南海北部陆架区内波的演变与耗散机制

海洋是多尺度强迫-耗散系统,机械能主要在大尺度输入,在小尺度耗散。在大、中尺度运动的能量向小尺度湍流传递过程中,内波扮演着重要角色。内波的生成和破碎可打破海洋动力平衡,而在陆架区,内波（主要是内孤立波）的浅化演变与耗散则是驱动湍流混合的关键过程。通过长期的理论、观测与数值模拟研究,目前已认识到内波浅化过程中主要发生如下演变：波形调制、极性转变、裂变、破碎与耗散。相较于直接发生破碎,浅化演变过程中的裂变及其引发的剪切不稳定和对流不稳定是内孤立波在陆架区的主要耗散机制,显著调制陆架区的跃层混合。从能量串级的角度讲,内孤立波浅化裂变为动力不稳定的高频内波是潮能串级的重要通道。本文简要回顾南海北部陆架区内波的研究历史,并着重总结内波在陆架区演变与耗散机制的研究进展。     

Wave-induced Benthic Velocity Variations in Shallow Waters

Waves propagating from deep water into shallow coastal areas produce oscillatory currents near the sea bottom. The magnitude of these currents depend upon the period and amplitude of the incoming waves, and the dissipation mechanism such as wave breaking and bottom friction. Field experiments in a gently shoaling bay, i.e. Cleveland Bay, Northern Australia, showed that there is a broad band of water at around 6 m depth, where the benthic surge velocities are maximum. Both further inshore and offshore, the bottom velocities were less than at 6 m depth, contrary to the normal expectation that the velocities should increase as the water becomes shallower. A new and computationally efficient wave model was developed and was able to reproduce experimental results for waves above 50 cm wave height, but not for small waves (wave height about 30 cm). One implication of this higher band of benthic surge velocities may be to produce high water turbidities in this region. Turbidity data from Cleveland Bay is consistent with this hypothesis.     

Internal tide and nonlinear internal wave behavior at the continental slope in the northern south China Sea

A field program to measure acoustic propagation characteristics and physical oceanography was undertaken in April and May 2001 in the northern South China Sea. Fluctuating ocean properties were measured with 21 moorings in water of 350- to 71-m depth near the continental slope. The sea floor at the site is gradually sloped at depths less than 90 m, but the deeper area is steppy, having gradual slopes over large areas that are near critical for diurnal internal waves and steep steps between those areas that account for much of the depth change. Large-amplitude nonlinear internal gravity waves incident on the site from the east were observed to change amplitude, horizontal length scale, and energy when shoaling. Beginning as relatively narrow solitary waves of depression, these waves continued onto the shelf much broadened in horizontal scale, where they were trailed by numerous waves of elevation (alternatively described as oscillations) that first appeared in the continental slope region. Internal gravity waves of both diurnal and semidiurnal tidal frequencies (internal tides) were also observed to propagate into shallow water from deeper water, with the diurnal waves dominating. The internal tides were at times sufficiently nonlinear to break down into bores and groups of high-frequency nonlinear internal waves.     

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。     

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.     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

Acoustic measurements of the velocity field beneath shoaling and breaking waves

An acoustic current meter attached to a servo-hydraulic surface-following device was used to obtain near-surface velocity measurements beneath breaking and near breaking surface gravity waves shoaling on a 1:40 beach. The data are compared to velocities predicted by two adaptations of linear theory: superposition and stretching. For unbroken and near breaking waves, the predictions are in close agreement with the measurements. For breaking and broken waves, near surface crest velocity measurements are influenced by air entrainment; trough velocities are relatively well predicted. The problems associated with the acoustic measurement of near-surface velocities are highlighted.     

Laboratory modeling of the propagation of periodic internal waves over bottom slopes

The experimental investigation of the run-up of periodic internal waves in a two-layer fluid on the coastal slope is performed in an open hydrochannel at the Physical Department of the Lomonosov Moscow State University. The waves are produced by a wave generator. We study the transformation of waves, the vertical structure of the field of velocities of mass transfer, and the behavior of the parameters of internal waves propagating over the sloping bottom. It is shown that the run-up and breaking of internal waves are accompanied by periodic emissions of portions of the heavier fluid from the bottom layer upward along the slope. The Stokes drift velocity changes its sign as a function of depth. Moreover, both the wave length (the horizontal distance between the neighboring crests) and the height of waves over the sloping bottom (the elevation of the crest over the slope along the vertical) decrease as the wave approaches the coast.     

Energy properties and shoaling of higher-order stokes waves on a current

The energy density, the energy flux, the set-down, the radiation stress, and some wave energy velocities have been derived correct to fourth order in wave steepness for waves on a vorticity-free current. The energy flux and the set-down have been used for shoaling predictions for finite amplitude waves with and without a net volume flux. The results with a zero volume flux are compared with more accurate shoaling predictions showing rather good accordance, except for large steepnesses. This also applies to the deep water wave energy transport velocity. The results with a net volume flux show that the steepness of the waves reduces the influence of this flux on the wave evolution. Some problems in connection with the orders in Stokes waves are discussed, among others concerning the dispersion relation and the orders of integral properties. Bed shear and accompanying dissipation is neglected.     

Investigation of transformations of barotropic tides in the coastal zone

Within the framework of the linear theory of long waves, we perform the numerical investigation of transformations of a barotropic diurnal tide in the process of its motion from the deepwater region of the sea into the region of continental slope and shelf zone at any angle to the coast line. For a linear profile of the bottom of the continental slope and shelf, we establish dependences of the amplitudes and velocities of waves on the direction of propagation of the tidal wave and the latitude of the place. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

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.     

Generation of internal waves by a barotropic tide in the coastal zone

Within the framework of the linear theory of long waves, we study internal waves generated by a barotropic tide in a two-layer ocean of variable depth taking into account the influence of the Coriolis force. Barotropic waves run over an extended unevenness of the bottom at an arbitrary angle. This unevenness is regarded as a model of the continental slope and shelf. We establish the dependences of the amplitudes of generated internal waves on the angle of incidence of the barotropic tide, topography of the bottom, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Examination of empirical formulas for wave shoaling and breaking on steep slopes

Estimation of the wave height transformation of shoaling and breaking is essential for the nearshore hydrodynamics and the design of coastal structures. Many empirical formulas have been well recognized to the wave height transformation, but most of them were only applicable for gentle slopes. This paper reports the experimental results of wave shoaling and breaking over the steep slopes to examine the applicability of the previous empirical formulas. Two steep bottom slopes of 1/3 and 1/5, and one gentle slope of 1/10 were conducted in the present experiments. Experimental results show that the shoaling distance of steep slopes become short and the surface waves may be partially reflected from the steep bottom, thus the estimation of wave shoaling using the well-known previous formula did not conform completely to the experimental results. The previous empirical formulas for the wave breaking criteria were also examined, and the modified equations to the steep beaches were proposed in this work. A numerical model was finally adopted to calculate the wave height transformation in the surf zone by introducing the modified breaking index.     

Momentum balance in shoaling gravity waves: Comment on ’shoaling surface gravity waves cause a force and a torque on the bottom’ by K. E. Kenyon

In a recent paper, Kenyon (2004) proposed that the wave-induced energy flux is generally not conserved, and that shoaling waves cause a mean force and torque on the bottom. That force was equated to the divergence of the wave momentum flux estimated from the assumption that the wave-induced mass flux is conserved. This assumption and conclusions are contrary to a wide body of observations and theory. Most importantly, waves propagate in water, so that the momentum balance generally involves the mean water flow. Although the expression for the non-hydrostatic bottom force given by Kenyon is not supported by observations, a consistent review of existing theory shows that a smaller mean wave-induced force must be present in cases with bottom friction or wave reflection. That force exactly balances the change in wave momentum flux due to bottom friction and the exchange of wave momentum between incident and reflected wave components. The remainder of the wave momentum flux divergence, due to shoaling or wave breaking, is compensated by the mean flow, with a balance involving hydrostatic pressure forces that arise from a change in mean surface elevation that is very well verified by observations.     

The FUNWAVE model application and its validation using laboratory data

In this paper, the performance of a well known and widespread Boussinesq model is evaluated for its ability to predict deep waters and shoaling zone velocity and elevation, comparing them with laboratory data. The model evaluation places emphasis on the parameters of the wave field that could be used for the prediction of coastal phenomena. It was found that the model proved its ability to predict regular wave velocity and elevation both in deep waters and shoaling zones right up to the breaking region. In contrast to previous works found in literature, the comparisons in this case are not limited to modelled and measured wave elevations, but also involve horizontal velocities. As a result, experimental and computed time series of wave elevations and horizontal velocities and their corresponding phase-averaged values are investigated along the wave channel, showing a good performance of the model.     

Influence of quasi-geostrophic currents and inertial waves on the elution of fine sediments in the Southeast Baltic

Numerical simulation based on the Princeton Ocean Model (POM) was performed for a region of the Southeast Baltic in order to compare data on the spatial distribution of velocity and bottom sediments. Special attention was focused on the influence of western and northeastern winds, which generate intense quasi-geostrophic currents can may cause very high velocities in the near bottom layer, which results in the elution of bottom sediments and transport of their fine fractions. An abrupt change in wind velocity intensifies the effect of elution due to generation of inertial internal waves that penetrate into the bottom layer. The spatial distributions of the velocity in the surface and near bottom layers are compared with data on bottom sediments. It turned out that areas with the highest velocities that formed under the effect of western and northeastern winds in most cases coincide with areas where bottom sediments are represented by coarse-grain fractions of gravel and sands.     

A case study of internal solitary wave propagation during ASIAEX 2001

During the recent Asian Seas International Acoustics Experiment (ASIAEX), extensive current meter moorings were deployed around the continental shelf-break area in the northeastern South China Sea. Thirteen RADARSAT SAR images were collected during the field test to integrate with the in situ measurements from the moorings, ship-board sensors, and conductivity/temperatire/depth (CTD) casts. Besides providing a synoptic view of the entire region, satellite imagery is very useful for tracking the internal waves, locating surface fronts, and identifying mesoscale features. During ASIAEX in May 2001, many large internal waves were observed at the test area and were the major oceanic features studied for acoustic volume interaction. Based on the internal wave distribution maps compiled from satellite data, the wave crests can be as long as 200 km with an amplitude of 100 m. Environmental parameters have been calculated based on extensive CTD casts data near the ASIAEX area. Nonlinear internal wave models have been applied to integrate and assimilate both synthetic aperture radar (SAR) and mooring data. Using SAR data in deep water as an initial condition, numerical simulations produced the wave evolution on the continental shelf and compared reasonably well with the mooring measurements at the downstream station. The shoaling, turning, and dissipation of large internal waves at the shelf break have been studied and are very important issues for acoustic propagation.     

南海北部沙波区海底强流的内波特征及其对沙波运动的影响

2008年3月6日至2008年4月9日, 在南海北部外陆架与陆坡上的沙波区进行了海底流速的连续观测,观测结果表明潮流与海流较弱,但时有流速达30—77cm.s-1的海底强流发生。强流方向与南海北部内波传播方向相对应,多分布在偏NW向与偏SE向。偏SE向流强于偏NW向流,与内波在传播方向上的下坡流大于上坡流的特征一致。对流速序列进行了旋转功率谱分析,结果表明,高于M2分潮的频率中,众多的振荡分量具有内波流性质,说明阵发性强流为内波所致。采用观测流速计算了沙波的移动速度,计算结果得出强流能起动海底泥沙,由于NW向传播（上坡方向）的内波导致了SE向（下坡方向）的净流动,沙波偏SE向移动,但沙波移动速度不大,小型沙波移动速度小于1.6m.a-1。采用潮流、风暴潮耦合模型计算了强台风驱动的海底流速过程,表明潮流、风暴潮耦合也能移动海底沙波,但沙波移动方向与台风路径相关,不一定为SE向,且移动距离更小,潮流、风暴潮耦合不是沙波移动的主要动力机制。     

One-dimensional modelling of individual waves and wave-induced longshore currents in the surf zone

A probabilistic model ( -model) was developed to describe the propagation and transformation of individual waves (wave by wave approach). The individual waves shoal until an empirical criterion for breaking is satisfied. Wave height decay after breaking is modelled by using an energy dissipation method. Wave-induced set-up and set-down and breaking-associated longshore currents are also modelled. Laboratory and field data were used to calibrate and verify the model. The model was calibrated by adjusting the wave breaking coefficient (as a function of local wave steepness and bottom slope) to obtain optimum agreement between measured and computed wave height. Four tests carried out in the large Delta flume of Delft Hydraulics were considered. Generally, the measured H_1/3-wave heights are reasonably well represented by the model in all zones from deep water to the shallow surf zone. The fraction of breaking waves was reasonably well represented by the model in the upsloping zones of the bottom profile. Verification of the model results with respect to wave-induced longshore current velocities was not extensive, because of a lack of data. In case of a barred profile the measured longshore velocities showed a relatively uniform distribution in the (trough) zone between the bar crest and the shoreline, which could to some extent be modelled by including space-averaging of the radiation force gradient, horizontal mixing and longshore water surface gradients related to variations in set-up. In case of a monotonically upsloping profile the cross-shore distribution of the longshore current velocities is reasonably well represented.