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.     

High-frequency sediment-level oscillations in the swash zone

Sediment-level oscillations with heights of about 6 cm and shore-normal lengths of order 10 m have been measured in the swash zone of a high-energy, coarse-sand beach. Crests of oscillations were shore parallel and continuous alongshore. The oscillations were of such low steepness (height-to-length ratio approximately 0.006) that they were difficult to detect visually. The period of oscillation ranged between 6 and 15 min and decreased landward across the swash zone. The sediment-level oscillations were progressive landward with an average migration rate in the middle to upper swash zone of 0.8 m min⁻¹. Migration was caused mostly by erosion on the seaward flank of the crest of an oscillation during a period of net seaward sediment transport. Thus, the observed migration was a form migration landward rather than a migration involving net landward sediment transport. The observed sediment-level oscillations were different than sand waves or other swash-zone bedforms previously described.     

Prediction of swash motion and run-up including the effects of swash interaction

Modifications to a model describing swash motion based on solutions to the non-linear shallow water equations were made to account for interaction between up-rush and back-wash at the still water shoreline and within the swash zone. Inputs to the model are wave heights and arrival times at the still water shoreline. The model was tested against wave groups representing idealized vessel-generated wave trains run in a small wave tank experiment. Accounting for swash interaction markedly improved results with respect to the maximum run-up length for cases with rather gentle foreshore slopes (tanβ=0.07). For the case with a steep foreshore slope (tanβ=0.20) there was very little improvement compared to model results if swash interaction was not accounted for. In addition, an equation was developed to predict the onset and degree of swash interaction including the effects of bed friction.     

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.     

Morphodynamics and cobbles behavior in and near the surf zone

The evolution of an initially flat sandy slope and the dynamics of large objects (cobbles/mines) emplaced on it are studied in a laboratory wave tank under simulated surf conditions. Upon initiation of wave forcing, the initially flat beach undergoes bedform changes before reaching a quasi-steady morphology characterized by a system of sand ripples along the slope and a large bar near the break point. Although the incoming wave characteristics are held fixed, the bottom morphology never reaches a strict steady state, but rather slowly changes due to the migration of ripples and bar transformation. When the wave characteristics are changed, the bedform adjusts to a new quasi-steady state after a suitable adjustment time. Studies conducted by placing model cobbles/mines on the evolving sandy bottom subjected to wave forcing show four distinct scenarios: (i) periodic cobble oscillations with zero mean displacement and small scour around the cobbles, (ii) mean onshore motion of relatively light cobbles, (iii) periodic burial of relatively heavy cobbles when their sizes are comparable to those of sand ripples, and (iv) the burial of relatively large cobbles under the bar, when the bar migrates due to changes of incoming waves. Quantitative data on the characteristics and dynamics of the bedform, including ripple-formation front propagating down the slope, ripple growth and drift, and flow around ripples, are presented. Physical explanations are provided for the observations.     

Measurement of wave-by-wave bed-levels in the swash zone

A technique is described to observe and quantify wave-by-wave bed-level changes in the swash zone. The ultrasonic instrument system is non-contact with the beach face surface being measured and the sensors remain outside of the fluid flows causing sediment movement. Sensor resolution combined with the electronic noise inherent within a digital network data-logging system results in a (conservative) measurement accuracy of ± 1 mm, equating to a couple of sand grain diameters in height. Illustrative field results demonstrate the practical use of the instrumentation, and a simple data pre-processing method to separate swashes and intervening bed-level ‘events’ is discussed. These example data reveal rather complex fluctuations of the bed observed over time periods of minutes to hours. Rather strikingly, gross bed-level changes per wave are revealed to be up to many orders of magnitude larger than the observed net rate of beach face evolution. It is outlined how observations of successive bed-level changes at multiple locations within a dense grid, combined with a consideration of sediment continuity, will now enable the total net sediment transported per uprush–backwash to be quantified.     

Dynamics of cobbles in the shoaling region of a surf zone

The motion of large bottom particles (cobbles/mines) was studied in the laboratory under simulated surf conditions. A series of experiments was conducted in a large wave tank, 32×0.9×1.8 m, equipped with a computer-controlled wave maker and a sloping beach. As a first step, a solid impermeable beach with artificial roughness was used in the experiments. Cobbles of different size were placed along the floor and their evolution with time was studied and compared with the model predictions. Onshore and offshore mean motions of cobbles, as well as steady oscillations with zero mean displacement, were observed for different conditions. To explain the results of observations a theoretical model was advanced. The model takes into account all main governing parameters (size and density of cobbles, bottom slope, dynamic and static friction at the bottom, background flow characteristics, etc.). Standard parameterizations were used for a pressure accelerating term, drag, lift and other nonlinear forces. For the range of parameters used in the experiments, satisfactory agreement between the measured and calculated values of the cobble displacements as a function of time was obtained. The model is practically insensitive to the vertical accelerating pressure term but sensitive to the dynamic and static friction. One of the most important variables in the model, which is known with the least accuracy, is the virtual mass coefficient for disk-shaped cobbles moving with variable velocity along a solid boundary.     

海滩冲流带高频振动地形动力过程分析

在粤东汕尾后江湾海滩冲流带布设2条观测剖面,共计6个观测点,对滩面冲流带在约一个潮周期内的高频振动进行了观测,取得采样频率分别为1min/次和6min/次的滩面数据各1组.结合同步观测的碎波带波浪潮汐数据,分析探讨了海滩高频振动特征.分析认为在涌浪条件下,滩面高频振动的日内变化主要受到潮位变化过程的控制,涨潮堆积,落潮侵蚀.利用交叉谱分析的结果表明滩面高程变化滞后于潮位变化.滩面下部比上部振动幅度大,变化复杂,滩角脊部比凹部活跃.波群对滩面高频振动有显著影响,特别是波高大于有效波高的波群.滩面高频振动没有表现出明显的泥沙逐渐向陆地堆积过程,有一定的振动周期.     

Estimating swash zone friction coefficients on a sandy beach

Video-based swash motions from three studies (on two separate beaches) were analyzed with respect to theoretical swash trajectories assuming plane beach ballistic motions under quadratic friction. Friction coefficient values for both the uprush and backwash were estimated by comparing measured swash space–time trajectories to these theoretical expectations given an initial velocity and beach slope. Observations were made spanning high tides, and in one case, during a light rain. Analysis of over 4500 individual swash events showed that the uprush friction coefficient was nearly constant during all three studies with a mean value of roughly 0.007 and showed no trends over a tidal cycle. In contrast, backwash friction coefficient values varied over the tidal cycles ranging between 0.01 and 0.07 with minimum values corresponding to the highest tides. Although these values are close to the theoretical estimates based on a Law of the Wall formulation and values commonly referenced in the literature, these observations show a consistent tendency for backwash friction estimates to greatly exceed uprush friction estimates. The disparity between uprush and backwash friction coefficients can be partially attributed to the exclusion of a pressure gradient term in the ballistic model. However, results indicate that backwash friction coefficients adjusted to account for this effect may be three times larger than the uprush friction values during lower tides. This tidal dependence for backwash friction coefficients is attributed to a complex interaction between swash infiltration and entrained sediment loads. These findings imply that friction estimates (necessary for sediment transport calculations and hydrodynamic predictions) based solely on grain roughness may not be correct for backwash flows.     

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.     

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.     

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.     

An integral swash zone model with friction: an experimental and numerical investigation

Experimental and numerical analyses have been used to assess the validity and potentialities of the integral swash zone model by Brocchini and Peregrine (Proc. Coastal Dynamics '95, ASCE 1 (1996) 221) which is extended to include seabed friction effects previously neglected. Applications of the model to experimental data show it represents a simple and useful tool for modelling swash zone flows. The model allows for computation of integral swash zone properties and shoreline motion from local variables defined at the seaward limit of the swash. For most properties, correlation between local and integral properties is very good (correlation coefficient about 0.80).A suitable parametric form of frictional forces in the swash zone is defined on the basis of both experimental data and analytical investigation. Numerical tests showed that the proposed parameterization models well integral frictional forces within the swash zone. The parametric friction force improves capabilities of the integral swash zone model of representing real swash motions. This is particularly evident when considering the momentum equation: the correlation coefficient between the rate of change of the onshore momentum in the swash zone and its forcings increases from about 0.85 to about 0.95 due to the inclusion of the seabed friction.     

Alongshore fluid motions in the swash zone of a sandy and gravel beach

Field experiments were conducted on a low-gradient, high-energy sandy beach (Truc Vert, France) and a steep, low-energy gravel beach (Slapton, UK) to examine alongshore-directed currents within the swash zone. At Truc Vert, data were collected over 33 tidal cycles with offshore significant wave heights of 1–4 m and periods of 5–12 s. At Slapton data were collected during 12 tides with wave heights of 0.3–1 m and periods of 4–9 s. The swash motion was predominantly at infragravity frequencies at Truc Vert and incident frequencies at Slapton.     

The role of combined laser scanning and video techniques in monitoring wave-by-wave swash zone processes

Simulating swash zone morphodynamics remains one of the major weaknesses of beach evolution models. One of the reasons is the limited availability of data on morphological changes at the temporal scales of individual swash events. This paper sets out to present a new hybrid system, consisting of 2D/3D laser scanners and several video cameras, which was designed to monitor swash zone topographic change on a wave-by-wave basis. A methodology is proposed consisting of sensor calibration and several data processing steps, allowing a fusion of different sensors. Such an approach can improve the performance of several field/laboratory, optical technique applications for nearshore hydro- and morpho-dynamic measurements. Digital Elevation Models from a 3D scanner were used in the extrinsic camera calibration procedure and reduced the geo-rectification errors from 0.035 m < RMSE < 0.071 m to 0.008 m < RMSE < 0.013 m. The 2D scanner provided instantaneous measurements of the water and dry beach surface elevation along a 10 m cross-shore section, and comparison with ultrasonic sensor measurements resulted in RMS errors within the 1.7 cm < RMSE < 3.2 cm range. The combination of 2D scanner and video data (i) reduced geo-rectification errors by more than one order of magnitude; and (ii) made 2D laser point cloud processing easier and more robust. The hybrid monitoring system recorded the morphological change of a replenished beach-face on a wave-by-wave basis, during large-scale, physical modeling experiments and the observations showed that individual swash events could result in elevation changes up to dz = ± 10 cm. The sediment transport direction and intensity of the monitored swash events was relatively balanced and sediment transport rates ranged between − 3.5 kg m^− 1 s^− 1 > Q_t > 3.5 kg m^− 1 s^− 1. Extreme transport swash events became rarer as the morphology was reaching equilibrium.     

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.     

A Lagrangian model for boundary layer growth and bed shear stress in the swash zone

A new model for the boundary layer development and associated skin friction coefficients and shear stress within the swash zone is presented. The model is developed within a Lagrangian reference frame, following fluid trajectories, and can be applied to both laminar flow and smooth turbulent flow. The model is based on the momentum integral approach for steady, flat-plate boundary layers, with appropriate modifications to account for the unsteady flow regime and flow history. The model results are consistent with previous measurements of bed shear stress and skin friction coefficients within the swash zone. These indicate strong temporal and spatial variation throughout the swash cycle, and a clear distinction between the uprush and backwash phase. This variation has been previously attributed the unsteady flow regime and flow history effects, both of which are accounted for in the new model. Fluid particle trajectories and velocity are computed using the non-linear shallow water wave equations and the boundary layer growth across the entire swash zone is estimated. Predictions of the bed shear stress and skin friction coefficients agree reasonably well with direct bed shear stress measurements reported by Barnes et al. (Barnes, M.P., O’Donaghue, T., Alsina, J.M., Baldock, T.E., 2009. Direct bed shear stress measurements in bore-driven swash. Coastal Engineering 56 (8), 853–867) and, for a given flow velocity, give stresses which are consistent with the bias toward uprush sediment transport which has consistently been observed in measurements. The data and modelling suggest that the backwash boundary layer is initially laminar, which results in the late development of significant bed shear during the backwash, with a transition to a turbulent boundary layer later in the backwash. A new conceptual model for the boundary layer structure at the leading edge of the swash is proposed, which accounts for both the no-slip condition at the bed and the moving wet–dry interface. However, further development of the Lagrangian Boundary Layer Model is required in order to include bore-generated turbulence and to account for variable roughness and mobile beds.     

Maximum run-up,breaking conditions and dynamical forces in the swash zone: a boundary value approach

On the basis of the approximate analytical solution for the nonlinear shallow water equations of Antuono and Brocchini [M. Antuono & M. Brocchini, The boundary value problem for the nonlinear shallow water equation, Stud. Appl. Maths, 119, 71–91 (2007).], we propose useful regression curves for the prediction of maximum run-up and dynamical forces in the swash zone on a frictionless, uniformly sloping beach. For the first time the dependence of the results on both the wave height and the wave steepness is analyzed in detail providing formulae able to describe a wide class of wave inputs. Finally, the regression formulae are validated through comparison with maximum run-up laws and breaking conditions already available in the literature, the present model results appearing to better account for nonlinear effects.