Wave Power Focusing due to the Bragg Resonance

Wave energy has drawn much attention as an achievable way to exploit the renewable energy. At present, in order to enhance the wave energy extraction, most efforts have been concentrated on optimizing the wave energy convertor and the power take-off system mechanically and electrically. However, focusing the wave power in specific wave field could also be an alternative to improve the wave energy extraction. In this experimental study, the Bragg resonance effect is applied to focus the wave energy. Because the Bragg resonance effect of the rippled bottom largely amplifies the wave reflection, leading to a significant increase of wave focusing. Achieved with an energy conversion system consisting of a point absorber and a permanent magnet single phase linear motor, the wave energy extracted in the wave flume with and without Bragg resonance effect was measured and compared quantitatively in experiment. It shows that energy extraction by a point absorber from a standing wave field resulted from Bragg resonance effect can be remarkably increased compared with that from a propagating wave field (without Bragg resonance effect).     

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。     

Scattering of Semidiurnal Internal Kelvin Wave at Step Bottom Topography

A three-dimensional, multi-level model was used to study the energy dissipation of semidiurnal internal Kelvin waves due to their interaction with bottom topography. A simplified topography consisting of a channel with an additional shallow bay was used to clarify the wave’s scattering process. When the first mode semidiurnal internal wave given at an open boundary arrives at the bay mouth, higher-mode internal waves are generated at a step bottom of the bay mouth. As a result, the energy of the first mode internal Kelvin wave is effectively decayed. The decay rate of the internal Kelvin wave depends on both the width and length of the additional bay. The maximum decay rate was found when a resonance condition occurs the bay, that is, the bay length is equal to a quarter of wave length of the first mode internal wave on the shallow region. The decay rate in the wide bay cases is higher than that in a narrow case, due to a contribution from the scattering due to the Poincare wave that emanates from the corners of the bay head. The decay rate with the additional bay is 1.1–1.8 times that of the case without the additional bay. The decay rate due to the scattering process is found to be of the same order as that of the internal and bottom friction.     

The RIDE model: an enhanced computer program for wave transformation

A wave transformation model (RIDE) was enhanced to include the process of wave breaking energy dissipation in addition to water wave refraction, diffraction, reflection, shoaling, bottom friction, and harbor resonance. The Gaussian Elimination with partial Pivoting (GEP) method for a banded matrix equation and a newly developed bookkeeping procedure were used to solve the elliptic equation. Because the bookkeeping procedure changes the large computer memory requirements into a large hard-disk-size requirement with a minimum number of disk I/O, the simple and robust GEP method can be used in personal computers to handle realistic applications. The computing time is roughly proportional to N^1.7, where N is the number of grid points in the computing domain. Because the GEP method is capable of solving many wave conditions together (limited by having the same wave period, no bottom friction and no breaking), this model is very efficient compared to iteration methods when simulating some of the wave transformation process.     

Effects of scattering and resonance on energy dissipation of an internal tide in a narrow shelf

The effects of scattering and resonance on the energy dissipation of an internal tide were investigated using a two-dimensional model which is a reassembled version of the theoretical generation model devised by Rattray et al. (1969) for internal tide. The basic character of the scattering process at the step bottom was first investigated with a wide shelf model. When the internal wave incited from a deep region (Region II) into the shallow shelf region (Region I), a passing wave into the shallow region, a reflected wave into the deep region, and a beam-like wave, i.e. a scattered wave (SW), emanated at the step bottom. The SW, which consists of the superposition of numerous internal modes, propagated upward/downward into both regions. The general properties of the SW were well expressed around the shelf edge, even in the present model with viscosity effect. The amplitude of the SW decreased dramatically when the depth of the velocity maximum of the incident internal wave in Region II corresponded with the depth of the shelf edge. In the narrow shelf model, where the decay distance of the internal wave in Region I is longer than the shelf width, the incident internal wave reflected at the coast to form a standing wave. When the internal wave in Region I is enhanced by the resonance, the energy of the SW in Region II is also intensified. Furthermore, the energy of the modes in Region II predominated when the velocity maximum is identical to that of the dominant mode in Region I. These results suggest that the spatial scale of shelf region is a very important factor governing the energy dissipation of the internal tide through reflection and scattering in a narrow shelf.     

On the Downshift of Wave Frequency for Bragg Resonance

For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples, strong wave reflection occurs under the Bragg resonance condition. The critical wave frequency, at which the peak reflection coefficient is obtained, has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction. It has long been speculated that the downshift may be attributed to higher-order rippled bottom a...     

Effect of higher-order bottom variation terms on the refraction of water waves in the extended mild-slope equations

This study investigates how the refraction of water waves is affected by the higher-order bottom effect terms proportional to the square of bottom slope and to the bottom curvature in the extended mild-slope equations. Numerical analyses are performed on two cases of waves propagating over a circular shoal and over a circular hollow. Numerical results are analyzed using the eikonal equation derived from the wave equations and the wave ray tracing technique. It is found that the higher-order bottom effect terms change the wavelength and, in turn, change the refraction of waves over a variable depth. In the case of waves over a circular shoal, the higher-order bottom effects increase the wavelength along the rim of shoal more than near the center of shoal, and intensify the degree of wave refraction. However, the discontinuity of higher-order bottom effects along the rim of shoal disperses the foci of wave rays. As a result, the amplification of wave energy behind the shoal is reduced. Conversely, in the case of waves over a circular hollow, the higher-order bottom effects decrease the wavelength near the center of the hollow in comparison with the case of neglecting higher-order bottom effects. Consequently, the degree of wave refraction is decreased, and the spreading of wave energy behind the hollow is reduced.     

Effect of a submerged plate on the near-bed dynamics underincoming waves in deep water conditions

It is well known that wave induced bottom oscillations become more and more negligible when the water depth exceeds half the wavelength of the surface gravity wave. However, it was experimentally demonstrated for regular waves that the bottom pressure oscillations at both first and second wave harmonic frequencies could be significant even for incoming waves propagating in deep water condition in the presence of a submerged plate [16]. For a water depth h of about the wavelength of the wave, measurements under the plate (depth immersion of top of plate h/6, length h/2) have shown bottom pressure variations at the wave frequency, up to thirty times larger than the pressure expected in the absence of the plate. In this paper, not only regular but also irregular wave are studied together with wave following current conditions. This behavior is numerically verified by use of a classical linear theory of waves. The wave bottom effect is explained through the role of evanescent modes and horizontally oscillating water column under the plate which still exist whatever the water depth. Such a model, which allows the calculation of the velocity fields, has shown that not only the bottom pressure but also the near bed fluid velocity are enhanced. Two maxima are observed on both sides of the location of the plate, at a distance of the plate increasing with the water depth. The possible impact of such near bed dynamics is then discussed for field conditions thanks to a scaling based on a Froude similarity. It is demonstrated that these structures may have a significant impact at the sea bed even in very deep water conditions, possibly enhanced in the presence of current.     

Surface waves and bottom sediment response

Abstract

Field measurements of bottom oscillations and wave characteristics have been made in a study of the interaction of fine‐grained sediments and surface waves. A wave staff, pressure sensor, and accelerometer were used in East Bay, Louisiana, an area that has a fine‐grained clay bottom. The accelerometer contained three solid‐state accelerometers mounted at right angles. The instrument was placed about 0.3 m below the mudline. The results of the study indicate that bottom motions under wave action show well‐defined periodic features. The bottom sediments appear to be undergoing an elastic response to bottom pressures, such that the bottom is depressed under a surface wave crest. Under the range of bottom pressures measured, bottom displacement varied linearly with bottom pressure. Measured bottom pressures were up to 35% larger than predicted by linear wave theory. The effect of a movable bottom on wave pressure is considered. The energy lost from the surface wave to the bottom in forcing the bottom response is shown to be significant and larger than the energy lost to bottom friction.     

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.     

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.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

Introduction of a new friction routine into the SWAN model that evaluates roughness due to bedform and sediment size changes

The significant loss of wave energy due to seabed interaction in finite depths is a known effect and bottom friction terms are used in the wave models to account for this dissipation. In this paper, a new bottom-interaction function is tested by means of the SWAN model, based on measurements at two field sites, Lake George and Lakes Entrance, both in Australia. The function accounts for dependence of the friction on the formation process of bottom ripples and on the grain size of the sediment. The overall improvement of the model prediction both for the wave height and wave period is demonstrated.     

中长周期波作用下的斜坡堤胸墙波浪力试验研究

在印度洋、大西洋沿岸,海岸工程设计波浪周期多在14 s以上,具有显著的中长周期波特征。通过以往工程项目的试验结果发现中长周期波下,规范计算的斜坡堤胸墙波浪力明显小于试验结果。因此,通过系列物理模型试验研究了中长周期波下的斜坡堤胸墙波浪力。分析斜坡坡度、肩台宽度和波浪条件对胸墙波浪力的影响。通过将试验结果与我国现有规范中的经验公式计算所得结果进行对比,发现规范更适用于胸墙底淹没的情况,而对于肩台出水情况,规范计算结果小于试验结果。由此提出了一种新的波浪力计算方法,计算准确度得到明显提高。     

Surface gravity wave interaction with elastic bottom

In the present paper, a hydroelastic model is developed to deal with surface gravity wave interaction with an elastic bed based on the small amplitude water wave theory and plate deflection in finite water depth. The elastic bottom bed is modelled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The wave characteristics in the presence of the elastic bed is analyzed in both the cases of deep and shallow water waves. Further, the linearized long wave equation is generalized to include bottom flexibility. A generalized expansion formula for the velocity potential is derived to deal with the boundary value problems associated with surface gravity waves having an elastic bed. The utility of the expansion formula is illustrated by demonstrating specific physical problems which will play significant role in the analysis of wave structure interaction problems. Behavior of the wave spectra are discussed in the case of closed basin having a free surface and an elastic bottom topography.     

Impact of parameterized lee wave drag on the energy budget of an eddying global ocean model

The impact of parameterized topographic internal lee wave drag on the input and output terms in the total mechanical energy budget of a hybrid coordinate high-resolution global ocean general circulation model forced by winds and air-sea buoyancy fluxes is examined here. Wave drag, which parameterizes the generation of internal lee waves arising from geostrophic flow impinging upon rough topography, is included in the prognostic model, ensuring that abyssal currents and stratification in the model are affected by the wave drag.An inline mechanical (kinetic plus gravitational potential) energy budget including four dissipative terms (parameterized topographic internal lee wave drag, quadratic bottom boundary layer drag, vertical eddy viscosity, and horizontal eddy viscosity) demonstrates that wave drag dissipates less energy in the model than a diagnostic (offline) estimate would suggest, due to reductions in both the abyssal currents and stratification. The equator experiences the largest reduction in energy dissipation associated with wave drag in inline versus offline estimates. Quadratic bottom drag is the energy sink most affected globally by the presence of wave drag in the model; other energy sinks are substantially affected locally, but not in their global integrals. It is suggested that wave drag cannot be mimicked by artificially increasing the quadratic bottom drag because the energy dissipation rates associated with bottom drag are not spatially correlated with those associated with wave drag where the latter are small. Additionally, in contrast to bottom drag, wave drag is a non-local energy sink.All four aforementioned dissipative terms contribute substantially to the total energy dissipation rate of about one terawatt. The partial time derivative of potential energy (non-zero since the isopycnal depths have a long adjustment time), the surface advective fluxes of potential energy, the rate of change of potential energy due to diffusive mass fluxes, and the conversion between internal energy and potential energy also play a non-negligible role in the total mechanical energy budget. Reasons for the <10% total mechanical energy budget imbalance are discussed.     

Characteristics of the boundary layer at the bottom of a solitary wave

The results of direct numerical simulations of the boundary layer generated at the bottom of a solitary wave are described. The numerical results, which agree with the laboratory measurements of Sumer et al. (2010) show that the flow regime in the boundary layer can be laminar, laminar with coherent vortices and turbulent. The average velocity and bottom shear stress are computed and the results obtained show that the logarithmic law can approximate the velocity profile only in a restricted range of the parameters and at particular phases of the wave cycle. Moreover, the maximum value of the bottom shear stress is found to depend on the dimensionless wave height only, while the minimum (negative) value depends also on the dimensionless boundary layer thickness. Diagrams and simple formulae are proposed to evaluate the minimum and maximum bottom shear stresses and their phase shift with respect to the wave crest.     

基于潮间带现场数据的底部切应力算法对比

底部切应力作为水动力和泥沙输移模型中的关键参数,对底床泥沙起动、侵蚀淤积速率的研究十分重要.目前基于现场实测流速数据计算底部切应力的理论方法有6种:LP-mean法、LP-max法、TKE法、TKE W法、RS法和ID法,这些方法都有其特定的适用条件.河口海岸浅水区域水流和波浪作用复杂,遴选合适的方法计算底部切应力非常...     

考虑底摩擦的波浪折射计算

本文用考虑底摩擦的折射模式计算了浅水中波高和波向分布。作为一个例子,根据不同的摩擦系数和不同的边界条件计算了一种简单海底地形的折射系数、衰减系数和折射角,所得结果与不考虑底摩擦的折射模式结果进行比较,发展它们之间存在一些差异,表明在浅水中底摩擦对波高有一定影响。     

考虑弹性变形铰接塔平台非线性动力响应

研究计入弹性变形铰接塔平台在深水中的非线性动力响应。将铰接塔平台简化为顶部具有集中质量,底部具有扭转线性弹簧约束的均匀弹性梁,考虑波浪对平台的作用,应用莫里森(Morison)公式计算铰接塔平台瞬时位置所受水动力,建立了铰接塔平台横向运动的偏微分方程,采用伽辽金方法计算波浪作用下铰接塔平台非线性动力响应。计算了铰接塔平台的固有频率和模态,得到了铰接塔平台不同频率波浪激励下各阶模态的动力响应。计算结果表明,在波浪激励下系统二阶模态将发生2、34、倍超谐共振运动,并且揭示了弹性铰接塔平台在波浪作用下振动的不对称性。