A numerical shoreline model for shorelines with large curvature

This paper presents a new numerical model for shoreline change which can be used to model the evolution of shorelines with large curvature. The model is based on a one-line formulation in terms of coordinates which follow the shape of the shoreline, instead of the more common approach where the two orthogonal horizontal directions are used. The volume error in the sediment continuity equation which is thereby introduced is removed through an iterative procedure. The model treats the shoreline changes by computing the sediment transport in a 2D coastal area model, and then integrating the sediment transport field across the coastal profile to obtain the longshore sediment transport variation along the shoreline. The model is used to compute the evolution of a shoreline with a 90° change in shoreline orientation; due to this drastic change in orientation a migrating shoreline spit develops in the model. The dimensions of the spits evolving in the model compare favorably to previous model results and to field observation of the Skaw Spit in the north of Denmark.     

Alongshore Sediment Transport Near Tidal Inlets of Chilika Lagoon; East Coast of India

ABSTRACT

Chilika, a lagoon along the east coast of India, is undergoing transformation due to frequent shoreline change near inlet(s). Shoreline change near inlet includes change in position and shape of inlet, inlet channel length, and spit growth/erosion. These variable features of lagoon inlet(s) critically depend on alongshore sediment transport (LST) and discharge (water and sediment) from the lagoon to the sea. The LST and the processes responsible for sand spit growth/erosion, considered as important attributes of inlet stability, are the subject matter of the present investigation and hence the study assumes importance. The study includes integration of observational and modeling framework. Observations include nearshore wave, bathymetry, beach profile, shoreline and sediment grain size of spits while numerical modeling includes simulation of the wave using MIKE 21 Spectral Wave model and LST simulation using LITtoral DRIFT. The results indicate that the predominant wave directions as S and SSE, which induces round the year south to north alongshore transport with significant seasonal variation in magnitude. The estimated LST closely matches with previous studies near Chilika inlet and for other locations along the Odisha coast. Besides temporal variability, the study reveals spatial variability in alongshore transport near Chilika inlet and considers it as one of the important attributes along with northward spit growth for inlet migration/closure/opening.     

Numerical modeling of crenulate bay shapes

A numerical model is developed to compute the shoreline planform in a crenulate bay beach. The new model combines polar and Cartesian coordinates and can be used effectively to compute a hooked zone shoreline in the lee of upcoast headland. The model is calibrated using laboratory data with an incident wave angle ranging from 25° to 60°. The results of calibration and verification suggest that the ratio of the sediment transport parameters by wave and longshore current in this model is close to unity, and the computed shoreline planforms for the hooked and unhooked zones are in good agreement with the ones measured, especially when a bay is close to static equilibrium. In addition, the bay shape calculated by the present model is similar to that given by the well-known empirical parabolic equation for a bay in static equilibrium. The process of bay shape development from a straight beach to a static equilibrium bay is studied using laboratory experiments and the present numerical model. The temporal variations in the computed longshore sediment transport at different locations within a bay beach are analyzed. From this the decrease in the sediment transport becomes apparent while a bay beach changes its shape from straight toward a state of equilibrium. Based on this experience, it may be concluded that the present numerical model can produce a temporal change in the shoreline planform of a crenulate bay beach from a transition state to static equilibrium subject to seasonal wave action.     

Spit and Inlet Morphodynamics of a Tropical Coastal Lagoon

The morphological changes of spits and inlets of the Chilika lagoon, the largest brackish water tropical coastal lagoon in Asia, are investigated using real-time kinematic GPS observation and numerical models during 2009–2013. The seasonal/interannual variations of the spit and inlet cross-sectional areas with varying widths and depths are recorded in association with different physical processes. The results show significant changes in spit morphology: particularly, the south spit accreted continuously, while the middle and north spits eroded. The cross-sectional depth of inlets becomes narrower and deeper during summer and winter seasons, while they are wider and shallower during the monsoon. The model results show that sediment transport rate is larger during monsoon and summer, while it is relatively less during the winter. Alongshore, sediment transport is predominantly northward throughout the study period. The result shows that gain/loss of the spits and closure/opening of inlets are significantly controlled by the high wave power, longshore drifts, and river discharge. The study demonstrates that the combined use of observational and numerical models is very effective to understand the changes of spit and inlet morphology and their impact on ecological conditions of the lagoon environment.     

Numerical Simulation of Sand Shoreline Evolution Under Action of Regular Waves and Irregular Waves

Based on the singleline theory, a numerical simulation is presented to predict the shoreline evolution on sand beach. A parabolic equation of longshore sediment transport and boundary conditions are proposed. The combined effect of wave diffraction and refraction on the shoreline evolution on the downdrift side of the breakwater is taken into account and is calculated using the theory of regular waves and irregular waves. The present model is verified by the field observation data of erosion for half a year on the downdrift side of a harbor, and compared with some experimental results. The numerical results are in good agreement with the field measured and experimental data.     

Determination and control of longshore sediment transport: A case study

The fishery harbor of Karaburun coastal village is located at the south west coast of the Black Sea. The significant waves coming from north eastern direction cause considerable rate of sediment transport along 4 km sandy beach towards the fishery harbor in the region. The resulting sediment deposition near and inside the harbor entrance prevents the boat traffic and cause a vital problem for the harbor operations. In order to determine the level and reasons of the sediment transport, the long-term observations of shoreline changes, the long-term statistical analysis of wind and wave characteristics in the region, and sediment properties have been performed. The data obtained from observations, measurements and analysis were discussed. The long-term statistics of deep water significant wave heights for each direction was discussed by comparing the results obtained from different data sources and methods. For shoreline evolution, the numerical study using one-line model was applied to describe the shoreline changes with respect to probable wave conditions. Initial shoreline was obtained from the digitized image in 1996 since there was no previous shoreline measurement of the site. The results were compared using the techniques of remote sensing obtained from sequent images using IKONOS and IRS1C/D satellites.     

Sediment distribution and transport along a rocky, embayed coast: Monterey Peninsula and Carmel Bay, California

Field measurements of beach morphology and sedimentology were made along the Monterey Peninsula and Carmel Bay, California, in the spring and summer of 1997. These data were combined with low-altitude aerial imagery, high-resolution bathymetry, and local geology to understand how coastal geomorphology, lithology, and tectonics influence the distribution and transport of littoral sediment in the nearshore and inner shelf along a rocky shoreline over the course of decades. Three primary modes of sediment distribution in the nearshore and on the inner shelf off the Monterey Peninsula and in Carmel Bay were observed. Along stretches of the study area that were exposed to the dominant wave direction, sediment has accumulated in shore-normal bathymetric lows interpreted to be paleo-stream channels. Where the coastline is oriented parallel to the dominant wave direction and streams channels trend perpendicular to the coast, sediment-filled paleo-stream channels occur in the nearshore as well, but here they are connected to one another by shore-parallel ribbons of sediment at depths between 2 and 6 m. Where the coastline is oriented parallel to the dominant wave direction and onshore stream channels are not present, only shore-parallel patches of sediment at depths greater than 15 m are present. We interpret the distribution and interaction or transport of littoral sediment between pocket beaches along this coastline to be primarily controlled by the northwest-trending structure of the region and the dominant oceanographic regime. Because of the structural barriers to littoral transport, peaks in wave energy appear to be the dominant factor controlling the timing and magnitude of sediment transport between pocket beaches, more so than along long linear coasts. Accordingly, the magnitude and timing of sediment transport is dictated by the episodic nature of storm activity.     

Numerical simulation of non-linear regular and focused waves in an infinite water-depth

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.     

Short-term shoreline changes due to cross-shore structures: a one-line numerical model

The proposed numerical model simulates the short-term temporal changes in shoreline position due to a structure interrupting the longshore sediment flux. The impacts of both the groin-type construction and underwater trench of arbitrary orientation relative to the shore are discussed. In order to estimate the sediment mass trapped by the structure, a submodel of the longshore sediment transport induced by a random wave field is developed. The contribution of the surface roller in momentum balance as well as in sediment suspension is included. The shoreline changes are computed from the equation deduced from the mass conservation. The perturbations in the longshore sediment discharge caused by a structure are assumed to concentrate within some boundary area of which the spatial scale is proportional to the structure's length until the latter is exceeded by the width of the sediment flux. It is shown in particular that the total effect of a long trench (channel) and a pier in its nearshore part results in general shoreline recession except for the vicinity of a pier. The model is tested against the laboratory data of Baidei et al. (1994) and applied to the Baidara Bay coast (Kara Sea) where a pipeline would be designed.     

Numerical Modeling of the Undertow Structure and Sandbar Migration in the Surfzone

A process-based 3D numerical model for surfzone hydrodynamics and beach evolution was established. Comparisons between the experimental data and model results proved that the model could effectively describe the hydrodynamics, sediment transport feature and sandbar migration process in the surfzone with satisfactory precision. A series of numerical simulations on the wave breaking and shoaling up to a barred beach were carried out based on the model system. Analyzed from the model results, the wave-induced current system in the surfzone consists of two major processes, which are the phase-averaged undertow caused by wave breaking and the net drift caused by both of the nonlinear wave motion and surface roller effect. When storm waves come to the barred beach, the strong offshore undertow along the beach suppresses the onshore net drift, making the initial sandbar migrate to the seaside. Under the condition of calm wave environment, both the undertow and net drift flow to the shoreline at the offshore side of the sandbar, and then push the initial sandbar to the shoreline. The consideration of surface roller has significant impact on the modeling results of the sandbar migration. As the roller transfer rate increases, the sandbar moves onshore especially under the storm wave condition.     

Numerical experiments of swash oscillations on steep and gentle beaches

A weakly non-linear Boussinesq model with a slot-type shoreline boundary is used to simulate swash oscillations on beaches. Numerical simulations of swash were compared with laboratory measurements and in general good agreement found (less than 15% root-mean-square error of surface elevation except in regular waves). A series of numerical experiments on shoreline movement were then performed for a range of beach slopes and incident wave conditions. The resulting swash characteristics are then discussed in terms of their physical nature and spectral properties. On steep slopes, both individual bores and infragravity waves are equally significant in driving the swash while infragravity waves alone drive them on mild slopes. Swash excursions on any given slope are found to be highest when individual bores from a partially saturated surf zone ride on top of low-frequency waves. This is confirmed by the relationship found between swash excursion and wave groupiness in the surf zone. Swash excursions increase with increasing incident wave energy, even in fully saturated surf zones. However, a poor correlation is found between swash excursion and the surf similarity parameter due to the involvement of infragravity wave energy in the swash.     

琼州海峡南岸海岸动力地貌研究

岬湾相间的琼州海峡南岸在海岸动力条件作用下,岸滩发生侵蚀或堆积,特别是南岸中部的南渡江三角洲沿岸岸滩演变剧烈。该文从海岸动力地貌的角度,对琼州海峡南岸的海岸动力特征、泥沙运动以及岸滩演变进行分析。根据海峡南部三维潮流场数值模拟结果,结合经验公式初步分析潮流引起的泥沙运移速率和方向,得到岸外水域总的泥沙运移趋势为从西向东。根据波浪动力计算分析沿岸泥沙运移,探讨沙质岸滩的动态与地貌演变之间的关系,得出海峡南岸海岸地貌演变与盛行的NE和NNE向风浪有密切关系,岸滩的演变过程主要受制于这两个方向的风浪及其引起的泥沙沿岸运移。     

The coast between Cabo de Santa Maria (Portugal) and Rabat (Morocco): a mega-size headland-bay shoreline under control of the North Atlantic swell?

Equilibrium headland-bay beach systems have been mathematically described by logarithmic, parabolic and hyperbolic curve functions. The largest system of this type reported to date has a shoreline length of about 62 km. In the present study, an apparent headland-bay system is presented which has a shoreline length of about 500 km. It was discovered on satellite images, and is located between Cabo de Santa Maria in Portugal and the coastal city of Rabat in Morocco. It appears to be controlled by long-period North Atlantic swells diffracting around Cabo São Vicente at the south-western tip of Portugal, in combination with SW–SE wind wave climates impinging on the northern shoreline of Cádiz Bay. The coast shows two marked departures from the equilibrium shoreline along its central section north and south of the Strait of Gibraltar, which are easily explained. Thus, the promontories to the north of the strait still exist because there has not been sufficient time to erode these back to the equilibrium shoreline since postglacial sea-level recovery. The coastal indentation to the south is explained by an insufficient sediment supply from terrestrial sources to facilitate the required beach accretion. Perfectly adjusted planimetric headland-bay shoreline shapes represent situations where wave orthogonals approach the coast at right angles everywhere, i.e. there is no longer any alongshore sediment transport. Equilibrium shorelines form independently of the grain size of the beach sediment, whereas morphodynamic beach states are indirectly affected by the shoreline shapes because the latter are modulated by wave period and breaker height which also control the morphodynamic response of the beach in combination with the local grain size.     

南渡江三角洲海岸泥沙纵向运移与岸滩演变的响应

南渡三角洲沿岸在盛行ＮＮＥ向波浪等动力条件的作用下,泥沙产生纵向运移,岸滩遭受侵蚀或堆积,岸滩演变剧烈。本文利用基于网格的波注折射绕射模型,分析南渡江三角洲海岸波浪动力过程、破波带波能与辐射应力分布及其引起的沿岸泥沙纵向运称。浴海岸动力学地貌的角度,通过三角洲沿岸波浪动力特征、泥沙运动的分析,探讨沙质岸滩的动态与地貌演变。     

Prediction of shoreline behaviour for Madras, India-a numerical approach

A satellite port has been proposed about 14.8 km north of Madras port on the east coast of India. As the interference of a satellite port with the existing pattern of longshore sediment transport will generate coastal imbalance in the region, a numerical model study involving sediment transport and combined wave refraction-diffraction was conducted to predict the shoreline behaviour. A realistic approach to the study was made to meet the objectives by considering wave height-wave period distributions in the region and duration and sequence of their occurrence during major monsoon seasons. This method of analysis enabled us to predict: (i) the extent of general shoreline advancement, particularly in front of a tidal inlet—a source of the cooling water requirement for an existing thermal power plant; (ii) the extent of the coastal region that will be affected owing to recession of shoreline and its impact on: (a) the fishing community living along the coastal stretch; (b) the national highway running along the coast; and (c) the changes in nearshore bathymetry. Based on the studies, management plans were drawn to safeguard the coastal region from imbalances that will arise out of construction of the satellite port. This paper highlights the effects of a satellite port on the coastal region and the need for proper management.     

A morphological stability analysis for a long straight barred coast

A morphological stability analysis is carried out for a long straight coast with a longshore bar. The situation with oblique wave incidence and a wave-driven longshore current is considered. The flow and sediment transport are described by a numerical modelling system. The models comprise: (i) a wave model with depth refraction, shoaling and wave breaking, (ii) a depth integrated model for wave driven currents and (iii) a sediment transport model for the bed load transport and the suspended load transport in combined waves and current. The direction of the sediment transport is taken to be parallel to the depth integrated mean current velocity, neglecting the effects of a bed slope and secondary currents. An instability is found to develop around the bar crest. The instability is periodic in the alongshore direction, and tends to form rip channels and to steepen the offshore face of the bar between the rip channels. The alongshore wave length of the most unstable perturbation is determined for different combinations of the wave conditions and the geometry of the profile.     

Scour around coastal structures: a summary of recent research

This paper summarizes the results of the European Union Marine Science and Technology (EU MAST) III project “Scour Around Coastal Structures” (SCARCOST). The summary is presented under three headings: (1) Introduction; (2) Flow and scour processes with the subheadings: flow and scour processes around vertical cylinders; flow and scour processes at detached breakwaters; flow and scour processes at submerged breakwaters; and the effect of turbulence on sediment transport; and (3) Sediment behaviour close to the structure with the subheadings: field measurement and analysis of wave-induced pore pressures and effective stresses around a bottom seated cylinder; non-linear soil modelling with respect to wave-induced pore pressures and gradients; wave-induced pressures on the bottom for non-linear coastal waves, including also wave kinematics; development of a numerical model (linear soil modelling) to calculate wave-induced pore pressures—the effect of liquefaction on sediment transport; penetration of blocks in non-consolidated fine soil; and cyclic stiffness of loose sand.The paper also includes a discussion of the role of scale effects in laboratory testing and the applicability of the results obtained in supporting engineering design.     

高阶非线性完全频散性波浪数值模型及应用

为更精确地模拟强非线性完全频散性波浪的传播,采用长波上非线性重力表面波传播高阶数学模型,综合参考此模式已有的研究成果,建立了一个高达五阶的完全频散性非线性数值模型。应用该五阶模式对斜坡地形、潜堤地形及正弦沙链地形进行模拟计算,并与已有的实验资料进行对比,结果显示五阶模式较低阶模式模拟结果的精度上有了明显提高,模拟波形与实验结果吻合度良好,证明高阶模式更适用于高频散高非线性波浪传播的数值模拟。     

Longshore sediment transport estimation using a fuzzy inference system

Accurate prediction of longshore sediment transport in the nearshore zone is essential for control of shoreline erosion and beach evolution. In this paper, a hybrid Adaptive-Network-Based Fuzzy Inference System (ANFIS), Fuzzy Inference System (FIS), CERC, Walton–Bruno (WB) and Van Rijn (VR) formulae are used to predict and model longshore sediment transport in the surf zone. The architecture of ANFIS consisted of three inputs (breaking wave height), (breaking angle), (wave period) and one output (longshore sediment transport rate). For statistical comparison of predicted and measured sediment transport, bias, root mean square error and scatter index are used. The longshore sediment transport rate (LSTR) and wave characteristics at a 4 km-long beach on the central west coast of India are used as case studies. The CERC, WB and VR methods are also applied to the same data. Results indicate that the errors of the ANFIS model in predicting wave parameters are less than those of the empirical formulas. The scatter index of the CERC, WB and VR methods in predicting LSTR is 51.9%, 27.9% and 22.5%, respectively, while the scatter index of the ANFIS model in the prediction of LSTR is 17.32%. A comparison of results reveals that the ANFIS model provides higher accuracy and reliability for LSTR estimation than the other techniques.