Field investigation on the results of non-linear shallow water equations in the Swash Zone

For the study of the cross-shore wave-induced hydrodynamics in the swash zone, a numerical model is developed based on the one-dimensional non-linear shallow water (NSW) equations for prediction of hydrodynamic parameters in the swash zone. In order to evaluate the accuracy of the outputs of the numerical model, the model's predictions in terms of water surface elevations and cross-shore velocities, are compared to field data from full-scale experiments conducted on three sites with different beach slope; mild and steep, several bed particle sizes and under various incident wave conditions. The quantitative and qualitative comparison of the results of the numerical model and the full-scale data reveals that the model can generally predict many aspects of the flow in the surf and swash zone on both types of beach. The accuracy is adequate for application in a sediment transport study. Considering the time-history and probability distribution of water surface elevation, the model is generally more accurate on steep beaches than on the mild beach. The model can adequately simulate the dominant frequency across the beach and saturation of higher frequencies on both mild and steep beaches for various incident wave energy characteristics. With regard to the horizontal (cross-shore) velocity, the sawtooth shape of time-history and negative acceleration of water are well predicted by the model for both mild and steep beaches. Due to the uncertainties in maximum and minimum values of velocity data, clear judgement about the accuracy of the numerical model in this matter was not possible. However, the comparison of the minimum velocities (offshore direction) revealed that the application of friction factors below the range which is suggested by literature best match the data.     

Direct bed shear stress measurements in bore-driven swash

Direct measurements of bed shear in the swash zone are presented. The data were obtained using a shear plate in medium and large-scale laboratory bore-driven swash and cover a wide range of bed roughness. Data were obtained across the full width of the swash zone and are contrasted with data from the inner surf zone. Estimates of the flow velocities through the full swash cycle were obtained through numerical modelling and calibrated against measured velocity data. The measured stresses and calculated flow velocities were subsequently used to back-calculate instantaneous local skin friction coefficients using the quadratic drag law. The data show rapid temporal variation of the bed shear stress through the leading edge of the uprush, which is typically two–four times greater than the backwash shear stresses at corresponding flow velocity. The measurements indicate strong temporal variation in the skin friction coefficient, particularly in the backwash. The general behaviour of the skin friction coefficient with Reynolds number is consistent with classical theory for certain stages of the swash cycle. A spatial variation in skin friction coefficient is also identified, which is greatest across the surf-swash boundary and likely related to variations in local turbulent intensities. Skin friction coefficients during the uprush are approximately twice those in the backwash at corresponding Reynolds number and cross-shore location. It is suggested that this is a result of the no-slip condition at the tip leading to a continually developing leading edge and boundary layer, into which high velocity fluid and momentum are constantly injected from the flow behind and above the tip region. Finally, the measured stress data are used to determine the asymmetry and cross-shore variation in potential sediment transport predicted by three forms of sediment transport formulae.     

Swash zone sediment fluxes: Field observations

This paper describes newly obtained, high-frequency observations of beach face morphological change over numerous tidal cycles on a macrotidal sandy beach made using a large array of ultrasonic altimeters. These measurements enable the net cross-shore sediment fluxes associated with many thousands of individual swash events to be quantified. It is revealed that regardless of the direction of net morphological change on a tidal time scale, measured net fluxes per event are essentially normally distributed, with nearly equal numbers of onshore and offshore-directed events. The majority of swash events cause net cross-shore sediment fluxes smaller than ± 50 kg m^− 1 and the mean sediment flux per swash event is only O(± 1 kg m^− 1) leading to limited overall morphological change. However, much larger events which deposit or remove hundreds of kilograms of sand per meter width of beach occur at irregular intervals throughout the course of a tide. It was found that swash–swash interactions tend to increase the transport potential of a swash event and the majority of the swash events that cause these larger values of sediment flux include one or more interactions. The majority of the larger sediment fluxes were therefore measured in the lower swash zone, close to the surf/swash boundary where swash–swash interactions are most common. Despite the existence of individual swash events that can cause fluxes of sediment that are comparable to those observed on a tidal time scale, frequent reversals in transport direction act to limit net transport such that the beach face volume remains in a state of dynamic equilibrium and does not rapidly erode or accrete.     

Suspended sediment transport in the swash zone of a dissipative beach

Simultaneous high frequency field measurements of water depth, flow velocity and suspended sediment concentration were made at three fixed locations across the high tide swash and inner surf zones of a dissipative beach. The dominant period of the swash motion was 30–50 s and the results are representative of infragravity swash motion. Suspended sediment concentrations, loads and transport rates in the swash zone were almost one order of magnitude greater than in the inner surf zone. The vertical velocity gradient near the bed and the resulting bed shear stress at the start of the uprush was significantly larger than that at the end of the backwash, despite similar flow velocities. This suggests that the bed friction during the uprush was approximately twice that during the backwash.The suspended sediment profile in the swash zone can be described reasonably well by an exponential shape with a mixing length scale of 0.02–0.03 m. The suspended sediment transport flux measured in the swash zone was related to the bed shear stress through the Shields parameter. If the bed shear stress is derived from the vertical velocity gradient, the proportionality coefficient between shear stress and sediment transport rate is similar for the uprush and the backwash. If the bed shear stress is estimated using the free-stream flow velocity and a constant friction factor, the proportionality factor for the uprush is approximately twice that of the backwash. It is suggested that the uprush is a more efficient transporter of sediment than the backwash, because the larger friction factor during the uprush causes larger bed shear stresses for a given free-stream velocity. This increased transport competency of the uprush is necessary for maintaining the beach, otherwise the comparable strength and greater duration of the backwash would progressively remove sediment from the beach.     

Morphodynamic zone variability on a microtidal barred beach

This paper builds on the work of Masselink [Masselink, G., 1993. Simulating the effects of tides on beach morphodynamics. J. Coast. Res. SI 15, 180–197.] on the use of the residence times of shoaling waves, breaking waves and swash/backwash motions across a cross-shore profile to qualitatively understand temporal beach behaviour. We use a data set of in-situ measurements of wave parameters (height and period) and water depth, and time-exposure video images overlooking our single-barred intertidal measurement array at Egmond aan Zee (Netherlands) to derive boundaries between the shoaling zone, the surf zone and the swash zone. We find that the boundaries are functional dependencies of the local relative wave height on the local wave steepness. This contrasts with the use of constant relative wave heights or water levels in earlier work. We use the obtained boundaries and a standard cross-shore wave transformation model coupled to an inner surf zone bore model to show that large (> 5) relative tide ranges (RTR, defined as the ratio tide range–wave height) indicate shoaling wave processes across almost the entire intertidal profile, with surf processes dominating on the beach face. When the RTR is between 2 and 5, surf processes dominate over the intertidal bar and the lower part of the beach face, while swash has the largest residence times on the upper beach face. Such conditions, associated with surf zone bores propagating across the bar around low tide, were observed to cause the intertidal bar to migrate onshore slowly and the upper beach face to steepen. For RTR values less than about 2, surf zone processes dominate across the intertidal bar, while the dominance of swash processes now extends across most of the beach face. The surf zone processes were now observed to lead to offshore bar migration, while the swash eroded the upper beach face.     

Laboratory and numerical study of dambreak-generated swash on impermeable slopes

New laboratory experiments have produced detailed measurements of hydrodynamics within swash generated by bore collapse on a steep beach. The experiments are based on a dambreak rig producing a highly repeatable, large-scale swash event, enabling detailed measurements of depths and velocities at a number of locations across the swash zone. Experiments were conducted on two beaches, differentiated by roughness. Results are presented for uprush shoreline motion, flow depths, depth-averaged velocity, velocity profiles and turbulence intensity. Estimates of the time- and spatially-varying bed shear stress are obtained via log-law fitting to the velocity profiles and are compared with the shear plate measurements of Barnes et al. (2009) for similar experimental conditions. Experimental results are compared with model predictions based on a NLSWE model with momentum loss parameterised using the simple quadratic stress law in terms of the depth-averaged velocity. Predicted and measured flow depths and depth-averaged velocities agree reasonably well for much of the swash period, but agreement is not good at the time of bore arrival and towards the end of the backwash. The parameterisation of total momentum loss via the quadratic stress law cannot adequately model the swash bed shear stress at these critical times.     

Large scale experiments on gravel and mixed beaches: Experimental procedure,data documentation and initial results

This paper provides information on the experimental set-up, data collection methods and results to date for the project “Large scale modelling of coarse grained beaches”, undertaken at the Large Wave Channel (GWK) of FZK in Hannover by an international group of researchers in Spring 2002. The main objective of the experiments was to provide full scale measurements of cross-shore processes on gravel and mixed beaches for the verification and further development of cross-shore numerical models of gravel and mixed sediment beaches. Identical random and regular wave tests were undertaken for a gravel beach and a mixed sand/gravel beach set up in the flume. Measurements included profile development, water surface elevation along the flume, internal pressures in the swash zone, piezometric head levels within the beach, run-up, flow velocities in the surf-zone and sediment size distributions.The purpose of the paper is to present to the scientific community the experimental procedure, a summary of the data collected, some initial results, as well as a brief outline of the on-going research being carried out with the data by different research groups. The experimental data is available to all the scientific community following submission of a statement of objectives, specification of data requirements and an agreement to abide with the GWK and EU protocols.     

On the cross-shore profile change of gravel beaches

This paper investigates cross-shore profile changes of gravel beaches, with particular regard to discussing the tendency for onshore transport and profile steepening in the swash zone. The discussion includes observed morphological changes on a gravel beach from experimental investigations at the Large Wave Flume (GWK) in Hanover, Germany. During the tests all the profile changes occurred in the swash zone, resulting in erosion below the still water line (SWL) and formation of a berm above the SWL. We investigate the profile evolution evaluating the transport rates from a bed load sediment transport formulation coupled with velocities calculated from a set of Boussinesq equations that have been validated for its use in the surf and swash zones [Lynett, P.J., Wu, T.-R., and Liu, L.-F., P., 2002. Modelling wave runup with depth-integrated equations. Coastal Engineering, 46, 89–107; Otta, A.K., and Pedrozo-Acuña, A., 2004. Swash boundary and cross-shore variation of horizontal velocity on a slope. In: J.M. Smith (Editor), Proceedings 29th International Conference on Coastal Engineering. World Scientific, Lisbon, Portugal, pp. 1616–1628]. We discuss the influence of bottom friction on the predicted profiles, using reported friction factors from experimental studies. It is shown that the use of a different friction factor within a realistic range in each phase of the swash (uprush and backwash) improves prediction of the beach profiles, although quantitative agreement between the measured and computed profile evolutions is not satisfactory. Furthermore, if the friction factor and the transport efficiency (C) of the sediment transport formulation are kept the same in the uprush and backwash, accurate representation of profile evolution is not possible. Indeed, the features of the predicted profiles are reversed. However, when the C parameter is set larger during the uprush than during the backwash, the predicted profiles are closer to the observations. Differences between the predicted profiles from setting non-identical C-values and friction factors for the swash phase, are believed to be linked to both the infiltration effects on the flow above the beachface and the more accelerated flow in the uprush.     

海滩层理中的反递变纹层

本文提出海滩反递变纹层自下而上粒度由小到大,重矿物富集于纹层底部,它是前滨冲流“剪切分选”的产物。原生反递变纹层常被激浪破坏和再造,遇到后期加积海滩过程时,才能保存于海滩层理中。海滩层理的现场观测是研究海滩层理反递变纹层形成机理的重要方法之一。     

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.     

Modeling sediment transport in the swash zone: A review

A critical review of conceptual and mathematical models developed in recent decades on sediment transport in the swash zone is presented. Numerous studies of the hydrodynamics and sediment transport in the swash zone in recent years have pointed out the importance of swash processes in terms of science advancement and practical applications. Evidently, the hydrodynamics of the swash zone are complex and not fully understood. Key hydrodynamic processes include both high-frequency bores and low-frequency infragravity motions, and are affected by wave breaking and turbulence, shear stresses and bottom friction. The prediction of sediment transport that results from these complex and interacting processes is a challenging task. Besides, sediment transport in this oscillatory environment is affected by high-order processes such as the beach groundwater flow. Most relationships between sediment transport and flow characteristics are empirical, based on laboratory experiments and/or field measurements. Analytical solutions incorporating key factors such as sediment characteristics and concentration, waves and coastal aquifer interactions are unavailable. Therefore, numerical models for wave and sediment transport are widely used by coastal engineers. This review covers mechanisms of sediment transport, important forcing factors, governing equations of wave-induced flow, groundwater interactions, empirical and numerical relations of cross-shore and longshore sediment transport in the swash zone. Major advantages and shortcomings of various numerical models and approaches are highlighted and reviewed. These will provide coastal modelers an impetus for further detailed investigations of fluid and sediment transport in the swash zone.     

Measurements of the time-varying free-surface profile across the swash zone obtained using an industrial LIDAR

The use of an industrial LIDAR instrument to measure time-varying water-surface elevations within the swash zone is investigated. The propagation of the swash lens across the beach face was measured simultaneously by a LIDAR instrument and a network of precision ultrasonic altimeters at a sandy beach. Comparison of the two datasets indicates that the time-varying swash free-surface profile obtained using a LIDAR compare favourably with point measurements obtained using ultrasonic altimeters. Significantly, the use of a continuously scanning laser beam enables a single LIDAR instrument to obtain measurements of free-surface elevation near-synchronously at several hundred points throughout the swash zone. This high spatial resolution permits small-scale flow features such as the swash-front gradient and the presence of secondary bores to be detailed, and negates the need for the deployment of a large, multi-sensor array.     

The influence of seaward boundary conditions on swash zone hydrodynamics

The influence of the seaward boundary condition on the internal swash hydrodynamics is investigated. New numerical solutions of the characteristics form of the nonlinear shallow-water equations are presented and applied to describe the swash hydrodynamics forced by breaking wave run-up on a plane beach. The solutions depend on the specification of characteristic variables on the seaward boundary of the swash zone, equivalent to prescribing the flow depth or the flow velocity. It is shown that the analytical solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. J. Fluid Mech. 16, 113–125] is a special case of the many possible solutions that can describe the swash flow, but one that does not appear appropriate for practical application for real waves. The physical significance of the boundary conditions is shown by writing the volume and momentum fluxes in terms of the characteristic variables. Results are presented that illustrate the dependence of internal flow depth and velocity on the boundary condition. This implies that the internal swash hydrodynamics depend on the shape and wavelength of the incident bore, which differs from the hydrodynamic similarity inherent in the analytical solution. A solution appropriate for long bores is compared to laboratory data to illustrate the difference from the analytical solution. The results are important in terms of determining overwash flows, flow forces and sediment dynamics in the run-up zone.     

Wave-induced water table fluctuations,sediment transport and beach profile change: Modeling and comparison with large-scale laboratory experiments

Coastal groundwater systems can have a considerable impact on sediment transport and foreshore evolution in the surf and swash zones. Process-based modeling of wave motion on a permeable beach taking into account wave-aquifer interactions was conducted to investigate the effects of the unconfined coastal aquifer on beach profile evolution, and wave shoaling on the water table. The simulation first dealt with wave breaking and wave runup/rundown in the surf and swash zones. Nearshore hydrodynamics and wave propagation in the cross-shore direction were simulated by solving numerically the two-dimensional Navier–Stokes equations with a k–ε turbulence closure model and the Volume-Of-Fluid technique. The hydrodynamic model was coupled to a groundwater flow model based on SEAWAT-2000, the latter describing groundwater flow in the unconfined coastal aquifer. The combined model enables the simulation of wave-induced water table fluctuations and the effects of infiltration/exfiltration on nearshore sediment transport. Numerical results of the coupled ocean/aquifer simulations were found to compare well with experimental measurements. Wave breaking and infiltration/exfiltration increase the hydraulic gradient across the beachface and enhance groundwater circulation inside the porous medium. The large hydraulic head gradient in the surf zone leads to infiltration across the beachface before the breaking point, with exfiltration taking place below the breaking point. In the swash zone, infiltration occurs at the upper part of the beach and exfiltration at the lower part. The simulations confirm that beaches with a low water table tend to be accreted while those with a high water table tend to be eroded.     

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.     

RANS v2–f simulation of a swash event: Detailed flow structure

The flow structure of a swash event over a uniform slope is studied using a RANS-VOF numerical model coupled with a v²–f turbulence closure. The model is compared with experimental data of recent laboratory experiments. The ability of the turbulence modelling for simulating swash flow and the evolution of the computed bed shear stress during run-up and run-down are investigated. The agreement between numerical results and measured data, such as water depth, depth-averaged velocity and bed shear stress is very good during run-up. Main discrepancies are found during run-down. The paper also examines the aeration of the water layer in the swash flow, taking advantage of the PLIC method for computing the air–water interfaces. Air is continuously entrapped in the swash front and released at its rear during run-up. A detailed analysis indicates that the flow reversal is initiated near the bottom at the outer boundary of the swash zone and progresses landward. The study highlights the asymmetry between run-up and run-down. During run-up, the swash front propagation determines the turbulence properties and the bed shear stress profile on the beach, whereas the flow properties are more homogeneously distributed in the swash area during run-down.     

长江口崇明东滩盐沼前缘地带悬浮泥沙横向通量的潮周期变化

对长江口崇明东滩盐沼边缘及邻近光滩处的水深、流速和悬沙含量的潮周期变化过程进行了现场实测,并对横向悬沙通量进行了计算和分析。研究结果表明,在平静天气条件下光滩和盐沼上的流速过程有明显差异,植被缓流作用在落潮期更为显著,流速在涨潮由光滩向盐沼不断增大。与涨潮流速优势相对应,涨潮期平均悬沙含量是落潮期的1.8倍。横向悬沙通量以向岸输移为主,悬沙总通量与潮次内最大水深的四次方呈显著正相关。在平静天气条件下潮汐作用控制着盐沼前缘地带泥沙输移水平,盐沼滩面保持稳定淤积,前缘光滩淤积速率高于盐沼处的,盐沼逐渐向海延伸。在大风天气条件下潮次内的流速和悬沙含量水平提高了数倍,悬沙输移量大增,净输移仍以向岸方向为主,在盐沼上部和前缘光滩均可能在短期内发生大量淤积。     

粤东后江湾冲流带滩面高频振动及动力作用分析

利用涌浪影响下短时段内的冲流带滩面高频高程数据和碎波带波流资料,在奇异谱分析(SSA)的基础上,对比研究了不同形态滩面的冲淤变化趋势、趋势分布形状、冲淤变化周期和冲淤变化强度,以及同一条剖面不同桩点间各因素间的变化关系;用交叉谱方法探索了每分钟滩面高频冲淤变化与碎波带长重力波间的作用关系。分析结果表明,滩角韵律地形引起的冲流分流作用促进了滩脊向滩谷的泥沙转运,冲流带滩面存在明显的长重力波频段的周期性冲淤振动,滩面冲淤振动强度由滩面下部向上部递减,碎波带长重力波对滩面高频冲淤变化起重要作用。     

Measurements and modelling of the advection of suspended sediment in the swash zone by solitary waves

Novel laboratory experiments and numerical modelling have been performed to study the advection scales of suspended sediment in the swash zone. An experiment was designed specifically to measure only the sediment picked up seaward of the swash zone and during bore collapse. The advection scales and settling of this sediment were measured during the uprush along a rigid sediment-free beach face by a sediment trap located at varying cross-shore positions. Measurements were made using a number of repeated solitary broken waves or bores. Approximately 25% of the pre-suspended sediment picked up by the bores reaches the mid-swash zone (50% of the horizontal run-up distance), indicating the importance of the sediment advection in the lower swash zone. The pre-suspended sediment is sourced from a region seaward of the shoreline (still water line) which has a width of about 20% of the run-up distance. An Eulerian–Lagrangian numerical model is used to model the advection scales of the suspended sediment. The model resolves the hydrodynamics by solving the non-linear shallow water equations in an Eulerian framework and then solves the advection–diffusion equation for turbulence and suspended sediment in a Lagrangian framework. The model provides good estimates of the measured mass and distribution of sediment advected up the beach face. The results suggest that the correct modelling of turbulence generation prior to and during bore collapse and the advection of the turbulent kinetic energy into the lower swash is important in resolving the contribution of pre-suspended sediment to the net sediment transport in the swash zone.     

Modelling gravel beach dynamics with XBeach

Numerical cross-shore profile evolution models have been good at predicting beach erosion during storm conditions, but have difficulty in predicting the accretion of the beach during calm periods. This paper describes the progress made in modifying and applying the public domain XBeach code to the prediction and explanation of the observed behaviour of coarse-grained beaches in the laboratory and the field under accretive conditions. The paper outlines in details the changes made to the original code (version 12), including the introduction of a new morphological module based upon Soulsby's sediment transport equation for waves and currents, and the incorporation of Packwood's infiltration approach in the unsaturated area of the swash region. The competence of this modified model during calm conditions for describing the steepening of the profile, and the growth of the beach berm is demonstrated. Preliminary results on the behaviour of the beach subject to both waves and tides are presented. Good agreement is found between the model simulations and large-scale laboratory measurements, as well as field observations from a composite beach in the UK. The reasons for the model's capabilities are discussed.