Lagrangian measurements and modelling of fluid advection in the inner surf and swash zones

New laboratory and field data are presented on fluid advection into the swash zone. The data illustrate the region of the inner surf zone from which sediment can be directly advected into the swash zone during a single uprush, which is termed the advection length. Experiments were conducted by particle tracking in a Lagrangian reference frame, and were performed for monochromatic breaking waves, solitary bores, non-breaking solitary waves and field conditions. The advection length is normalised by the run-up length to give an advection ratio, A, and different advection ratios are identified on the basis of the experimental data. The data show that fluid enters the swash zone from a region of the inner surf zone that can extend a distance seaward of the bore collapse location that is approximately equal to half of the run-up length. This region is about eight times wider than the region predicted by the classical swash solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. Journal of Fluid Mechanics 16, 113–125], as illustrated by Pritchard and Hogg [Pritchard, D., Hogg, A.J., 2005. On the transport of suspended sediment by a swash event on a plane beach. Coastal Engineering 52, 1–23]. Measured advection ratios for periodic waves show no significant trend with Iribarren number, consistent with self-similarity in typical swash flows. The data are compared to recent characteristic solutions of the non-linear shallow water wave (NLSW) equations and both finite difference and finite volume solutions of the NLSW equations.     

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.     

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.     

Simulation and prediction of swash oscillations on a steep beach

This paper presents numerical simulations and analytical predictions of key aspects of swash oscillations on a steep beach. Simulations of the shoreline displacement based on bore run-up theory are found to give excellent agreement with recent experimental data for regular waves, wave groups and random waves. The theory is used to derive parameters that predict the onset of swash saturation and the spectral characteristics of the saturated shoreline motion. These parameters are again in good agreement with the measured laboratory data and are also consistent with previous experimental data. Simulation of irregular wave run-up using a series of overlapping monochromatic swash events is found to reproduce typical features of swash oscillations and can accurately describe both the low and high frequency spectral characteristics of the swash zone. In particular, the low frequency components of the run-up can be modelled directly using a sequence of incident short wave bores, with no direct long wave input to the numerical simulations. This suggests that wave groupiness must be accounted for when modelling shoreline oscillations.     

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.     

Swash overtopping and sediment overwash on a truncated beach

New experimental laboratory data are presented on swash overtopping and sediment overwash on a truncated beach, approximating the conditions at the crest of a beach berm or inter-tidal ridge-runnel. The experiments provide a measure of the uprush sediment transport rate in the swash zone that is unaffected by the difficulties inherent in deploying instrumentation or sediment trapping techniques at laboratory scale. Overtopping flow volumes are compared with an analytical solution for swash flows as well as a simple numerical model, both of which are restricted to individual swash events. The analytical solution underestimates the overtopping volume by an order of magnitude while the model provides good overall agreement with the data and the reason for this difference is discussed. Modelled flow velocities are input to simple sediment transport formulae appropriate to the swash zone in order to predict the overwash sediment transport rates. Calculations performed with traditional expressions for the wave friction factor tend to underestimate the measured transport. Additional sediment transport calculations using standard total load equations are used to derive an optimum constant wave friction factor of f_w = 0.024. This is in good agreement with a broad range of published field and laboratory data. However, the influence of long waves and irregular wave run-up on the overtopping and overwash remains to be assessed. The good agreement between modelled and measured sediment transport rates suggests that the model provides accurate predictions of the uprush sediment transport rates in the swash zone, which has application in predicting the growth and height of beach berms.     

Numerical study on wave-induced filtration flow across the beach face and its effects on swash zone sediment transport

A numerical model, coupling an analysis of beach groundwater flow with an analysis of swash wave motion over a uniform slope, is presented. Model calculations are performed to investigate the variations of swash-induced filtration flows across the beach face for different input parameters. Swash zone sediment transport under the influence of such filtration flow across the beach face is investigated through modification of effective weight of sediment particle and modification of swash boundary layer thickness. These effects are quantified based on a bed load transport model with a modified Shields parameter.     

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.     

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.     

The role of bore collapse and local shear stresses on the spatial distribution of sediment load in the uprush of an intermediate-state beach

Spatial variations in sediment load in the swash uprush and textural properties of sediment in transport were evaluated to investigate the mechanisms responsible for sediment transport during wave uprush. Four streamer traps were deployed at 2.0-m intervals across the swash zone of a sheltered, microtidal sandy beach at Port Beach, Western Australia, over a 4-day period. During these trapping experiments, offshore significant wave heights were 0.3–0.5 m and wave periods were about 10 s. The average width of the uprush zone was 6.9 m and the average uprush duration was 5.9 s. Cross-shore distributions of sediment load for 70 uprush events reveal a maximum in sediment load landward of the base of the swash (at about 20% of swash width) during single events and a maximum closer to mid-swash (at about 40% of swash width) during multiple events characterized by swash interactions. Settling velocity distributions of trap samples during individual uprush events are similar to distributions found on the beach surface, with the lowest settling velocities (finest sediments) near the base of the swash zone and maximum settling velocities (coarsest sediments) around the mid-swash position. It was found that sediment transport during wave uprush occurs through two distinct mechanisms: (1) sediment entrainment during bore collapse seaward of the base of the swash zone and subsequent advection of this bore-entrained sediment up the beach by wave uprush; and (2) in situ sediment entrainment and transport induced by local shear stresses during wave uprush. Both mechanisms are considered important, but the first mechanism is considered most significant during the early stages of wave uprush when sediment is transported mainly in suspension, while the second mechanism is likely to dominate the mid- to later stages of wave uprush when sediment is transported mainly by sheet flow. The relative importance of the two mechanisms will vary between different beaches with the morphodynamic state of the beach (reflective versus dissipative) expected to play a major role.     

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.     

Validation of volume continuity method for estimation of cross-shore swash flow velocity

The use of flow volume continuity to estimate depth-averaged cross-shore swash flow velocity is validated using appropriate field data. Swash surface and beach face elevation were measured by a network of ultrasonic altimeters mounted through the swash zone of a sandy beach. Estimates of cross-shore flow velocity derived from these data compare well with concurrent measurements obtained from a vertical array of four electromagnetic current meters (EMCMs). Significantly, the continuity technique allows swash velocity to be estimated throughout the full swash cycle. This is not possible using fixed current meters and the new measurements indicate that swash velocity is more negatively skewed than previously observed.     

On low-frequency waves in the surf and swash

Low-frequency waves in the surf and swash zones on various beach slopes are discussed using numerical simulations. Simulated surface elevations of both primary waves and low-frequency waves across the surf zone were first compared with experimental data and good agreement found. Low-frequency wave characteristics are then discussed in terms of their physical nature and their relationship to the primary wave field on a series of sea bottom slopes. Unlike primary waves, low-frequency wave energy increases towards the shoreline. Low-frequency waves in the surf and swash are a function of incident waves and the sea bottom slope and hence the saturation level of the surf zone. Wave energy on a gently sloping beach is dominated by low-frequency waves while primary waves play a significant role on a steep beach. Low-frequency wave radiation from the surf zone on a given beach depends on primary wave frequency and beach slope. However, a very poor correlation was found between surf similarity parameter and low-frequency wave radiation.     

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.     

Kinematics of breaking tsunami wavefronts: A data set from large scale laboratory experiments

This paper provides an overview of a new large scale laboratory data set on the kinematics of breaking tsunami wavefronts. The aim of the experiments was to provide an open access data set for model testing, calibration and verification, with particular emphasis on fluid kinematics in the wave breaking and run-up (swash) zones. The experiments were performed over a composite slope in the tsunami wave basin at the O. H. Hinsdale Wave Research Laboratory at Oregon State University. Data for ten different wave conditions were collected, including non-breaking and breaking waves, and both shore breaks and fully developed long bores.Surface elevation and fluid kinematics were measured with a closely spaced array of surface piercing wave gauges, non-contact ultrasonic wave gauges and four 3-D side-looking Acoustic Doppler Velocimeters. The array was traversed from the nearshore (depth = 0.2 m) to the middle and upper run-up zone, providing kinematic data at 30 cross-shore locations. Video was also recorded from 4 cameras covering the propagation, breaking and run-up zones. Surface elevation, flow velocities and the wave maker displacement were also recorded to provide offshore boundary conditions.The experiments include conditions with wave heights up to 0.55 m, notional wave periods up to 20 s and run-up lengths of up to 15.2 m on a 1/30 slope. In terms of the slope in the shoaling and breaker zones, the data correspond to Iribarren numbers in the range of 0.26–5.6. Raw, calibrated and processed data are stored with open access within the OSU Tsunami Wave Basin Experiment Notebook, which provides full access to all the wave maker control signals, data, instrument coordinates, and processing and plotting software. This paper serves as an introduction to the data set, demonstrates data quality and provides an initial analysis of some key parameters that govern the impact of tsunami events, including run-up versus offshore wave conditions and nearshore bore height, the maximum inundation depths at the original shoreline position, and the time to maximum inundation depth and flow reversal. Examples of temporal and convective accelerations and turbulent flow components are also presented to illustrate further details of the kinematics.     

A numerical experiment on nearshore circulation in standing edge waves

The unsteady shallow-water vorticity equation dominating nearshore flow on a gently sloping plane beach has been solved by using the implicit finite difference technique under the assumption of constant viscosity over the flow field. The result of computation showed that pairs of nearshore circulation cells are generated through the nonlinear effect of flow in the boundary layer formed by the run-up movement of a standing edge wave along a shoreline and the paired cell has the spacing of half a wavelength of the edge wave. When the leaky-mode standing wave of Lamb with the same wave period as the edge wave and the wave crest parallel to a shoreline was superposed on the edge wave field, the alongshore spacing of circulation cell doubled and seaward flow in the cell concentrated in the narrow zone like a ‘rip current’. Although no effect of breaking waves is considered in the computation, such a mechanism may also generate some kinds of nearshore circulation systems observed in a sea.     

Shoreline motion in nonlinear shallow water coastal models

Different shoreline boundary conditions for numerical models of the Non-Linear Shallow Water Equations based on Godunov-type schemes are compared. The study focuses on the Peregrine and Williams [Peregrine, D.H., Williams, S.M., 2001. Swash overtopping a truncated plane beach. Journal of Fluid Mechanics 440, 391–399.] problem of a single bore collapsing on a slope. This is considered the best test to assess performances of the shoreline boundary treatments in terms of all the parameters of interest in swash zone modelling. Emphasis is given to the shoreline trajectory and flow velocity modelling. A mismatch of the velocity at the early stage of the motion is highlighted. Most of the tested techniques perform similarly in terms of maximum run-up, the backwash phase is critical in all cases. Starting from the Brocchini et al. [Brocchini, M., Bernetti, R., Mancinelli, A., Albertini, G., 2001. An efficient solver for nearshore flows based on the WAF method. Coastal Engineering 43(2), 105–129.] shoreline boundary treatment, a simple technique that improves the accuracy of velocity predictions is also developed. A sensitivity analysis of the domain resolution and the threshold value of the water depth that defines a wet cell is also presented.     

On the transport of suspended sediment by a swash event on a plane beach

We develop solutions for the transport of suspended sediment by a single swash event following the collapse of a bore on a plane beach, and we investigate the morphodynamical role that such transport may play. Although the intrinsic asymmetry between uprush and backwash velocities tends to encourage the export of sediment, we find that swash events may be effective in distributing across the swash zone much or all of the sediment mobilised by bore collapse; additionally, settling lag effects may promote a weak onshore movement of sediment. We quantify both effects in terms of the properties of the sediment and of the swash event, and comment on the relationship between our findings and recent field studies of swash zone sediment transport.     

Run-up of tsunamis and long waves in terms of surf-similarity

In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3–6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.