Coastal current on the eastern shelf of Hidaka Bay

In order to examine seasonal variation in a coastal current and the dynamics of the current, we carried out a mooring current measurement near the coast on the eastern shelf of Hidaka Bay from December 2002 to July 2003. There seemed to be two current regimes during the observed period; one a southeastward current from December to March, and the other a northwestward current after April. Arrested topographic wave dynamics was used to understand along-shore steady momentum balance at the mooring site. It was found that the friction term was negligible during the former regime, that is, the wind stress term roughly counterbalanced the pressure gradient term. On the other hand, the contribution of each term to the momentum balance was sensitive to the resistance coefficient value during the latter regime. A numerical study showed that wind forcing alone could not reproduce the observed current velocity and momentum balance during the former regime. One possible interpretation of the observed results is superposition of the arrested topographic waves forced by the along-shore wind stress and downstream extension of the Coastal Oyashio. Numerical experiments using combined forcing of the wind stress and an inflow associated with the Coastal Oyashio supported the expected dynamics.     

Flow under standing waves: Part 1. Shear stress distribution,energy flux and steady streaming

The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet–Higgins from 1953. The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two-dimensional simulations of standing waves have also been made by application of a general purpose Navier–Stokes solver. The results agree well with those obtained by the boundary layer analysis. Wave reflection from a plane sloping wall is also investigated by using the same numerical model and by physical laboratory experiments. The phase shift of the reflected wave train is compared with theoretical and empirical models.     

波浪作用下异重流运动特性研究

本文通过水槽试验和理论分析手段对波浪作用下异重流运动特性进行了研究，应用流体运动基本方程推导了异重流在水平底面运动时的运动速度、厚度和流量表达式。结果表明，计算结果与水槽试验较一致     

New model to determine forces at on-bottom slender pipelines

The present paper proposes a numerical model to determine horizontal and vertical components of the hydrodynamic forces on a slender submarine pipeline lying at the sea bed and exposed to non-linear waves plus a current. The new model is an extension of the Wake II type model, originally proposed for sinusoidal waves (Soedigdo et al., 1999) and for combined sinusoidal waves and currents (Sabag et al., 2000), to the case of periodic or random waves, even with a superimposed current. The Wake II type model takes into account the wake effects on the kinematic field and the time variation of drag and lift hydrodynamic coefficients. The proposed extension is based on an evolutional analysis carried out for each half period of the free stream horizontal velocity at the pipeline. An analytical expression of the wake velocity is developed starting from the Navier–Stokes and the boundary layer equations. The time variation of the drag and lift hydrodynamic coefficients is obtained using a Gaussian integration of the start-up function. A reduced scale laboratory investigation in a large wave flume has been conducted in order to calibrate the empirical parameters involved in the proposed model. Different wave and current conditions have been considered and measurements of free stream horizontal velocities and dynamic pressures on a bottom-mounted pipeline have been conducted. The comparison between experimental and numerical hydrodynamic forces shows the accuracy of the new model in evaluating the time variation of peaks and phase shifts of the horizontal and vertical wave and current induced forces.     

Interaction of higher-order water waves with uniform currents

The interaction between current-free higher-order water waves with a wave-free uniform current normal to the wave crests is considered. The combined wave-current motion resulting from the interaction is assumed stable and irrotational. The velocity potential, dispersion relation, the particle kinematics and pressure distribution up to the third order in wave amplitude are developed. The conservation of mean mass, momentum and energy, together with the dispersion relation on the free surface are used to derive a set of four nonlinear equations, through which the relationship between wave-free current, current-free wave and the combined wave-current parameters is established. Numerical results for a range of current values are also presented.     

CALCULATION OF WAVE-CURRENT FORCE ON ISOLATED PILE

By means of photography the author has investigated the mechanism of wave and current motion to measure simultaneously orbital path, velocity and acceleration of water particles. This new experimental system consists of a camera, a special light source, an intermittent exposure unit and a chemical liquid tracer.On the basis of theoretical analysis of combined effects of current and wave and the results of experiments, a model of total wave and current velocity is provided to calculate wave-current forces on a pile according to Morison's Formula. The calculated results from three different sets of wave and current data have been compared with experimental data and they are found in excellent agreement.     

Shoaling waves: A discussion

Surface gravity waves are commonly observed to slow down and to stop at a beach without any noticeable reflection taking place. We assume that as a consequence the waves are continuously giving up their linear and angular momenta, which they carry with them, along with energy, as they propagate into gradually decreasing mean depths of water. It takes a force to cause a time rate of decrease in the linear momentum and a torque to produce a time rate of decrease in the angular momentum. Both a force and a torque operate on the shoaling waves, due to the presence of the sloping bottom, to cause the diminution of their linear and angular momenta. By Newton’s third law, action equals reaction, an equal but opposite force and torque are exerted on the bottom. No other mechanisms for transferring linear and angular momenta are included in the model. Since the force on the waves acts over a horizontal distance during shoaling, work is done on the waves and energy flux is not conserved. Bottom friction, wave interaction with a mean flow, scattering from small-scale bottom irregularities and set-up are neglected. Mass flux is conserved, which leads to a shoreward monotonic decrease in amplitude consistent with available swell data. The formula for the time-independent force on the bottom agrees qualitatively with observations in seven different ways: four for swell attenuation and three for sediment transport on beaches. Ardhuin (2006) argues against a mean force on the bottom that is not hydrostatic, mainly by using conservation of energy flux. He also applies the action balance equation to shoaling waves. Action is a difficult concept to grasp for motion in a continuum; it cannot be easily visualized, and it is not really necessary for solving the shoaling wave problem. We prefer angular momentum because it is clearly related to the observed orbital motion of the fluid particles in progressive surface waves. The physical significance of wave action for surface waves has been described recently by showing that in deep water action is equivalent to the magnitude of the wave’s orbital angular momentum (Kenyon and Sheres, 1996). Finally, Ardhuin requires that there be a significant exchange of linear momentum between shoaling waves and an unspecified mean flow, although the magnitude and direction of the exchange are not predicted. No mention is made of what happens to the orbital angular momentum during shoaling. Mass flux conservation is not stated.     

赤道海洋波致Lagrange余流的弱非线性动力学模型及其解

基于一个连续层化赤道海洋波动的弱非线性动力学系统,推导并建立了由最低阶Ｌａｇｒａｎｇｅ余流体现的包含波致、风生等效应在内的热带海洋余环流基本方程组,经分析发现,零阶赤道以动自身的非线性耦合可产生一阶余流,其量级对于热带上层海洋准定常环流而言是不可忽略的。波致环流的产生紧缩联系于Ｌａｇｒａｎｇｅ轨迹运动与波流的非线性耦合效应,所导出的最低阶赤道波致Ｌａｇｒａｎｇｅ余 一般解具有与零阶波动不同的垂直与     

非线性流函数在实验风浪场计算中的应用

风作用于水面产生风浪, 其中由于波流紊动产生的动量和能量的交换机制是一个很复杂的过程。风应力一般用来描述这种能量交换, 可以分为3个部分: 水面的剪切力、波生应力以及紊动应力。采用一种有效的非线性波流分离方法——NSFM(Nonlinear Stream Function Method)对波流运动的动量和能量输移进行定性描述。构造能够有效表达非线性波浪的解析流函数, 摄动求解使其满足拉普拉斯方程、动力边界条件和运动边界条件, 结合实验室风浪数据, 分离出波生速度场。通过交叉谱分析, 得到波生雷诺应力在不同风速下对风应力的贡献。结果表明: NSFM对不同工况条件下的风浪的处理具有较高的精度, 模型适应性良好; 且风速越大, 波生应力沿着水深衰减得越快, 且自由面波生应力在动量输移中的比重会逐渐减弱。     

Laboratory study on wave dissipation by vegetation in combined current–wave flow

Coastal wetlands such as salt marshes and mangroves provide valuable ecosystem services including coastal protection. Many studies have assessed the influence of plant traits and wave conditions on vegetation-induced wave dissipation, whereas the effect of tidal currents is often ignored. To our knowledge, only two studies investigated wave dissipation by vegetation with the presence of following currents (current velocity is in the same direction as wave propagation) (Li and Yan, 2007; Paul et al., 2012). However, based on independent experiments, they have drawn contradictive conclusions whether steady currents increase or decrease wave attenuation. We show in this paper that this inconsistency may be caused by a difference in ratio of imposed current velocity to amplitude of the horizontal wave orbital velocity. We found that following currents can either increase or decrease wave dissipation depending on the velocity ratio, which explains the seeming inconsistency in the two previous studies. Wave dissipation in plant canopies is closely related to vegetation drag coefficients. We apply a new approach to obtain the drag coefficients. This new method eliminates the potential errors that are often introduced by the commonly used method. More importantly, it is capable of obtaining the vegetation drag coefficient in combined current–wave flows, which is not possible for the commonly used calibration method. Based on laboratory data, we propose an empirical relation between drag coefficient and Reynolds number, which can be useful for numerical modeling. The characteristics of drag coefficient variation and in-canopy velocity dynamics are incorporated into an analytical model to help understand the effect of following currents on vegetation-induced wave dissipation.     

Interaction between the surface and internal waves: The modulation and maser mechanisms

Two feedback mechanisms are considered which emerge from the interaction between the surface and internal waves. The energy exchange between the wave systems is coupled with the periodic variations of momentum and the losses of the wind wave momentum during their interaction with the internal wave (IW) current field. These mechanisms result in the IW attenuation which is the strongest when IW and wind propagate in the same direction. When attenuating, the IWs give rise to the inertial currents comparable to the Ekman background current.Translated by Mikhail M. Trufanov. UDK 551.466.3: 551.466.8.     

Short gravity waves on steady non-uniform currents obtained through up-/downwelling

Small amplitude water waves propagating in a medium with a steady non-uniform current are investigated. The non-uniform current is obtained by up- or downwelling through the horizontal bed. A new locally valid velocity potential correct to the second order is derived describing the combined wave–current motion. From this solution expressions for the local evolution of the wave amplitude and the wave number are extracted. These expressions are compared with the results found using the principle of wave action conservation and the linear dispersion relation, and good agreement is found at small distances compared to the wavelength. Unlike earlier works there is no restriction to deep water. The results valid for deep water are found as a special case of the general solution and agree with the solution found by Longuet-Higgins, M.S. and Stewart, R.W. (1961) The changes in amplitude of short gravity waves on steady non-uniform currents. Journal of Fluid Mechanics, 10(4), 529–549. Furthermore, it is shown that the principle of wave action conservation in fact holds for waves propagating in a medium with a steady non-uniform current maintained by up-/downwelling also on finite depth.     

基于长期观测的辽东湾口东部海域水动力特征研究

辽东湾口东部海域是辽东湾与渤海中部进行物质和能量交换的主要通道之一。本文利用坐底式海床基平台获取的近8个月的水动力连续观测资料,通过谱分析和调和分析方法对该海域的潮汐、潮流特征进行分析,并讨论了余流及底层温度的季节变化规律。研究结果表明:该海域潮汐属于不规则半日潮,平均潮差为0.95 m,最大可能潮差为2.27 m。潮流属于不规则半日潮流,M₂分潮流为其优势分潮流。主要分潮流运动形式为往复流,最大流速方向为西南-东北向。余流的季节性特征较为明显:秋季,余流流速在中层达到最大,流向以西南向为主;冬季,余流流速垂向变化较小,并呈西南偏西向流动;春季,流速随深度增加而减小,流向从表层至底层呈现逆时针旋转的特征。受底层潮流、水平温度梯度及海面温度日变化的影响,底层温度表现出短期的高频变化特征:秋季,短期振荡以半日周期信号为主;冬季,全日周期信号较为显著;春季,短期振荡的现象较弱。     

Effects of following and opposing vertical current shear on nonlinear wave interactions

A Navier-Stokes solver in OpenFOAM^® is combined with the Volume of Fluid (VOF) surface capturing method to investigate the wave interaction with depth-varying currents in intermediate and shallow waters. A special attention is paid to the separate effect of vertical current shear on near resonant triad wave interactions. It was found that in the presence of following vertical current shear, the wave exhibits a sharper crest and flatter trough, and the opposite is true in the presence of opposing vertical current shear. Our model results indicate that the wave steepness at which the current shear starts to affect the crest elevation is greater in deeper water than in shallower water. We found that adding vertical current shear to the uniform current further enhances the relative harmonic wave energy and the extent of triad interaction in the following current while weakens them in the opposing current. As a result, following and opposing current shear may cause wave to break at a lower and higher sea state respectively. Due to the increased wave nonlinearity in the presence of a following current shear, a linear superposition of the individual wave and current velocities is no longer adequate to represent the total horizontal velocity close to the free surface.     

Wave-formed structures and paleoenvironmental reconstruction

Wave-formed sedimentary structures can be powerful interpretive tools because they reflect not only the velocity and direction of the oscillatory currents, but also the length of the horizontal component of orbital motion and the presence of velocity asymmetry within the flow. Several of these aspects can be related through standard wave theories to combinations of wave dimensions and water depth that have definable natural limits. For a particular grain size, threshold of particle movement and that of conversion from a rippled to flat bed indicate flow-velocity limits. The ratio of ripple spacing to grain size provides an estimate of the length of the near-bottom orbital motion. The degree of velocity asymmetry is related to the asymmetry of the bedforms, though it presently cannot be estimated with confidence. A plot of water depth versus wave height (h—H diagram) provides a convenient approach for showing the combination of wave parameters and water depths capable of generating any particular structure in sand of a given grain size. Natural limits on wave height and inferences or assumptions regarding either water depth or wave period based on geologic evidence allow refinement of the paleoenvironmental reconstruction. The assumptions and the degree of approximation involved in the different techniques impose significant constraints. Inferences based on wave-formed structures are most reliable when they are drawn in the context of other evidence such as the association of sedimentary features or progradational sequences.     

Forced convection accompanying wind waves

Wind-wave tunnel experiments reveal, by use of techniques of the flow visualization, that wind waves are accompanied by the wind drift surface current with large velocity shear and with horizontal variation of velocity relative to the wave profile. The surface current converges from the crest to a little leeward face of the crest, making a downward flow there, even though the wave is not breaking. Namely, wind waves are accompanied by forced convections relative to the crests of the waves. Since the location of the convergence and the downward flow travels on the water surface as the crest of the wave propagates, the motion as a whole is characterized by turbulent structure as well as by the nature of water-surface waves. In this meaning, the term of real wind waves is proposed in contrast with ordinary water waves. The study of real wind waves will be essential in future development of the study of wind waves.     

Analysis of some key parametrizations in a beach profile morphodynamical model

A numerical process-based model to forecast beach profile morphodynamics has been developed. In the present paper, an analysis of various modelling approaches and key parametrizations involved in the estimation of the wave-driven current and the suspended sediment concentration is carried out.Several resolution techniques for the 1DV horizontal (i.e., in the x-direction perpendicular to coastline) momentum equation governing the Mean Horizontal Velocity (MHV) are analysed. In the first kind of techniques, the mean horizontal velocity is computed from the momentum equation, whereas the Mean Water Level (MWL) is computed using a parametrization of the depth-averaged momentum equation. Two boundary or integral conditions are thus needed. In the second kind, both mean horizontal velocity and mean water level gradient in the x-direction are the unknowns of the momentum equation, thus, three boundary or integral conditions are needed. Various additional conditions are discussed. We show that using a technique of the first kind is equivalent to imposing the difference between the surface and the bottom shear stresses in the 1D vertical equation. Both techniques lead to results that are in good agreement with the Delta Flume experimental data, provided the Stokes drift flow discharge is imposed as an additional condition. The influence of the breaking roller model and of the turbulent viscosity parametrization are also analysed.Suspended sediment transport by the mean current and wave-induced bedload transport are taken into account in the sediment flux. Three turbulent diffusivity parametrizations are compared for suspended sediment concentration estimations. A linear profile for the turbulent diffusivity taking into account the wave bottom shear stress and the surface wave breaking turbulence production is shown to give the best results. Using experimental data, we put forward the poor estimation of the bottom sediment concentration given by the three implemented parametrizations. We thus propose a new parametrization relying on a Shields parameter based on the breaking roller induced surface shear stress. Using this new parametrization, the bottom profile used in the tests keeps its two bars which disappear otherwise. However, the morphodynamical model still overestimates the bars offshore motion, a bias already observed in other models.     

波流共同作用下珊瑚礁冠层附近平均流分布及阻力特性试验

本文通过物理模型试验研究了波流共同作用下珊瑚礁冠层附近平均流的分布特征以及阻力特性,分析了典型波浪工况下无潮流、正向潮流和反向潮流分别作用下平均流速、摩阻流速、阻力系数的沿礁变化规律。结果表明：无潮流时礁前斜坡及外礁坪上存在海底回流且在礁缘附近回流最强,在礁坪上冠层附近平均流表现为向岸流,且该流沿礁向海岸方向持续增大。相较于无潮流时,正向潮流作用下冠层内外均为向岸流,在礁坪上冠层内外的向岸流显著增大;反向潮流作用下冠层内外均为离岸流且在礁缘处达到最大,该离岸流在礁坪上逐渐减小然后趋于稳定。无潮流时礁坪上摩阻流速呈小幅波动;相较于无潮流时,正向潮流、反向潮流影响下礁坪上摩阻流速显著增大,其中正向潮流影响下增幅更大;无潮流时礁坪上水力粗糙度沿礁减小,正向潮流和反向潮流影响下水力粗糙度普遍有幅度不等的增加。三种工况下礁坪上的阻力系数均沿礁整体呈下降趋势,相较于无潮流时,正向潮流和反向潮流影响下礁坪上的阻力系数显著增大,且正向潮流作用时增幅更大。