Numerical modelling of erosion and accretion of plane sloping beaches at different scales

The paper focuses on the numerical simulation of erosion of plane sloping beaches by irregular wave attack in three wave flumes of different scales. One of the prime objectives of the tests was to provide a consistent data set for the improvement of numerical beach profile models. A practical application of this research with wave attack on plane sloping beaches is the erosion of the plane beaches after nourishment. Three models (CROSMOR, UNIBEST-TC and DELFT3D) have been used to simulate the flume experimental results focusing on the wave height distribution and the morphological development (erosion and deposition) along the beach profiles. Overall, the model predictions for wave heights show consistent results. Generally, the computed wave heights (H_rms and H_1/3) are within 10% to 15% of the measured values for all tests (under-prediction of the largest wave heights close to the shore). The three models can simulate the beach erosion of the wave flume tests (erosive tests) reasonably well using default values of the sand transport parameters. The model performance for the accretive tests is less good than that for the erosive tests. A practical field application of this research is the erosion of nourished beaches, as these beaches generally have rather plane beach slopes immediately after nourishment. Various graphs are given to estimate the beach erosion of nourished beaches.     

Wave modelling in the vicinity of submerged breakwaters

This paper describes a simple method for modelling wave breaking over submerged structures, with the view of using such modelling approach in a coastal area morphodynamic modelling system.A dominant mechanism for dissipating wave energy over a submerged breakwater is depth-limited wave breaking. Available models for energy dissipation due to wave breaking are developed for beaches (gentle slopes) and require further modifications to model wave breaking over submerged breakwaters.In this paper, wave breaking is split into two parts, namely: 1) depth-limited breaking modelled using Battjes and Janssen's (1978) theory [Battjes, J.A. and Jannsen, J.P.F.M. (1978). Energy loss and setup due to breaking of random waves. Proceedings of the 16th Int. Conf. Coast. Eng., Hamburg, Germany, pp. 569-587.] and 2) steepness limited breaking modelled using an integrated form of the Hasselmann's whitecapping dissipation term, commonly used in fully spectral wind–wave models. The parameter γ₂, governing the maximum wave height at incipient breaking (H_max = γ₂d) is used as calibration factor to tune numerical model results to selected laboratory measurements. It is found that γ₂ varies mainly with the relative submergence depth (ratio of submergence depth at breakwater crest to significant wave height), and a simple relationship is proposed. It is shown that the transmission coefficients obtained using this approach compare favourably with those calculated using published empirical expressions.     

An experimental study on geometric characteristics of beach erosion profiles

The beach profile and sediment transport are very important factors in the design of coastal structures, and the beach profile is mainly affected by a number of parameters, such as wave height and period, beach slope, and the material properties of the bed. In this study, considering wave height (H₀=6.5, 11.5, 16, 20, 23, 26 and 30 cm), wave period (T=1.46 and 2.03 s), beach slope (m=1/10 and 1/15) and mean sediment diameter (d₅₀=0.18, 0.26, 0.33 and 0.40 mm), an experimental investigation of coastal erosion profile (storm profile) was carried out in a wave flume using regular waves, and geometric characteristics of erosion profile were determined by the resultant erosion profile. Dimensional and non-dimensional equations were obtained by using linear and non-linear regression methods through the experimental data and were compared with previously developed equations in the literature. The results have shown that the experimental data fitted well to the proposed equations with respect to the previously developed equations.     

Prediction model for occurrence of impact wave force

This study investigates the applicability of neural networks to predict whether impact wave force will act on the upright section of a composite breakwater. We employ a three-layered neural network whose units of input layer are h/L, H/h, d/h and B_M/h (h: the total water depth; L: the wavelength; H: the wave height; d: the water depth above the mound; B_M: the horizontal distance from the shoulder of mound to the caisson). Teach signals are 0.99 and 0.01 according to the cases of occurrence and absence of impact wave force, respectively. The neural network whose parameters are determined through self-learning can accurately predict whether impact wave force occurs.     

Improvement of sand activation depth prediction under conditions of oblique wave breaking

This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Arçay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Arçay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form $ Z_{0} = 1.6\tan {\left( \beta \right)}H^{{0.5}}_{{\text{s}}} {\sqrt {1 + \sin {\left( {2\alpha } \right)}} } This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Ar?ay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Ar?ay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form . The use of a dataset from the literature demonstrates the predictive skill of these new formulae for a wide range of wave heights, wave incidence and beach gradients.     

Numerical prediction of performance of submerged breakwaters

The results of a numerical model study on the transmission characteristics of a submerged breakwater are presented. Study aimed to determine the effect of depth of submergence, crest width, initial wave conditions and material properties on the transmission characteristics of the submerged breakwater. The results highlight the optimum crest width of the breakwater and optimum clear spacing between two breakwaters. A submerged permeable breakwater with d_s/d=0.5, p=0.3 and f=1.0, reduces the transmission coefficient by about 10% than the impermeable breakwater. The results indicates an optimum width ratio of B/d=0.75 for achieving minimum transmission. By restricting the effective width ratio of the series of breakwaters to 0.75, studies were conducted to determine the effect of clear spacing between breakwaters on transmission coefficient, suggesting an optimum clear spacing of w/b=2.00 to obtain K_t below 0.6.     

Prediction of wave pressures on smooth impermeable seawalls

Simple prediction methods are proposed to estimate the wave induced pressures on smooth impermeable seawalls. Based on the physics of the wave structure interaction, the sloped seawall is divided into a total of five zones (zones 1, 2 and 3 during run-up (corresponding pressures are called as positive pressures) and zones 4 and 5 during run-down (corresponding pressures are called negative pressures)) (Fig. 1). Zone 1 (0<z<d−H_i/2), where the wave pressure is governed by the partial reflection and phase shift; Zone 2 (d−H_i/2<z<d), where the effect of wave breaking and turbulence is significant; Zone 3 (d<z<Run-up height), where the pressure is induced by the run-up water; Zone 4 (Run-down<z<d), where the wave pressure is caused by the run-down effect and Zone 5 (0<z<d-Run down), where the negative wave pressures are due to partial reflection and phase shift effects. Here d is the water depth at the toe of the seawall, H_i is the incident wave height and z is the vertical elevation with toe of the seawall as origin and z is positive upward. For wave pressure prediction in zones 1 and 5, the empirical formula proposed by Ahrens et al. (1993) to estimate the wave reflection and Sutherland and Donoghue's recommendations (1998) for the estimation of phase shift of the waves caused by the sloped structures are used. Multiple regression analysis is carried out on the measured pressure data and empirical formulas are proposed for zones 2, 3 and 4. The recommendations of Van der Meer and Breteler (1990) and Schüttrumpf et al. (1994) for the prediction of wave run-down are used for pressure prediction at zone 4. Comparison of the proposed prediction formulas with the experimental results reveal that the prediction methods are good enough for practical purposes. The present study also shows a strong relation between wave reflection, wave run-up, wave run-down and phase shift of waves on wave pressures on the seawalls.     

Variations in grain‐size and sorting on two kaikoura beaches

Two exposed, high‐energy beaches on the Kaikoura coast of New Zealand are composed of sand and gravel derived from a greywacke terrain. Both beaches can be classified as mixed beaches although the sediment varies from dominantly gravel at the ends of the beach to dominantly sand at the centre, through transition zones in which sand and gravel are mixed. Sixty‐four surface samples were analysed for grain size; two sediment parameters, mean grain size (M_z) and sorting (σ_I), were calculated.

A striking feature of the cumulative frequency curves is that both unimodai and bimodal distributions include median sizes over the whole range of sampled material, even though bimodal samples display two strong modes in the sand and gravel grades. The general deficiency lof sediment dn the very coarse sand and granule classes (0 to — 2 _F ) noted by numerous authors in many parts of the world is apparent in the poorly‐sorted bimodal samples. However, the best‐sorted samples also occur in these two classes.

Mean grain size of samples ranges from medium sand (1.820) to medium pebbles (—4.7 _F ), and sorting ranges from very well sorted (0.250) to very poorly sorted (2.69 _F ). Mean erain size on the northern beach is significantly greater than on the southern beach, but values of sorting are comparable. The greater mean size on one beach compared with the other is thought to be a function of the grade of material supplied by local rivers; the similarity in sorting presumably reflects the similarity of the processes acting on the two beaches.

Mixed sand‐shingle beaches are relatively rare on a world scale but common in New Zealand. Sediment distributions along the Kaikoura beaches do not reveal a regular decrease in size away from the rivers which supply material to shore at present. Instead, the beaches are differentiated into a number of sediment zones composed of either sand, or mixed sand‐gravel, or gravel. On each beach a gravel zone is located furthest from the river outlets. Sorting generally improves toward the Kaikoura Peninsula. Explanations for these trends are not given. Variations in size and sorting across the two beaches do not show a well developed zonation because of the high level of wave energy which continually mixes the material across the beach.     

Wave interaction with ‘’-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of ‘’-type breakwaters were studied using physical models. Regular and random waves in a wide range of wave heights and periods and a constant water depth were used. Five different depths of immersion (two emerged, one surface flushing and two submerged conditions) of this breakwater were selected. The coefficient of transmission, K_t, and coefficient of reflection, K_r, were obtained from the measurements, and the coefficient of energy loss, K_l was calculated using the law of balance of energy. It was found that the wave transmission is significantly reduced with increased relative water depth, d/L, whether the vertical barrier of the breakwater is surface piercing or submerged, where ‘d’ is the water depth and ‘L’ is the wave length. The wave reflection decreases and energy loss increases with increased wave steepness, especially when the top tip of the vertical barrier of this breakwater is kept at still water level (SWL). For any incident wave climate (moderate or storm waves), the wave transmission consistently decreases and the reflection increases with increased relative depth of immersion, Δ/d from −0.142 to 0.142. K_t values less than 0.3 can be easily obtained for the case of Δ/d=+0.071 and 0.142, where Δ is the height of exposure (+ve) or depth of immersion (−ve) of the top tip of the vertical barrier. This breakwater is capable of dissipating wave energy to an extent of 50–80%. The overall performance of this breakwater was found to be better in the random wave fields than in the regular waves. A comparison of the hydrodynamic performance of ‘’-type and ‘T’-type shows that ‘T’-type breakwater is better than ‘’-type by about 20–30% under identical conditions.     

Reflection of a long wave from an underwater slope

Reflection of long sea waves from an underwater slope described by a power law is studied within the shallow water theory. The slope is connected with the flat bottom. This model allows us to estimate the roles of a pointwise reflection from the inflection point of the bottom profile and distributed reflection at the underwater slope. The case of the underwater slope described by the so-called nonreflecting beach (h(x) ∼ x ^4/3, where h is the depth of the basin and x is the coordinate) when the wave is reflected only from the inflection point (pointwise reflection) is specially considered. The reflection and transmission coefficients over the bottom topography were calculated, and it was shown that the sum of the squared absolute values of these values differs from unity for all profiles except the nonreflecting one. This difference is related to the distributed re-reflections (resonances) over the underwater slope that lead to the deviations in the wave height from the known Green’s law.     

孤立波与升沉水平板相互作用数值模拟研究

合理的刚度和潜深设计可以使升沉水平板获得优异的消浪性能。基于考虑流体黏性的二维不可压缩Navier-Stokes方程,以高阶紧致插值CIP(constrained interpolation profile)方法求解方程对流项,采用VOF(volume of fluid)方法重构自由液面,构建二维数值波浪水槽。采用试验数据验证模型后,研究孤立波与升沉水平板相互作用,分析相对刚度K*、相对潜深d/h、相对波高H/h对于升沉板的消浪性能和运动响应的影响,揭示升沉板对孤立波的消浪机理。研究表明:在孤立波通过时,升沉板会经历一个先上升后下降的运动,随后非线性自由振动,板下方水体近似均匀流动,且水流的垂向流动与板的垂荡方向一致;升沉板主要通过不对称涡旋脱落、浅水变形、波浪反射与辐射波转化等方式消耗孤立波能量;一定条件下,采用最优相对刚度K*=4.0和最优相对潜深d/h=0.52可以取得良好的消浪效果,此时透射系数最小,同时升沉板的运动响应在合理的范围内。     

Longshore sediment transport on non-planar beaches

For a concave-up $\text{2}\text{3}$ power Bruun beach profile, the following two energetics-based sediment transport models are developed: (1) a Bagnold-type model and (2) a combined wave-current stress model. The stress model is calibrated with the Bagnold model using observed transport rates on planar beaches. The sediment transport profiles for the two models are in agreement within the surf zone for the planar beach case; but the stress model is also applied seaward of the breaker line where the Bagnold model is not. A mean swash transport of sand is predicted by the Bagnold model for a $\text{1}\text{2}$ power least-squares approximation to total depth including setup/setdown on a Bruun beach profile. The total longshore transport of sand is determined for each transport model as a function of the turbulent lateral mixing strength. The total sand transport is found to be less on a concave-up beach profile than for the corresponding planar beach case.     

Physical modeling of the cross-shore short-term evolution of protected and unprotected beach nourishments

This paper illustrates the results of an experimental investigation (model-to-prototype length ratio equal to 12) carried out to reproduce the cross-shore evolution of nourished sandy beaches. New two-dimensional experiments were performed to study the short-term response of the cross-shore profile for both “soft” (unprotected) and “mixed” (protected by submerged breakwaters) beach fill projects. Due to the simplified reproduction of prototype conditions in a two-dimensional geometry, only cross-shore sediment transport is considered. The results are related to the immediate post-nourishment evolution and far from beach fill boundaries where long-shore gradients of long-shore sediment transport are likely to be negligible. Three different pseudo-random wave trains were generated in order to simulate both accretive and erosive conditions. A fourth wave train, characterised by time-varying incident wave spectrum was generated for the investigation of the beach response to simplified storm time evolution. Dimensionless experimental results are given in terms of wave parameters, key features of cross-shore profile evolution and sediment transport rates. Furthermore, being highly resolved in both time and space, experimental data are suitable for mathematical model validation. It was observed that submerged breakwater switches erosive conditions to slightly accretive, at least within the tested experimental range.     

岬湾海滩沉积动力地貌研究

岬湾海滩是砂质海岸稳定性及其演变的重要内容.介绍了岬间海湾平面形态平衡模型、海滩平衡剖面模式、海滩剖面主要类型的判别以及海岸泥沙运动,其中着重评述了现今岬间海湾平面形态平衡模型和海滩平衡剖面模式.通过它们的优缺点分析,认为人工神经网络模型是未来新型平面形态模型改进的方向;海滩平衡剖面模式分段使用,亦或2种或多种模式配合...     

Geological control of beach morphodynamic state

The concept of beach morphodynamic states has achieved widespread acceptance in the coastal geological literature since its inception in the mid-1980s and expansion in the 1990s. Much of the pioneering work was undertaken in Australia under a range of environmental conditions in microtidal environments and a close empirical relationship between beach 3-dimensional morphology and the Dean's parameter (H_b/W_sT) was established. Subsequently, the Relative Tidal Range parameter (H_b/TR) was extended to beaches of all tidal ranges.In this paper, observations are presented from 25 beaches around the north coast of Ireland. These beaches exist on an environmental gradient that encompasses marked tidal and wave energy variability (micro to macrotidal and low to high wave energy). Each beach was visually categorised into one of several established beach states described in the literature, on the basis of field observations. For each beach, the RTR and Dean's parameter were calculated for the immediately antecedent period and used to predict the beach state using published relationships. Observed and predicted beach states were then compared.Comparison of observed and predicted beach states showed that while beaches with observed dissipative morphology typically matched the expected criteria, most other beach states did not. Lack of agreement between predicted and observed beach states has been reported elsewhere and attributed to failings in the RTR and Dean's parameter. In addition, this study identifies geological factors as important constraints on actual beach state. In the majority of beaches studied, inherited geological factors appear to be more important determinants of beach morphology than contemporary dynamics.     

The effect of relative crest submergence on wave breaking over submerged slopes

Experiments were performed in a wave flume to measure the intensity, transmission and reflection of waves breaking over a submerged reef with an offshore gradient of 1:10. The results demonstrate that the relative water depth over the reef crest (h_c/H_o) is a dominant factor affecting the breaking characteristics. In particular it is found that as the relative crest submergence is reduced, there is a considerable increase in the intensity of wave breaking over the reef that can be quantified through measurements of the air cavity enclosed beneath the plunging jet. It is also shown that there is a corresponding decrease in wave transmission and reflection as the submergence is reduced.     

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.     

海南万宁岬湾海岸海滩稳定性研究

岬湾海岸海滩的稳定性及其演变是砂质海岸研究的重要内容。基于多期遥感影像、海滩沉积物粒度分布,并采用岬湾海滩平衡形态模型(MEPBAY),分析探讨了海南岛东部万宁4个典型岬湾海岸海滩的稳定性及其模型的应用。研究表明,除东澳湾凸角处于不稳定状态,其余海岸处于静态或准静态平衡状态;岬湾海滩沉积物粒度在遮蔽段和开敞段有明显的差异,相邻海滩之间没有明显的泥沙交换,每个岬湾海滩都是相对独立的地貌单元;模型中上岬角控制点选取应考虑岛礁及水下礁坪;抛物线模型可以拓展应用于有离岸岛情况下的海湾。研究成果可为岬湾海滩的稳定性评估和管理提供科学依据。     

The influence of coastal dynamics on the upper limit of the Posidonia oceanica meadow

The recognized ecological importance of Posidonia oceanica, the most important seagrass of the Mediterranean Sea, makes it crucial to assess the state of health of its meadows, discriminating natural from anthropogenic impacts. In this paper, the hydrodynamic conditions at the upper limit of P. oceanica meadows along the Ligurian coast (NW Mediterranean Sea) were investigated. A relationship between the distance of the upper limit of the meadow from the shoreline and the morphodynamic domain of the beach (i.e. distinctive types of beach produced by the topography, wave climate and sediment composition) was found. A zonation of the state of the shallow portions of the meadows down the submerged beach profile was identified. Zone a, from the shoreline to the breaking limit, is naturally critical for the development of the meadow. Zone b, from the breaking limit to the closure depth, is subjected to natural and human impacts. Zone c, below the closure depth, is little influenced by coastal dynamics. This study quantifies for the first time how much the status of the shallow portions of P. oceanica meadows is dependent on coastal dynamics, which is important for their proper management.     

基于类海啸波型的岛礁水动力特性数值模拟研究

基于非静压单相流模型NHWAVE建立了高精度二维数值波浪水槽,采用日本2011年实测真实海啸波型系统研究了海啸波在岛礁上传播变形的规律,并且分析了波高、礁坪淹没水深和礁前斜坡坡度等因素对孤立波和真实海啸传播变形的影响。结果表明,相比孤立波,类海啸波的波长明显大于孤立波波长,在测点处引起的水面变化持续时间更长,同等波高情况下真实海啸波型比孤立波能够携带更多的能量,与岛礁的相互作用也更为复杂,在礁坪上形成的淹没水深约为孤立波的两倍。礁前斜坡坡度和礁坪淹没水深均对类海啸波的反射和透射系数有显著影响。随着礁前斜坡坡度的增加,反射系数和透射系数均逐渐增加。随着礁坪淹没水深的增加,反射系数逐渐减小,而透射系数逐渐增大。但是,反射系数和透射系数均随着入射波高的增加而逐渐减小。