Process-based model for nearshore hydrodynamics, sediment transport and morphological evolution in the surf and swash zones

Hydrodynamics and sediment transport in the nearshore zone were modeled numerically taking into account turbulent unsteady flow. The flow field was computed using the Reynolds Averaged Navier–Stokes equations with a k–ε turbulence closure model, while the free surface was tracked using the Volume-Of-Fluid technique. This hydrodynamical model was supplemented with a cross-shore sediment transport formula to calculate profile changes and sediment transport in the surf and swash zones. Based on the numerical solutions, flow characteristics and the effects of breaking waves on sediment transport were studied. The main characteristic of breaking waves, i.e. the instantaneous sediment transport rate, was investigated numerically, as was the spatial distribution of time-averaged sediment transport rates for different grain sizes. The analysis included an evaluation of different values of the wave friction factor and an empirical constant characterizing the uprush and backwash. It was found that the uprush induces a larger instantaneous transport rate than the backwash, indicating that the uprush is more important for sediment transport than the backwash. The results of the present model are in reasonable agreement with other numerical and physical models of nearshore hydrodynamics. The model was found to predict well cross-shore sediment transport and thus it provides a tool for predicting beach morphology change.     

A wave-resolving model for nearshore suspended sediment transport

This paper presents a wave-resolving sediment transport model, which is capable of simulating sediment suspension in the field-scale surf zone. The surf zone hydrodynamics is modeled by the non-hydrostatic model NHWAVE (Ma et al., 2012). The turbulent flow and suspended sediment are simulated in a coupled manner. Three effects of suspended sediment on turbulent flow field are considered: (1) baroclinic forcing effect; (2) turbulence damping effect and (3) bottom boundary layer effect. Through the validation with the laboratory measurements of suspended sediment under nonbreaking skewed waves and surfzone breaking waves, we demonstrate that the model can reasonably predict wave-averaged sediment profiles. The model is then utilized to simulate a rip current field experiment (RCEX) and nearshore suspended sediment transport. The offshore sediment transport by rip currents is captured by the model. The effects of suspended sediment on self-suspension are also investigated. The turbulence damping and bottom boundary layer effects are significant on sediment suspension. The suspended sediment creates a stably stratified water column, damping fluid turbulence and reducing turbulent diffusivity. The suspension of sediment also produces a stably stratified bottom boundary layer. Thus, the drag coefficient and bottom shear stress are reduced, causing less sediment pickup from the bottom. The cross-shore suspended sediment flux is analyzed as well. The mean Eulerian suspended sediment flux is shoreward outside the surf zone, while it is seaward in the surf 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.     

Numerical study on vertical structures of undertow inside and outside the surf zone

Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and t...     

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.     

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.     

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.     

Tidal asymmetry in suspended sand transport on a macrotidal intermediate beach

Time-series of nearbed horizontal flow velocities and suspended sediment concentrations obtained from a colocated electromagnetic current meter (EMCM) and optical backscatter sensor (OBS), respectively, are used to examine the relative importance of steady and fluctuating components to the total sediment transport over a full tidal cycle on a macrotidal, intermediate beach (Spurn Head, UK). Fluctuating sediment fluxes are decomposed into gravity and infragravity contributions using co-spectral techniques. The relative importance of the oscillatory (gravity and infragravity) and steady (mean) transport components to the total sediment transport is analysed throughout the tidal cycle.

A continuum of 34 discrete suspended sediment-cross-shore velocity co-spectra are computed over a full tidal cycle for the OBS and EMCM measurements 0.10 m above the bed. These net transport spectra vary greatly both with cross-shore location and tidal state. In particular, a marked asymmetry in transport processes is evident between the flood and ebb tides, with high levels of sediment resuspension and transport occurring on the ebbing tide approximately two hours after high water (just seaward of the breakpoint). At this time the dominant transport was directed offshore (co-spectral peak, 0.04 kg/m²/s) at incident wave frequency.

Typical patterns are observed in transport spectra outside the surf zone and within the inner surf zone. Outside the narrow surf zone cross-shore transport spectra show weak offshore transport (co-spectral peak = 0.002 kg/m²/s) associated with bound long waves and stronger onshore transport (co-spectral peak = 0.006 kg/m²/s) at incident wave frequencies. Conversely, co-spectra computed within the inner surf zone show the offshore sediment fluxes (spectral peak = 0.010 kg/m²/s) at infragravity frequencies to be greater in magnitude than the corresponding onshore transport (co-spectral peak = 0.008 kg/m²/s) occurring at incident wave frequencies.     

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.     

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.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

Wave driven alongshore sediment transport and stability of the Dutch coastline

The wave-driven alongshore sediment transport is commonly supposed to smooth out the irregularities on the coastline. However, it has been shown that waves approaching the coast with a high angle with respect the shore-normal can reverse that tendency and cause the rectilinear coast to be unstable [Ashton, A., Murray, A.B., Arnault, O., 2001. Formation of coastline features by large-scale instabilities induced by high-angle waves. Nature 414, 296–300; Falqués, A., Calvete, D., 2005. Large scale dynamics of sandy coastlines. Diffusivity and instability. J. Geophys. Res. 110, doi:10.1029/2004JC002587]. The extended one-line coastline model presented in the latter paper is here applied to investigate the stability of the Dutch coast. The main aim is testing the hypothesis that the shoreline sand waves observed along this coast could be generated by such an instability. It is found that the Dutch coast has potential for instability. This is most prominent on the Holland coast, followed by the Delta coast and is very weak on the Wadden coast. Whether the instability actually occurs or not depends on the cross-shore bathymetric profile of the shoreline waves. Under the sensible assumption that the bathymetric perturbation is just a shift of the equilibrium beach profile, the Dutch coast is stable. In this case, the mean annual coastline diffusivity is evaluated and it is found to be typically about 0.010–0.015 m² s^− 1, that is, roughly smaller by a factor 2 than that predicted by the traditional one-line model. However, the Dutch coast may be unstable with respect to coastline waves with a maximum bathymetric signal at a few hundred meters from the coast. This is shown in one case where the shoals associated with the sand wave are inside the surf zone during moderate storm waves. Thus the sand waves could result from the cross-shore redistribution of the sand associated with an alongshore series of shoals and bed depressions generated by the alongshore transport in the surf zone. While the generation or not of such shoreline waves by this instability strongly depends on their profile, its propagation once they have been created is less sensitive and is well reproduced by the present model. It is explained why the propagation is to the NE along the Delta and Wadden coasts, why it is faster on the latter and why on the Holland coast there is no clear propagation direction.     

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.     

Surf zone dynamics simulated by a Boussinesq type model. Part II: surf beat and swash oscillations for wave groups and irregular waves

This is the second of three papers on the modelling of various types of surf zone phenomena. In the first paper the general model was described and it was applied to study cross-shore motion of regular waves in the surf zone. In this paper, part II, we consider the cross-shore motion of wave groups and irregular waves with emphasis on shoaling, breaking and runup as well as the generation of surf beats. These phenomena are investigated numerically by using a time-domain Boussinesq type model, which resolves the primary wave motion as well as the long waves. As compared with the classical Boussinesq equations, the equations adopted here allow for improved linear dispersion characteristics and wave breaking is modelled by using a roller concept for spilling breakers. The swash zone is included by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. Mutual interaction between short waves and long waves is inherent in the model. This allows, for example, for a general exchange of energy between triads rather than a simple one-way forcing of bound waves and for a substantial modification of bore celerities in the swash zone due to the presence of long waves. The model study is based mainly on incident bichromatic wave groups considering a range of mean frequencies, group frequencies, modulation rates, sea bed slopes and surf similarity parameters. Additionally, two cases of incident irregular waves are studied. The model results presented include transformation of surface elevations during shoaling, breaking and runup and the resulting shoreline oscillations. The low frequency motion induced by the primary-wave groups is determined at the shoreline and outside the surf zone by low-pass filtering and subsequent division into incident bound and free components and reflected free components. The model results are compared with laboratory experiments from the literature and the agreement is generally found to be very good. Finally the paper includes special details from the breaker model: time and space trajectories of surface rollers revealing the breakpoint oscillation and the speed of bores; envelopes of low-pass filtered radiation stress and surface elevation; sensitivity of surf beat to group frequency, modulation rate and bottom slope is investigated. Part III of this work (Sørensen et al., 1998) presents nearshore circulations induced by the breaking of unidirectional and multi-directional waves.     

Practical sand transport formula for non-breaking waves and currents

Many existing practical sand transport formulae for the coastal marine environment are restricted to a limited range of hydrodynamic and sand conditions. This paper presents a new practical formula for net sand transport induced by non-breaking waves and currents. The formula is especially developed for cross-shore sand transport under wave-dominated conditions and is based on the semi-unsteady, half wave-cycle concept, with bed shear stress as the main forcing parameter. Unsteady phase-lag effects between velocities and concentrations, which are especially important for rippled bed and fine sand sheet-flow conditions, are accounted for through parameterisations. Recently-recognised effects on the net transport rate related to flow acceleration skewness and progressive surface waves are also included. To account for the latter, the formula includes the effects of boundary layer streaming and advection effects which occur under real waves, but not in oscillatory tunnel flows. The formula is developed using a database of 226 net transport rate measurements from large-scale oscillatory flow tunnels and a large wave flume, covering a wide range of full-scale flow conditions and uniform and graded sands with median diameter ranging from 0.13 mm to 0.54 mm. Good overall agreement is obtained between observed and predicted net transport rates with 78% of the predictions falling within a factor 2 of the measurements. For several distinctly different conditions, the behaviour of the net transport with increasing flow strength agrees well with observations, indicating that the most important transport processes in both the rippled bed and sheet flow regime are well captured by the formula. However, for some flow conditions good quantitative agreement could only be obtained by introducing separate calibration parameters. The new formula has been validated against independent net transport rate data for oscillatory flow conditions and steady flow conditions.     

Predictability of wave-induced net sediment transport using the conventional 1DV RANS diffusion model

Based on a large database of laboratory experiments, the predictability of the conventional one-dimensional vertical Reynolds-averaged Navier–Stokes (RANS) diffusion model is systematically investigated with respect to wave-induced net sediment transport. The predicted net sediment transport rates are compared with the measured data of 176 physical experiments in wave flumes and oscillating water tunnels, covering a wide range of wave conditions (surface, skewed, and asymmetric waves with and without currents), sediment conditions (fine, medium, and coarse sands with median grain diameters ranging from 0.13 to 0.97 mm) and bed forms (flat beds and rippled beds), corresponding to various sediment dynamic regions in the near-shore area. Comparisons show that the majority (73 %) of predictions on a flat bed are within a factor 2 of the measurements. The model behaves much better for medium/coarse sand than for fine sand. The model generally underpredicts the transport rates beneath asymmetric waves and overpredicts the fine sand transport beneath skewed waves. Nevertheless, the model behaves well in reproducing the transport rates under surface waves. A detailed discussion and a quantitative measure of the overall model performance are made. The poor model predictability for fine sand cases is mainly due to the underestimation of unsteady phase-lag effect. It is revealed that the model predictability can be significantly improved by implementing alternative bedload formulas and incorporating more physical processes (mobile-bed roughness, hindered settling, and turbulence damping).