paper based on the Boussinesq equation and the wave action balance equation. Instead of the one-line wave generation method, a multi-line generation method is proposed for the combined model. Application of this method is given to a case that the harbor is designed with two entrances and the angle between the generation line and the isobath is large and the results are shown reasonable. We suggest that the wave generation method on multi-lines might also be introduced to the wave physical model as the replacement for the one-line generation method.     

Separation of incident and reflected waves in wave–current flumes

A technique is developed to separate the incident and reflected waves propagating on a known current in a laboratory wave–current flume by analyzing wave records measured at two or more locations using a least squares method. It can be applied to both regular and irregular waves. To examine its performance, numerical tests are made for waves propagating on quiescent or flowing water. In some cases, to represent the signal noise and measurement error, white noise is superimposed on the numerically generated wave signal. For all the cases, good agreement is observed between target and estimation.     

Numerical Modelling of Standing Waves with Three-Dimensional Non-Linear Wave Propagation Model

Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, .and the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions     

Transient response of harbours to long waves under resonance conditions

This paper presents the results of a study aimed at quantifying the time–response of harbour basins to long waves under resonance conditions. On the basis of numerical simulations reproducing long waves in the yacht harbour of Rome (Ostia, Italy), it shows that the results valid for periodic forcing waves, acting for an infinitely long time, as those provided by models based on elliptic equations like the Helmoltz and the mild-slope equations, can be misleading with respect to the more realistic ones that can be obtained using time-varying wave equations. Taking advantage of the similarity between the processes studied here and a simple one-dimensional resonator, a method is also proposed to roughly estimate a time–response parameter of each mode of the harbour, using results from steady-state numerical model results, commonly applied for studying harbour resonance in engineering practice. On the basis of further numerical simulations, aimed at reproducing schematic harbour layouts, the effect on resonance of the position of the entrance and of an outer harbour is studied. The results indicate that the effects of design solutions to reduce resonance, by placing the entrance at the middle of the harbour, or using the outer harbour as a resonator, can be correctly evaluated only when considering the time needed for the oscillations to fully develop.     

Modeling of propagation and transformation of transient nonlinear waves on a current

A novel theoretical approach is applied to predict the propagation and transformation of transient nonlinear waves on a current. The problem was solved by applying an eigenfunction expansion method and the derived semi-analytical solution was employed to study the transformation of wave profile and the evolution of wave spectrum arising from the nonlinear interactions of wave components in a wave train which may lead to the formation of very large waves. The results show that the propagation of wave trains is significantly affected by a current. A relatively small current may substantially affect wave train components and the wave train shape. This is observed for both opposing and following current. The results demonstrate that the application of the nonlinear model has a substantial effect on the shape of a wave spectrum. A train of originally linear and very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short distance from an initial position. The discrepancies between the wave trains predicted by applying the linear and nonlinear models increase with the increasing wavelength and become significant in shallow water even for waves with low steepness. Laboratory experiments were conducted in a wave flume to verify theoretical results. The free-surface elevations recorded by a system of wave gauges are compared with the results provided by the nonlinear model. Additional verification was achieved by applying a Fourier analysis and comparing wave amplitude spectra obtained from theoretical results with experimental data. A reasonable agreement between theoretical results and experimental data is observed for both amplitudes and phases. The model predicts fairly well multi-peak spectra, including wave spectra with significant nonlinear wave components.     

Characteristics of turbulent boundary layers over a rough bed under saw-tooth waves and its application to sediment transport

A large number of studies have been done dealing with sinusoidal wave boundary layers in the past. However, ocean waves often have a strong asymmetric shape especially in shallow water, and net of sediment movement occurs. It is envisaged that bottom shear stress and sediment transport behaviors influenced by the effect of asymmetry are different from those in sinusoidal waves. Characteristics of the turbulent boundary layer under breaking waves (saw-tooth) are investigated and described through both laboratory and numerical experiments. A new calculation method for bottom shear stress based on velocity and acceleration terms, theoretical phase difference, φ and the acceleration coefficient, a_c expressing the wave skew-ness effect for saw-tooth waves is proposed. The acceleration coefficient was determined empirically from both experimental and baseline k–ω model results. The new calculation has shown better agreement with the experimental data along a wave cycle for all saw-tooth wave cases compared by other existing methods. It was further applied into sediment transport rate calculation induced by skew waves. Sediment transport rate was formulated by using the existing sheet flow sediment transport rate data under skew waves by Watanabe and Sato [Watanabe, A. and Sato, S., 2004. A sheet-flow transport rate formula for asymmetric, forward-leaning waves and currents. Proc. of 29th ICCE, ASCE, pp. 1703–1714.]. Moreover, the characteristics of the net sediment transport were also examined and a good agreement between the proposed method and experimental data has been found.     

Generation and propagation of transient nonlinear waves in a wave flume

A semi-analytical nonlinear wavemaker model is derived to predict the generation and propagation of transient nonlinear waves in a wave flume. The solution is very efficient and is achieved by applying eigenfunction expansions and FFT. The model is applied to study the effect of the wavemaker and its motion on the generation and propagation of nonlinear waves. The results indicate that the linear wavemaker theory may be applied to predict only the generation of waves of low steepness for which the nonlinear terms in the kinematic wavemaker boundary condition and free-surface boundary conditions are of secondary importance. For waves of moderate steepness and steep waves these nonlinear terms have substantial effects on wave profile and wave spectrum just after the wavemaker. A wave spectrum corresponding to a sinusoidally moving wavemaker possesses a multi-peak form with substantial nonlinear components, which disturbs or may even exclude physical modeling in wave flumes. The analysis shows that the widely recognized weakly nonlinear wavemaker theory may only be applied to describe the generation and propagation of waves of low steepness. This is subject to further restrictions in shallow and deep waters because the kinematic wavemaker boundary condition as well as the nonlinear interaction of wave components and the evolution of wave energy spectrum is not properly described by weakly nonlinear wavemaker theory. Laboratory experiments were conducted in a wave flume to verify the nonlinear wavemaker model. The comparisons show a reasonable agreement between predicted and measured free-surface elevation and the corresponding amplitudes of Fourier series. A reasonable agreement between theoretical results and experimental data is observed even for fairly steep waves.     

波浪运动在底边界层的湍流结构数值研究

本文基于$ k $-$ \varepsilon $ 模型研究了波流边界层内湍流结构特征。研究结果表明,时均流速分布数值解与实验结果高度吻合。一个波周期内湍流结构特征（如：涡量、湍动能、湍动能耗散率等）呈周期性变化规律,波浪作用引起涡量、湍动能及湍动能耗散率均在减速阶段减小,在波谷处达到最低值,而后在加速阶段增大,并在波峰处达到最大值。近壁面处湍流结构变化幅值较大（湍动能耗散率变化可达53%）,远离壁面处变化幅值较平均值较小（仅3%）。波流边界层厚度在减速阶段增加,在加速阶段减小。本文所建立的数值模型克服了现有模型因采用“高雷诺数方法”引起的近壁区精度不高问题,可较好地描述波浪作用下湍流结构演变过程的物理机制,为河口海岸地区泥沙运动、岸滩演变及海洋可再生能源的开发利用提供一些指导意义。     

Reply to “Discussion of wave setup and setdown generated by obliquely incident waves” by F. Shi and J.T. Kirby

The authors are grateful to the derivation and correction addressed by Shi and Kirby (2008) for the calculation of the wave setup and setdown induced by obliquely incident waves. The mathematical equations for the expression of setup and setdown are rederived in which the velocity potential is expanded to the second-order on the still water lever. The correct form of setdown presented by Shi and Kirby is confirmed in the present paper.     

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.     

风浪和海洋飞沫对海表面拖曳系数和风廓线的影响

基于埃克曼理论,本文将波致应力和飞沫应力引入到海-气边界层的界面应力中,来研究海表面风浪和海洋飞沫对海-气边界层动量交换的影响,并得到修改后的埃克曼模型的理论解。波致应力是由风浪谱和波增长函数估计,并得到在中低风速下,波致应力、飞沫应力与湍流应力相比,对海表面拖曳系数和风廓线的影响非常小。当风速高于25米/秒时,海洋飞沫通过飞沫应力对海-气界面应力的作用远高于波致应力,以至于波致应力可以忽略。海表面拖曳系数在高风速下,随着风速的增大而减小。通过采用风浪谱的不同波龄,得到海洋飞沫的产生会导致海-气边界层风速的增加。最后,理论解与现场的观察数据进行了对比。对比后的数据表明,在中高风速下,飞沫对海-气边界层的影响远大于表面风浪。     

波浪水槽中非线性浅水波传播特性与模拟

通过建立解析解、进行数值模拟和物理实验，研究了波浪水槽中非线性浅水波浪传播特性，给出了数值模拟中对应造波板做正弦运动的二阶入射边界条件。数值模拟采用高阶Boussinesq方程。实验结果、数值结果和解析解进行对比，并讨论了解析解的适用范围、高次谐波的产生及三波相互作用问题。     

Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity U at each phase is non-uniform, which is directly affected by the mean velocity, . The magnitude of increases from zero at the bottom to a local positive maximum at about z/δ2.02.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ6.07.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component is greater than that of the offshore counterpart except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components, and are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although is greater than and the asymmetry of the maximum free stream velocities (i.e. ) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus ( ) or ( ). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone.     

太平洋涌浪分布特征及其对海-气边界层的影响

本文对海-气边界层波致风机制的相关理论进行了阐述,并利用ERA-40再分析资料给出了太平洋谱峰速度、波龄、波陡等描述涌浪和波致风机制物理量的年际和季节空间分布特征。分析表明:东太平洋赤道地区等海域涌浪速度最大且涌浪由南向北传播明显;太平洋波边界层高度基本呈现出东高西低的分布形势;波致风机制主要发生在赤道热带海域,北半球夏季波致风机制偏强,冬季偏弱,南半球反之;北半球北部海域夏季更易发生波致风机制,赤道附近海域相反;南海为风浪与涌浪组成的混合浪,对其波候等相关研究有必要分开进行讨论。