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.     

Longshore current and sediment transport on composite beach profiles

Natural beaches tend to exhibit an equilibrium profile that is planar nearshore and nonplanar, concave-up offshore. The longshore current on this type of beach profile depends on the horizontal distance to the location of the intersection between the planar and nonplanar profiles. As the width of the planar beach face decreases, the location of the maximum longshore current moves closer to the shore. The dependency of the corresponding longshore sediment transport rate on the location of the intersection between the two profiles is demonstrated for two energetics-based sediment transport models. Again, a narrower beach face results in the maximum sediment transport being closer to the shore. Total sediment transport rates are also a function of the planar beach face width. This suggests that longshore transport rates are modulated by the tidal elevation.     

Longshore Current on an Equilibrium Beach

Natural beaches tend to be concave-up rather than planar and are reasonable to be modeled by an equilibrium beach profile. A governing equation for longshore current on an equilibrium beach is derived and its analytical solution is given in this paper. Through comparisons of the present solution and field data of longshore current for a step-type beach, the present solution is found to have fairly agreeable prediction to longshore current inside the surf zone. The effects of the shape of a concave-up beach and turbulent mixing stress on longshore current inside the surf zone are discussed in the present paper.     

Wave setup and setdown generated by obliquely incident waves

An analytical theory is developed for the wave setup and setdown induced by obliquely incident waves on an impermeable swell-built beach profile. The wave setup and setdown are found to decrease as wave obliquity increases. The incorporation of wave obliquity in wave setup and setdown formulation offers the physical reality in engineering applications. The general solutions presented in this paper yield the limiting case of normal wave incidence and the result is consistent with the classical theories published. The present theory is primarily applicable to the spilling and plunging breaker across the surf zone, within which wave amplitude is assumed to be linearly related to the local water depth. Experiments were conducted in a large-scale wave basin to compare with theoretical results and especially to investigate the applicability of this assumption to the case of obliquely incident waves. The dimensionless setup versus the distance offshore within the surf zone is found to depend on wave breaking angle and the shape of the beach profile; and it has a non-zero value at the original shoreline position. This implies that the original shoreline will advance landwards, and that the extent of this movement can be related to wave angle at breaking and the beach profile under consideration. The results of the present theory are in good agreement with experimental data and field measurements available.     

Influence of lateral mixing on longshore currents

A variety of different lateral mixing models have been employed in the equation of motion for determining wave-induced longshore currents. The equation of motion is cast into a general form which enables a comparison of the various models. Analytic solutions for longshore currents are developed for seven different mixing models. A nonplanar beach profile is employed because it has been found to be representative of many beaches and it allows for a distinction between offshore and depth scaling of eddies. The seven different mixing models include models which vary monotonically with horizontal distance offshore and models which change form at the breaker line. Numerical results indicate that the longshore current profile is rather insensitive to the form of the mixing model for nonplanar beach profiles.     

Discussion of “Wave setup and setdown generated by obliquely incident waves” by T.-W. Hsu et al., Coastal Engineering, 53, 865–877, 2006

In the recent paper by Tai-Wen Hsu, John R.-C. Hsu, Wen-Kai Weng, Swun-Kwang Wang, and Shan-Hwei Ou (Coastal Engineering, 53, 865–877, 2006), the authors derived theoretical formulations for calculating the wave setup and setdown induced by obliquely incident waves on a beach. The derivation of an expression for setdown contains errors which would lead to an imbalance in longshore momentum flux outside the surfzone. We correct their derivation and give results in terms of the radiation stress concept in a general case including an oblique wave incidence. We also point out that the correct form of wave setdown is important to describe the zero-net force in the momentum balance outside the surfzone.     

The coastal undercurrent— A role of longshore scales in coastal upwelling dynamics

A simple three-dimensional model of a time-dependent coastal upwelling is discussed for time scales of several days to a week, with the linear, two-layer, flat-bottom and $\text{?-}\text{plane}$ approximation. Emphasis is placed on the effects of longshore scales determined by the longshore variabilities in the wind stress distributions. The responses of the inshore motions are shown to depend critically on the longshore scales. For a certain wide range of the scales, the system reveals dominantly baroclinic responses and a full development of the poleward coastal undercurrent without β effect. Somewhat detailed discussions are given on the coastal upwelling, the coastal jet and the poleward undercurrent, which are interpreted simply as the orbital velocities of the forced Kelvin-type waves.     

厦门岛海滩剖面对9914号台风大浪波动力的快速响应

根据 9914号台风发生前后对厦门岛滨岸海滩剖面地形的重复测量结果及有关台风要素和潮位的实测资料 ,探讨了台风袭击厦门岛期间海滩的变形特征和侵蚀状态。分析得出 ,海滩地形受台风暴浪冲击普遍发生急剧变化。横向冲淤变形以东岸海滩为最剧烈 :滩肩蚀退可达 2 5m ;滩面呈上冲下淤 ,上段和滩肩的单宽冲蚀量达 30m3 /m ;下段单宽淤积量达 17m3 /m ;剖面类型由滩肩式断面向沙坝式断面转变。这种变形特点是在台风大浪波动力和潮位暴涨的双重作用下造成的。台风期间 ,沿岸输沙能力以北岸最高 ,南岸次之 ,东岸较低 ;且自南岸到东岸 ,随着沿岸输沙量减少 ,横向变形相应有增大的趋势。这是9914号台风以偏东方向袭击厦门的结果。表明不同方向海岸岸滩地形对同一台风大浪波动力作用具有不同响应特征。     

Horizontal and vertical cylinders in waves

The present investigation examines a vertical cylinder and a horizontal cylinder in progressive waves. The physical differences between the flows are explored and experimental results are compared to previous planar harmonic flow measurements. It is found that modifications to the usual Morison approach are required in some cases to adequately account for the orbital motions of the fluid and to account for the orientation of the orbits with respect to the cylinder axis. The axial variations of the wave force on vertical cylinders are considered in order to evaluate the common practice of assuming constant values of $\text{C}{}_{\mathrm{m}}\text{and}\text{C}{}_{\mathrm{D}}$ over the entire span. Lastly, the methods of computing force transfer coefficients from a force record are examined and several sources of error are identified and briefly discussed.     

A compact representation of ocean wave directionality

The spectrum of the longshore component of shoreward directed momentum flux ($\text{S}{}_{\mathrm{xy}}$) due to ocean waves, taken with the energy spectrum for the same wave field, is shown to provide a compact and useful representation of ocean wave directionality. Records of orthogonal surface slope components are demonstrated to yield an unbiased estimate of $\text{S}{}_{\mathrm{xy}}$. One method for estimation of $\text{S}{}_{\mathrm{xy}}$ using this relationship is investigated. Error analysis provides means for optimal selection of measurement parameters. Experimental verification is provided from laboratory tests and from field comparison with a five-element linear array.     

Laboratory measurements of uniform longshore currents

Experiments on uniform longshore currents in a wave basin are described. The measurements were performed in a basin with a pumped recirculation through openings in the wave guides. Minimal return flows in the offshore region of the basin are found to be accompanied with longshore currents which are virtually uniform alongshore. Three-dimensional longshore current velocity distributions were measured with much attention to quality control. Detailed experimental results are presented for different wave fields, two beach slopes and two beach roughnesses.     

Numerical simulation of time-dependent beach and dune erosion

A computational procedure is developed for predicting the time-dependent, two-dimensional beach and dune erosion during severe storms due to elevated water levels and waves. The model employs the equation of sediment continuity and a dynamic equation governing the cross-shore sediment transport due to a disequilibrium of wave energy dissipation levels. These equations are solved numerically by an implicit, double-sweep procedure to determine the change in position of elevation contours in the profile. Given sufficient time, the profile will evolve to a form where the depth, h, in the surf zone is related to the distance seaward of the waterline by the relationship: $\text{h = Ax}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$, which is consistent with many natural profiles and in which A depends on sediment characteristics.The model is verified qualitatively and quantitatively through application to several idealized cases and through a preliminary simulation of erosion during Hurricane Eloise. In general, the time scales for shoreline response were found to be quite long relative to natural storm systems and erosion in the early response stages was found to be sensitive to storm surge height, but much less sensitive to wave height. The model response characteristics for simulation of erosion due to time-varying storm conditions show a lag between the maximum storm surge elevation and maximum erosion with the maximum erosion rate occurring at the time of the peak surge. For the simulated erosion due to Hurricane Eloise, reasonable agreement was found between the post-hurricane dune profiles and those calculated. However, the eroded volumes were in better agreement than the profile forms as the steepening of the natural dune profiles was not reproduced in the model.     

Boussinesq modelling of transient rip currents

The flow on a plane beach with a random, directionally spread wave field was simulated with a Boussinesq model. The random wave spectra were directionally symmetric with their central direction perpendicular to the beach, so no constant longshore current was generated. Variable wave-averaged currents were generated because of the spatially variable wave field, and sometimes formed offshore directed rip currents that appear in variable longshore locations. The rip currents are associated with a vortex pair which is generated within the surfzone and subsequently propagates offshore. Analysis of the vorticity balance show that the main vorticity input occurs within the inner surfzone. Three different beach slopes and four different wave spectra are simulated. The frequency, duration, and intensity of the transient rips depend on both the beach slope and the incident wave spectra. The results have important engineering implications for the transport of material in the nearshore zone, in particular on longshore uniform beaches.     

Physical impact on the reclamation area resulting from offshore dredging at the Changhwa coast, Taiwan

The physical impact of offshore dredging on the reclamation area at the Changhwa coast, Taiwan, is investigated using a three-dimensional movable-bed model test. A distorted modeling law consisting of maintaining similarity of the equilibrium beach profile between the model and prototype is proposed. The geometric distortion was verified through a series of preliminary experiments conducted in a wave flume. Experimental results show that the distorted modeling is able to reproduce the beach-face slope in nature. An appropriate long-term morphological time-scale was determined based on a comparison of model longshore littoral transport rates and equivalent prototype values. Seabed topographical changes before and after offshore dredging are evaluated in model tests. A suitable countermeasure to prevent beach erosion from wave attack along the reclamation area is suggested from the experimental results.     

Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications

Regional Ocean Modeling System (ROMS v 3.0), a three-dimensional numerical ocean model, was previously enhanced for shallow water applications by including wave-induced radiation stress forcing provided through coupling to wave propagation models (SWAN, REF/DIF). This enhancement made it suitable for surf zone applications as demonstrated using examples of obliquely incident waves on a planar beach and rip current formation in longshore bar trough morphology (Haas and Warner, 2009). In this contribution, we present an update to the coupled model which implements a wave roller model and also a modified method of the radiation stress term based on Mellor (2008, 2011a,b,in press) that includes a vertical distribution which better simulates non-conservative (i.e., wave breaking) processes and appears to be more appropriate for sigma coordinates in very shallow waters where wave breaking conditions dominate. The improvements of the modified model are shown through simulations of several cases that include: (a) obliquely incident spectral waves on a planar beach; (b) obliquely incident spectral waves on a natural barred beach (DUCK'94 experiment); (c) alongshore variable offshore wave forcing on a planar beach; (d) alongshore varying bathymetry with constant offshore wave forcing; and (e) nearshore barred morphology with rip-channels. Quantitative and qualitative comparisons to previous analytical, numerical, laboratory studies and field measurements show that the modified model replicates surf zone recirculation patterns (onshore drift at the surface and undertow at the bottom) more accurately than previous formulations based on radiation stress (Haas and Warner, 2009). The results of the model and test cases are further explored for identifying the forces operating in rip current development and the potential implication for sediment transport and rip channel development. Also, model analysis showed that rip current strength is higher when waves approach at angles of 5° to 10° in comparison to normally incident waves.     

Beach profiles characteristics along Giao Thuy and Hai Hau coasts, Vietnam: A field study

Giao Thuy and Hai Hau coasts are located in Nam Dinh province, Vietnam, with a total coastline of 54.42 km in length. The sea-dike system has been seriously damaged and there have been many dike breaches which caused floods and losses. This situation is considered of a general representative for coastal area in the northern part of Vietnam. A variety of studies have shown that the gradient in the longshore sediment transport rate and the offshore ?ne sediment lost are the main mechanisms causing the beach erosion. This study presents a field investigation of the beach profiles at Giao Thuy and Hai Hau beaches. Three types of empirical functions for the equilibrium beach profile are applied and compared with the observations. Results show that all observed beach pro?les can be described by a single function. However, one specific equilibrium pro?le equation is not sufficient to assess all beach pro?les. In Section 1 of Giao Thuy and Section 3 of Hai Thinh beaches, beach profiles are consistent with the logarithmic function, while the exponential function fits well in Section 2. This difference is explained with respect to coastal morphology, sediment characteristics and hydrodynamic conditions which vary in site. An analysis of the validity of the beach profile functions is recommended for the numerical modeling and engineering designs in this area.     

Effects of cross-shore boundary condition errors in nearshore circulation modeling

The paper analyzes the effect which prescribed errors in the cross-shore boundary conditions for a computational domain along a beach have on the flow field predicted inside the domain. This problem is relevant because errors in boundary conditions are unavoidable when modeling limited domains of a nearshore region. For simplicity, we consider a longshore uniform plane beach with monochromatic, obliquely incident waves, and assume depth uniform currents. It is then studied analytically and numerically how small perturbations of the boundary conditions along both upstream and downstream cross-shore boundaries spread inside the computational domain. It is found that the errors at the upstream cross-shore boundary tend to spread over a long distance downstream of the boundary, while the influence of the errors in the downstream boundary condition is limited to the adjacent upstream area of the computational domain. Both the numerical and analytical solutions show that the errors introduced at the upstream boundary decay exponentially in the surf zone at a rate proportional to the bottom friction. A simple formula is developed to estimate the influence distance of the upstream errors. If we consider the mismatch in the volume flux at the upstream boundary, the error merely redistributes in the cross-shore direction to conserve volume. In the case of excessive flux or velocity specified at the cross-shore boundaries, a circulation cell tends to appear in the offshore region where the errors caused by the boundary mismatch increase with the cross-shore width of the model domain.     

企望湾砂质海滩剖面冲淤幅度的估算

以海滩沉积地貌现场观测资料为基础 ,通过海滩剖面形态组合 ,历史地形资料比较和特征地貌形态变化理论计算分析 ,对汕头南部企望湾弧形砂质海岸切线段的海滩剖面冲淤幅度进行了估算。结果表明 ,该海滩剖面冲淤幅度具有区段变化 ,低潮阶地和槽谷部位约 1 .5～ 2 .0m,滩肩和水下沙坝部位可达 3 .0 m。近 3 0年来 ,海滩剖面总体上趋于微冲刷 ,平均冲刷强度约为 1～ 2 cm/a,可能与近期人工挖砂有关。     

Marine Sand Resources Offshore Israel

Abstract

The continental margin of northern Sinai and Israel, up to Haifa Bay, is the northeastern limb of the submarine Nile Delta Cone. It is made up predominantly of clastics from the Nile and its predecessors. The continental shelf and coastal plain of Israel are built of a series of shore-parallel ridges composed of carbonate-cemented quartz sandstone (locally named kurkar), a lithification product of windblown sands that were piled up into dunes during the Pleistocene. The drop in global sea level and regression during the last glacial period exposed the continental shelf to subaerial erosion and created a widespread regional erosional unconformity which is expressed as a prominent seismic reflector at the top of the kurkar layers. The subsequent Holocene transgression abraded much of the westernmost kurkar ridges, drowned their cores, and covered the previous lowstand deposits with marine sands, which were in turn covered by a sequence of sub-Recent clayey silts.

The Mediterranean coasts of Sinai and Israel are part of the Nile littoral cell. Since the building of the Aswan dams the sand supplied to Israel's coastal system is derived mainly from erosion of the Nile Delta and from sands offshore Egypt that are stirred up by storm waves. The sands are transported by longshore and offshore currents along the coasts of northern Sinai and Israel. Their volume gradually declines northward with distance from their Nile source. The longshore transport terminates in Haifa Bay where some sand is trapped, and the test escapes to deeper water by bottom currents and through submarine canyons, thus denying Nile-derived sand supply to the 40-km-long Akko-Rosh Haniqra shelf.

The sand balance along Israel's coastal zone is a product of natural processes and human intervention. Losses due to the outgoing longshore transport, seaward escape, and landward wind transport exceed the natural gains from the incoming longshore transport and the abrasion of the coastal cliffs. The deficit is aggravated by the construction of (1) seaward-projecting structures that trap sands on the upstream side and (2) offshore detached breakwaters that trap sands between themselves and the coast. The negative sand balance is manifested by the removal of sand from the seabed and the consequent exposure of archaeological remains that were hitherto protected by it.

The sediments that escape seaward from the longshore transport system form a 2.5- to 4-km-wide sandy apron adjacent to the shore that extends to where the water is 30–40 m deep. The apron's slope (0.5–0.8°) is steeper than the theoretical equilibrium slope for the median grain-size diameter in this zone (0.1–0.3 mm).

The beach sands and the apron's surficial sands are well sorted. Their grain size decreases with distance from shore, from 0.2–0.3 mm nearshore to 0.11–0.16 mm by the drowned ridge. The coarse-grained fraction consists of skeletal debris (commonly 5–12% carbonate matter) and wave-milled kurkar grains (locally named zifzif). In deeper water, the basal sands underlying the fine-grained sediment cover consist of 1- to 30-cm layers whose composition ranges from silty sands to various types of sands (fine, medium, coarse, and gravelly) to zifzif. For the most part, they contain large amounts of skeletal debris (20–60%) and small fragments of kurkar.

Two types of kurkar rock were encountered offshore: a well-sorted, fine- to medium-grained (0.074–0.300 mm) lithified dune sand with variable amounts of carbonate cement, ranging from hard rock of low permeability to loose sand; and a porous sandstone made up predominantly of algal grains and skeletal debris (calcarenite).