The experimental study on infra-gravity wave

A series of experiments were conducted in a super-wave flume (300 m×5 m×5.2 m) to examine the low-frequency motion induced by waves with different incident steepness, sloping gradients and normalized frequency (sideband space). Two kinds of waves including initial uniform wave train and modulated wave train (one carrier with a pair of sidebands) are utilized for incident wave conditions. From the experimental results, it is found that for a given slope gradient the infra-gravity wave component decreases as wave nonlinearity increases and frequency downshift is a predominant factor. Furthermore, the magnitude of low-frequency component decreases with slope gradients for a given initial wave condition. In addition, the maximum value of low-frequency motion is found to be close to the normalized frequency, δ=1.0.     

Surf zone dynamics simulated by a Boussinesq type model. Part II: surf beat and swash oscillations for wave groups and irregular waves

This is the second of three papers on the modelling of various types of surf zone phenomena. In the first paper the general model was described and it was applied to study cross-shore motion of regular waves in the surf zone. In this paper, part II, we consider the cross-shore motion of wave groups and irregular waves with emphasis on shoaling, breaking and runup as well as the generation of surf beats. These phenomena are investigated numerically by using a time-domain Boussinesq type model, which resolves the primary wave motion as well as the long waves. As compared with the classical Boussinesq equations, the equations adopted here allow for improved linear dispersion characteristics and wave breaking is modelled by using a roller concept for spilling breakers. The swash zone is included by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. Mutual interaction between short waves and long waves is inherent in the model. This allows, for example, for a general exchange of energy between triads rather than a simple one-way forcing of bound waves and for a substantial modification of bore celerities in the swash zone due to the presence of long waves. The model study is based mainly on incident bichromatic wave groups considering a range of mean frequencies, group frequencies, modulation rates, sea bed slopes and surf similarity parameters. Additionally, two cases of incident irregular waves are studied. The model results presented include transformation of surface elevations during shoaling, breaking and runup and the resulting shoreline oscillations. The low frequency motion induced by the primary-wave groups is determined at the shoreline and outside the surf zone by low-pass filtering and subsequent division into incident bound and free components and reflected free components. The model results are compared with laboratory experiments from the literature and the agreement is generally found to be very good. Finally the paper includes special details from the breaker model: time and space trajectories of surface rollers revealing the breakpoint oscillation and the speed of bores; envelopes of low-pass filtered radiation stress and surface elevation; sensitivity of surf beat to group frequency, modulation rate and bottom slope is investigated. Part III of this work (Sørensen et al., 1998) presents nearshore circulations induced by the breaking of unidirectional and multi-directional waves.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

Formation of beach cusps in a wave tank

Beach cusps with a longshore spacing of 20 to 150 cm have been built by the continuous action of incident waves on a steep laboratory beach floor covered uniformly with a thin bed of glass beads. Breaking of incident waves was observed to induce vortices on the bed by interacting with swash motion along the beach face. Beach cusps formed when the value of a dimensionless parameter H_b/sgT_i² became smaller than 0.042; H_b is the breaking height of the incident waves, T_i their period, s the beach slope and g the acceleration due to gravity. This critical value occurred at a nearly central part of the generation region 0.003 < H_b/sgT_i² < 0.068 for plunging breakers presented by Galvin (1968). Breaking-wave-induced vortices rather than breaker types controlled the movement of bed material in the nearshore zone. Most of the measured spacings of beach cusps, including previous observations, were in good agreement with half a wavelength of the zero-mode subharmonic edge wave, which is generated on the beach by the refraction of incident waves and has twice the period of the waves. The role of edge waves at each stage of cusp formation still remains as an important problem to be clarified.     

Experimental study of long wave generation on sloping bottoms

Low-frequency waves generated on steep (1:10) and mild (1:40) slopes by six series of bichromatic wave groups are studied experimentally. The shorelines for both slopes are replaced by horizontal reaches of small depth. This reduces the reflection of long waves near the shoreline significantly, which for the first time makes possible the explicit observation of outgoing breakpoint forced long waves. The breakpoint and released bound long wave mechanisms on the different slopes are compared. Generally, the breakpoint forced long waves dominate the low-frequency wave field on the steep slope, while the released bound long waves are found to be more significant on the mild slope. Two parameters indexing the effectiveness of the breakpoint mechanism are compared and the normalized slope tends to give more realistic results. Shoaling of bound long waves is analyzed and the shallow-water equilibrium limit ~ h^−5/2 exhibits a good prediction of the variation of the bound long waves on both slopes.     

Breakpoint generated surf beat induced by bichromatic wave groups

This paper presents new experimental data on 2-D surf beat generation by a time-varying breakpoint induced by bichromatic wave groups. The experimental investigation covers a broad range of wave amplitudes, short wave frequencies, group frequencies and modulation rates. The data include measurements of incident and outgoing wave amplitudes, breakpoint position, shoreline run-up and the cross-shore structure of both the short and long wave motion. Surf beat generation is shown to be in good agreement with theory [Symonds, G., Huntley, D.A., Bowen, A.J., 1982. Two dimensional surf beat: long wave generation by a time-varying breakpoint. J. Geophys. Res. 87, 492–498]. In particular, surf beat generation is dependent on the normalised surf zone width, which is a measure of the phase relationship between the seaward and shoreward breakpoint forced long waves, and linearly dependent on the short wave amplitude. The cross-shore structure of the long wave motion is also consistent with theory; at maximum and minimum surf beat generation, the mean breakpoint coincides with the nodal and anti-nodal points, respectively, for a free long wave standing at the shoreline. A numerical solution, using measured data as input, additionally shows that the phase relationship between the incident bound long wave and the outgoing breakpoint forced wave is consistent with the time-varying breakpoint mechanism.     

潮汐影响下海滩前滨波浪传播耗能过程分析

文章基于长乐海滩前滨剖面的实测波浪数据, 通过统计分析以及谱分析的方法, 探讨了潮汐过程中长乐海滩波浪参数及耗能过程的变化规律。结果表明, 观测期间内波浪以混合浪为主, 各测点谱型较宽, 存在多峰振荡现象。向岸传播过程中, 波能耗散的形式为窄频域向宽频域转变, 能量分布趋于分散, 高频波能减小, 低频波能反而有所上升, 波浪破碎后生成长重力波。破波带内的能量衰减与波浪传播距离具有良好的相关性, 破碎波能在破波带内大约衰减了98.3%。潮汐水位对波浪具有明显的调制作用。入射波能随潮汐水位的增加而有所增加, 且水位越高, 入射波能分布越分散。破波带内的有效波高和潮汐水位具有显著的正相关关系。潮汐过程中固定测点的波谱变化与波浪沿剖面的波谱变化具有明显的相似性。     

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.     

Large-scale experiments on beach profile evolution and surf and swash zone sediment transport induced by long waves,wave groups and random waves

New large-scale laboratory data are presented on the influence of long waves, bichromatic wave groups and random waves on sediment transport in the surf and swash zones. Physical model testing was performed in the large-scale CIEM wave flume at UPC, Barcelona, as part of the SUSCO (swash zone response under grouping storm conditions) experiment in the Hydralab III program (Vicinanza et al., 2010). Fourteen different wave conditions were used, encompassing monochromatic waves, bichromatic wave groups and random waves. The experiments were designed specifically to compare variations in beach profile evolution between monochromatic waves and unsteady waves with the same mean energy flux. Each test commenced with approximately the same initial profile. The monochromatic conditions were perturbed with free long waves, and then subsequently substituted with bichromatic wave groups with different bandwidth and with random waves with varying groupiness. Beach profile measurements were made at half-hourly and hourly intervals, from which net cross-shore transport rates were calculated for the different wave conditions. Pairs of experiments with slightly different bandwidth or wave grouping show very similar net cross-shore sediment transport patterns, giving high confidence to the data set. Consistent with recent small-scale experiments, the data clearly show that in comparison to monochromatic conditions the bichromatic wave groups reduce onshore transport during accretive conditions and increase offshore transport during erosive conditions. The random waves have a similar influence to the bichromatic wave groups, promoting offshore transport, in comparison to the monochromatic conditions. The data also indicate that the free long waves promote onshore transport, but the conclusions are more tentative as a result of a few errors in the test schedule and modifications to the setup which reduced testing time. The experiments suggest that the inclusion of long wave and wave group sediment transport is important for improved near-shore morphological modeling of cross-shore beach profile evolution, and they provide a very comprehensive and controlled series of tests for evaluating numerical models. It is suggested that the large change in the beach response between monochromatic conditions and wave group conditions is a result of the increased significant and maximum wave heights in the wave groups, as much as the presence of the forced and free long waves induced by the groupiness. The equilibrium state model concept can provide a heuristic explanation of the influence of the wave groups on the bulk beach profile response if their effective relative fall velocity is larger than that of monochromatic waves with the same incident energy flux.     

波浪动力因素变化对沙质岸滩演变的影响

通过波浪水槽实验,对海平面变化造成的波浪动力因素改变引起的沙质岸滩形态响应开展机理性研究。实验采用1∶10单一沙质斜坡概化岸滩,利用3种不同实验水深模拟海平面变化,考虑椭圆余弦波、非规则波、规则波和孤立波4种类型波浪作用。实验对波浪在斜坡上的传播变形、破碎、上爬和回落过程的波高及波浪作用后的岸滩地形进行了测量。实验结果表明,椭圆余弦波、规则波和非规则波作用下,平衡岸滩呈现出滩肩形态,孤立波作用下则呈沙坝形态。海平面上升造成波浪动力增强,沙质岸滩平衡剖面形状基本保持不变向岸平移,槽谷、滩肩、沙坝位置以及岸线蚀退距离,均呈现出良好规律性。     

Experimental study of the transformation of bound long waves over a mild slope with ambient currents

The effect of currents on the variation of cross-shore bound long waves forced by bichromatic waves over a plane slope was investigated in the laboratory. In still water the growth rate of the shoaling bound long waves over the slope is proportional to h^– 5/2 (h is still-water depth). It was found that the opposing current makes the amplitudes of the bound long waves greater than those of still water for all cases. However, the amplitudes of bound long waves in a following current are reduced in the weakly modulated cases but are enhanced in the fully modulated case.     

Numerical study of wave and longshore current interaction

Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole（2001） and Reniers and Battjes（1997） were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.     

A new predictive formula for inception of regular wave breaking

Efforts are made to enhance the predictive formula for the inception of wave breaking. To achieve success, the existing formulas are extensively reviewed. They are categorized into four types, i.e., the McCowan type, the Miche type, the Goda type and the Munk type. The inherent relations among the different types are then exploited. The differences among each formula within a group are also discussed. Four representative formulas from the different types are chosen to compare with the measured data for a total number of 1193 cases reported in literatures. It is shown that Goda's and Ostendorf and Madsen's formulas are advantageous in general among the selected ones. Goda's formula, however, is found to be inaccurate as the beach slope becomes steeper than 1/10. Ostendorf and Madsen's formula is fairly good even for cases of very steep slopes, but its accuracy for the cases of ordinary slopes is not as good as Goda's. A new predictive formula for the inception of wave breaking is proposed. The unique index, defined by ψ′_b = (1.21 − 3.30λ_b)(1.48 − 0.54γ_b)ψ_b, where ψ_b = gH_b/C_b², H_b is the breaking wave height, C_b is the breaking wave celerity, λ_b is the breaking wave steepness, γ_b is the relative breaking wave height, and g is the gravity acceleration, is introduced. The incipient condition of wave breaking is then given by ψ′_b = 0.69. This formula is a significant improvement to the existing ones in terms of the accuracy. In addition, it is a local relation. Further verification shows that the proposed formula performs similarly well when applied to the field and to the waves over permeable bed.     

Laboratory study of wave and turbulence characteristics in narrow-band irregular breaking waves

Wave elevations and water particle velocities were measured in a laboratory surf zone created by the breaking of a narrow-band irregular wave train on a 1/35 plane slope. The incident waves form wave groups that are strongly modulated. It is found that the waves that break close to the shoreline generally have larger wave-height-to-water-depth ratios before breaking than the waves that break farther offshore. After breaking, the wave-height-to-water-depth ratio for the individual waves approaches a constant value in the inner surf zone, while the standard deviation of the wave period increases as the still water depth decreases. In the outer surf zone, the distribution of the period-averaged turbulent kinetic energy is closely correlated to the initial wave heights, and has a wider variation for narrow-band waves than for broad-band waves. In the inner surf zone, the distribution of the period-averaged turbulent kinetic energy is similar for narrow-band waves and broad-band waves. It is found that the wave elevation and turbulent kinetic energy time histories for the individual waves in a wave group are qualitatively similar to those found in a spilling regular wave. The time-averaged transport of turbulent kinetic energy by the ensemble-averaged velocity and turbulence velocity under the irregular breaking waves are also consistent with the measurements obtained in regular breaking waves. The experimental results indicate that the shape of the incident wave spectrum has a significant effect on the temporal and spatial variability of wave breaking and the distribution of turbulent kinetic energy in the outer surf zone. In the inner surf zone, however, the distribution of turbulent kinetic energy is relatively insensitive to the shape of the incident wave spectrum, and the important parameters are the significant wave height and period of the incident waves, and the beach slope.     

Magnitude and cross-shore distribution of bed return flow measured on natural beaches

Field measurements of cross-shore currents 0.25 m from the bed were made on two natural beaches under a range of incident wave conditions. The results indicated the presence of a relatively strong, offshore-directed mean current, both within and seaward of the surf zone. Typical velocities within the surf zone were of the order of 0.2–0.3 m/s. This bed return flow, or “undertow”, represents a mass conservation response, returning water seaward that was initially transported onshore in the upper water column, primarily above the trough of the incident waves. The measurements demonstrated that the bed return flow velocity increases with the incident wave height. In addition, the crossshore distribution of the bed return flow is characterised by a mid-surf zone maximum, which exhibits a strong decrease in velocity towards the shoreline and a more gradual decay in the offshore direction. Several bed return flow models based on mass continuity were formulated to predict the cross-shore distribution of the bed return flow under an irregular wave field and were compared with the field data. Best agreement was obtained using shallow water linear wave theory, after including the mass transport associated with unbroken waves. The contribution of the unbroken waves enables net offshore-directed bottom currents to persist outside the region of breaking waves, providing a mechanism, other than rip currents, to transport sediment offshore beyond the surf zone.     

Experimental study of the breaking limit of multi-directional random waves passing over an impermeable submerged breakwater

This study investigates experimentally the breaking wave height of multi-directional random waves passing over an impermeable submerged breakwater. Experiments have been conducted in a three-dimensional wave basin equipped with a multi-directional random wave generator. A special type of wave gauge has been newly devised to record the water surface elevations in the breaker zone as accurately as possible. The records are analyzed to estimate the location and limit of wave breaking. Comparisons have also been made with the results of regular waves. The influence of the incident wave conditions on the breaking wave height normalized by the breakwater dimensions has been investigated. Empirical formulae have been presented to estimate the breaking limit of multi-directional random waves based on the experimental records. The formulae have been tested and found to work well not only for multi-directional random waves, but for regular waves as well.     

Laboratory investigation on wave transmission through two rows of perforated hollow piles

Experimental investigations on perforated hollow piles in two rows were conducted in a two dimensional wave flume. The influence of water depth, incident wave steepness, clear spacing between the piles and the spacing of pile rows on transmission coefficient have been studied. The effect of staggering of piles in rows is investigated. The results are also compared with the results of experiments on piles without perforations. The investigations have revealed that perforated piles attenuate more wave energy than non-perforated piles. The transmission coefficient K_t decreases as the wave steepness increases for both non-perforated and perforated piles. For non-perforated piles as relative clear spacing between the piles (b/D) decreases, for waves of higher steepness, K_t decreases while for perforated piles as b/D decreases, K_t is decreasing for all the steepness considered. As the relative clear spacing between the pile rows (B/D) increases K_t initially decreases till B/D is around one and later it starts increasing for both non-perforated and perforated piles. Staggering of piles has little effect on K_t. It is also found that water depth has insignificant influence on transmission coefficient at higher steepness for both perforated and non-perforated piles. Wave period alone does not directly influence transmission coefficient K_t.     

卷破波作用下沙质岸滩剖面形态判别式初探

通过波浪水槽实验,开展不同类型波浪作用下的沙质岸滩演化规律研究工作。本次实验研究不考虑比尺,采用1:10与1:20组成的复合沙质斜坡对岸滩进行概化,选取规则波和椭圆余弦波两种典型波浪作用,对波浪的传播、变形和破碎、上爬、回落过程以及波浪作用前后沙质岸滩床面地形进行了观测,探讨波浪作用下沙质岸滩剖面演化规律。本文实验工况中,规则波作用下,岸滩剖面呈现出沙坝剖面和滩肩剖面,椭圆余弦波作用下的岸滩剖面均呈滩肩形态,发现岸滩剖面形态不仅与波浪作用类型、强度、周期等因素相关,还与波浪破碎的强度等因素有关。通过对实验过程中现象的进行观察和分析,引入了卷破波水舌冲击角的概念。对波浪卷破破碎后形成的水流挟沙运动与岸滩剖面形态的关系进行定性分析,对水舌冲击角与Irribarren参数之间的关系进行定量分析,基于Irribarren参数与岸滩剖面形态的关系初步建立了波浪作用下沙质岸滩剖面形态判别关系式。通过本文实验结果和前人实验结果对趋势线进行拟合,求得其判别系数,判别式能够较好地划分淤积型岸滩、侵蚀型岸滩及过渡型岸滩三种岸滩形态。     

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.     

Large-wave simulation of three-dimensional,cross-shore and oblique,spilling breaking on constant slope beach

In this work, the large-wave simulation (LWS) method is adapted for application in spilling wave breaking over a constant slope beach. According to LWS, large scales of velocities, pressure and free-surface elevation are numerically resolved, while the corresponding unresolved scale effects are taken into consideration by a subgrid scale (SGS) model for wave and eddy stresses. The model may be not fully applicable in very shallow water, close to the shoreline, where the unresolved, turbulent, free-surface oscillation is of the same order with the water depth. Time integration of the Euler equations is achieved by a two-stage fractional scheme, combined with a hybrid scheme for spatial discretization, consisting of finite difference and pseudospectral approximation methods. Model parameters are calibrated by comparison to available experimental data of free-surface elevation and velocities in the surf zone for cross-shore incoming waves. The action of the wave SGS stresses in the outer coastal and surf zones initiates breaking and generates appropriate vorticity, in the form of an eddy structure (surface roller), at the breaking wavefront. At incipient breaking, both advection and gravity contribute to the vorticity flux at the free surface, while only after the full development of the surface roller, the effect of advection becomes stronger. The SGS model is also utilized to simulate propagation, refraction and breaking of oblique incoming waves. The gradual breaking and dissipation of wave crestlines and the surface roller structure along the breaking wavefront are automatically captured without any empirical input, such as data for the roller shape or the wave propagation angle at breaking.