Application of the Delft3D System in the Modelling of Laboratory and Field Longshore Currents

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1 Application of the Delft3D System in the Modelling of Laboratory and Field Longshore Currents J.P. Gil, A. A. Pires-Silva, C. J. E. M. Fortes Abstract This study intended to test the Delft3D computational suite in the modelling of wave-driven longshore currents. Experiments conducted at the LSTF (Large-Scale Sediment Transport Facility, in Vicksburg, USA) were used to make a comparison between laboratory data and numerical results, regarding the spectral estimate of the significant wave height, variation of the mean water level and longshore currents (including vertical profiles). Also, an application of Delft3D to a field case (Cornélia beach, in Costa Caparica, Portugal) was carried out in order to predict the variables mentioned previously. 1. Introduction Breaking of wind-generated gravity waves is one of the major factors responsible for the longshore drift and, consequently, changes in beach morphology. After a rapid variation of wave height, energy is dissipated into the water column enhancing variation of the mean water level i.e. wave set-up/set-down. In case of an oblique incident wave field, longshore currents are generated, playing an important role in pollutant dispersion and sediment transport. Among the tools that allow a prediction of coastal behaviour, numerical models are used by coastal management teams in order to maintain the functionality and safety of the local coasts. In this study, the Delft3D computational suite was used so as to simulate wave-driven longshore currents inside the surf-zone. The hydrodynamic module (Delft3D-FLOW), which solves the RANS (Reynolds-Averaged Navier-Stokes) equations under the Boussinesq and shallow-water assumptions, was used together with the wave module (Delft3D- WAVE) that is responsible for the short wave generation and propagation in the nearshore areas. The two-way coupling between both modules allowed to take the effect of waves on currents and vice-versa into account (Deltares, 211). The Delft3D system integrates a three-dimensional (3D) approach that, in contrast to the two-dimensional (2D) approach, accounts for the vertical distribution of main kinematic variables. Moreover, the hydrodynamic module includes roller theory as a complement to the radiation stress theory, which could be described in general terms as delaying the transfer of wave energy into the water column by firstly converting it to a roller which travels with the wave at phase speed before being dissipated in the flow. In the first part of this study, a comparison between laboratory measurements and numerical results was carried out. The experimental data was obtained in the LSTF (Large-Scale Sediment Transport Facility), in Vicksburg, USA. This idealised case, modelled inside a finite-length basin, intended to reproduce the hydrodynamic phenomena that occur along the surf-zone of a long, straight and natural beach. Numerical data, including the spectral estimate of the significant wave height evolution, variation of the mean water level and longshore currents, is available along several cross-shore sections (Hamilton et al., 21; Hamilton and Ebersole, 21; Svendsen et al., 23). In a second stage, an application of the Delft3D system to a field case in the vicinity of Cornélia beach, in Costa da Caparica, western coast of Portugal, was also carried out so as to test the capability of the system to reproduce the distribution of the significant wave height and both longshore and cross-shore currents The WAVE module 2. Model description and the related theory This module is based on the third generation wave model SWAN (Simulating WAves Nearshore), which was developed by Delft University of Technology. The prognostic equation of the model is the wave action, N, balance equation Booij et al.(1999 apud Holthuijsen 27): N(σ fr, θ w ; x, y, t) t + c g,xn(σ fr, θ w ; x, y, t) x + c σn(σ fr, θ w ; x, y, t) σ fr = S(σ fr, θ w ; x, y, z) σ fr + c g,yn(σ fr, θ w ; x, y, t) y + c θn(σ fr, θ w ; x, y, t) θ w (1) Instituto Superior Técnico, ULisboa, Av. Rovisco Pais, 1, Lisboa, Portugal e-amil: joao.pedro.dos.santos.gil@ist.utl.pt Instituto Superior Técnico, ULisboa, Av. Rovisco Pais, 1, Lisboa, Portugal e-amil: aps@civil.ist.utl.pt Laboratório Nacional de Engenharia Civil, I.P., Av. do Brasil, 11, Lisboa, Portugal e-amil: jfortes@lnec.pt 1

2 in which σ fr is the relative frequency. It must be stressed that the wave action, N, is conserved in the presence of ambient currents and might be related with the wave energy, E w, according to: N(σ fr, θ w ) = E(ω, θ w) σ fr (2) The term presented in the right hand side of (1), S(σ, θ w ; x, y, z), represents the source and sink components: S(ω, θ w ) = S in (ω, θ w ) + S nl4 (ω, θ w ) + S nl3 (ω, θ w ) + S wcap (ω, θ w ) + S br (ω, θ w ) + S bot (ω, θ w ) (3) In this study, it is expected that the terms relative to the dissipation due to depth-induced breaking, S br, and due to bottom friction, S bot, will be the most relevant The FLOW module Governing equations This module is based on the Reynolds-Averaged Navier-Stokes (RANS) equations, which might be simplified for an incompressible fluid, under the Boussinesq approach and also with the shallow-water assumptions. According to Broomans (23), the momentum equations in both x- and ỹ- directions (σ coordinates) are given by (4) and (5), respectively, where h is the total water depth (h = d + η), d is the water depth according to a reference level and η is the variation of the water level: ũ t + ũũ x + ṽ ũ ỹ + w ũ h σ = 1 ( p ρ x + σ ) p + fṽ + Fx ν + 1 ( x σ h 2 σ ν t v ) ũ σ (4) ṽ t + ũ ṽ x + ṽ ṽ ỹ + w ṽ h σ = 1 ( p ρ x + σ ) p + fũ + Fy ν + 1 ( x σ h 2 σ ν t v ) ũ σ (5) where F ν x and F ν y represent the horizontal viscosity terms: F ν x = F ν y = ( x + σ x ( x + σ x ) ( τ xx + σ ỹ + σ ỹ ) ( τ xy + σ ỹ + σ ỹ ) τ xy (6) σ ) τ yy (7) σ and the Reynold stresses τ xx, τ xy and τ yy satisfy (under the Boussinesq approach): τ xy = ν t h τ xx = 2ν t h ( ũ x + σ ) ũ x σ ( ũ ỹ + σ ũ ỹ σ + ṽ x + σ ) ṽ x σ τ yy = 2ν t h ( ṽ ỹ + σ ) ṽ ỹ σ (8) (9) (1) In the previous equations, ũ, ṽ and w are the x-, ỹ- and z- Reynolds time-averaged components in σ-coordinates and ν t h, νt v are the horizontal and vertical turbulent viscosity, respectively. The vertical momentum equation is not presented here as it is reduced to the hydrostatic pressure distribution under the shallow-water assumption. Therefore, besides (4) and (5) one extra equation is needed in order to obtain the vertical velocity w, (Treffers, 29). This may be achieved by computing the continuity equation in σ-coordinates, (Broomans, 23): η t + hũ x + hṽ ỹ + w σ = (11) 2

3 The roller model Longuet-Higgins and Stewart (1962) proposed the concept of radiation stress, S x, which was defined as an excess of momentum due to the presence of waves: S xx = η h (p + ρu 2 )dz h (ρg( η z))dz (12) Moreover, increasing radiation stresses over an horizontal distance is equivalent to exerting an opposite force on the water body, (13). ( Sxx F xx = x + S ) yx y However, as Hsu et al. (26) showed, the computed cross-shore distribution of the longshore currents, based on the radiation stress concept, has its maximum too far offshore. Svendsen (1984) proposed that the energy released at breaking was first transferred to the energy of a roller which rode on the wave front with phase speed of the waves, c. Therefore, wave energy is firstly converted into turbulent kinetic energy before being dissipated into the water column, resulting in an onshore shift of the two hydrodynamic variables, the longshore currents and the variation of the mean water level, (Hsu et al., 26). Deltares (211) introduces the wave energy, E w, balance equation as part of the roller approach: (13) E w t + x (E wc g cos(θ w )) + y (E wc g sin(θ w )) = D w (14) In this equation, the short wave energy, E w, travels at a velocity equal to the wave group velocity, c g, and is dissipated, due to wave breaking, at a rate D w. Deltares (211) introduces a second equation as part of the roller approach, where the sink term D w of equation 14 is now a source a term, as the energy of the organized wave motion is converted into roller energy, Er (meaning turbulent energy): E r t + x (2E rc cos(θ w )) + y (2E rc sin(θ w )) = D w D r (15) 3.1. General description 3. Laboratory case: LSTF - Vicksburg, USA The Large-Scale Sediment Transport Facility (LSTF) was built at the U.S Army Engineer Research and Development Center s (ERDC) Coastal and Hydraulics laboratory (CHL), in Vicksburg, USA. The aim of the facility is to reproduce part of the processes which may occur in the surf zone of a long, straight and natural beach, inside a finite-length basin (Hamilton et al., 21). Also, it must be stressed that this study only focuses on the establishment of longshore currents on a fixed bed. The concrete beach has a longshore dimension of 31 m and a cross-shore dimension of 3 m, approximately. Furthermore, the main beach has a 1:3 slope followed by a toe with a 1:18 slope, which slopes down to the horizontal straight basin floor. The facility was designed so that, besides the wave generation a flow rate is continuously recirculated from the updrift lateral boundary to the downdrift lateral boundary Model settings Delft3D-WAVE A 1.8 m long and 3 m wide rectangular grid was generated in order to take into account the absence of lateral boundaries. This grid was extended 4 m upstream and 3 m downstream, in comparison with the physical domain, which measures, approximately, 3 m in the alongshore direction. This configuration allows the presence of an uniform wave field inside the hydrodynamic domain, which has the same alongshore length as the physical domain, as it will be seen in the next subsection. Also, each grid cell measures.8 m and.3 m in the longshore and cross-shore direction, respectively. 3

4 Delft3D-FLOW A rectangular grid with longshore dimension of 3.4 m and cross-shore dimension of 3 m was set up. In addition, each grid cell had.8 m and.3 m of length (longshore) and width(cross-shore), respectively. Two types of boundaries were used in the hydrodynamic module. Firstly, a Dirichlet type boundary (water level) was set for the offshore oriented boundary. This option can be justified by the fact that the water level is too far from the breaking line. Regarding the lateral boundaries, a Neumann type was chosen with a constant zero slope gradient of the mean water level, in the longshore direction. Measurements conducted in the laboratory facility showed that there was no gradient in the longshore direction as the variation of the mean water level was ±, 15cm (Hamilton et al., 21). The σ coordinate approach was used in the entire study, which means that each layer thickness is a percentage of the local water depth. In this particular case, the adopted layer distribution had a higher resolution near the bottom so as to accurately take the effect of the bottom friction on wave energy dissipation into account. The roller model includes several calibration parameters, including the angle of the roller at the wave front, β, and α, which is related to the precentage of energy dissipated at wave breaking. These parameters were adjusted in order to obtain the numerical distribution of the longshore currents that better represents the laboratory data. Regarding the breaker parameter γ b, the depth-varying formulation proposed by Ruessink et al. (23) was used: 3.3. Analysis of the results γ b =.76kh +.29 (16) Hm (m) η (cm) (a) Spectral estimate of the significant wave height, H m (b) Variation of the mean water, η. Lc(m/s) (c) Depth-averaged longshore currents, L C. Figure 1: Comparison between numerical and laboratory data measured inside the LSTF. The blue line represents the numerical data and the red sqaures display the experimental data Brief remarks The comparisons between numerical results and laboratory data made in this section are the result of adjusting numerical parameters, with a view to obtaining the most suitable cross-shore distribution of the spectral estimate of the significant wave height, variation of the mean water level and longshore currents (including vertical profiles) Depth-averaged cross-shore distribution As shown in Figure 1a, the computed H m is fairly similar to the values measured in the laboratory with a slight underestimation at the offshore limit of the surf zone. 4

5 Although the general trend is well represented by the model, the computed mean water level clearly overestimates LSTF data, Figure 1b, particularly at the seaward part of the surf-zone where wave set-down was found to occur. This might be explained by a possible excess of energy dissipated by the roller into the water column. Finally, the distribution of the long-shore currents are well represented by the model, however there is an overestimation of this physical parameter in the offshore and nearshore parts of the surf-zone, Figure 1c. The overestimation of this variable in the offshore part of the surf-zone might be related to the recirculation currents, which is an undesirable effect of laboratory modelling and have opposite direction in comparison with the longshore currents generated inside the surf-zone (a) y = 1.5m (b) y = 13.88m (c) y = 16.12m (d) y = 18.48m (e) y = 19.88m (f) y = (g) y = 22.88m (h) y = 24.28m (i) y = 25.88m Figure 2: Vertical structure of the longshore currents for the nine ADVs, from the most offshore (y = 1.5 m) to the most nearshore (y = m). The blue line displays the numerical results and the red squares represent the experimental measurements Vertical structure of the longshore and cross-shore currents In Figure 2 it is shown that the numerical results of the three most offshore ADVs are slightly overestimated by the model, in opposition to the other six ADVs, for which the laboratory measurement are overestimated. However, in both cases the numerical model well simulates the general trend of the measured data. Moreover, the most offshore ADV (y = 1.5 m) shows the effect of the recirculation currents, which are known to have opposite direction compared with the longshore currents generated inside the surf-zone. As mentioned, these currents are an undesired effect of the physical modelling inside a laboratory facility. Regarding the six closest ADVs to the shore, Delft3D is able to reproduce the general trend of the laboratory data. However, the model results overestimate the laboratory measurements for the 5

6 most nearshore instrument, in contrast with the five other ADVs (y = mtoy = m), for which the measured data is generally underestimated. Although the general trend of the vertical structure of the cross-shore currents, Figure 3, is well represented by the model, this vertical structure was found not to be the most realistic as the curvature of the laboratory data is not shown. This conclusion is particularly true for the two most seaward ADVs, where recirculation currents are known to be present. Also, it is concluded that the experimental measurements were underestimated by the model simulations for all the other seven ADVs (y = m to y = m) (a) y = 1.5 m (b) y = m (c) y = m (d) y = m (e) y = m (f) y = m (g) y = m (h) y = m (i) y = m Figure 3: Vertical structure of the cross-shore currents for the nine ADVs, from the most offshore (y = 1.5 m) to the most nearshore(y = m). The blue line displays the numerical results and the red squares represent the experimental measurements Introduction 4. Field case: Cornélia beach - Costa da Caparica, Portugal A field campaign, BRISA II, was carried out, between the 11 th and the 15 th of May, 21, in the vicinity of Cornélia beach, 2 m south of Saúde beach, in Costa da Caparica, west coast of Portugal. BRISA II was conducted by LNEC (Laboratório Nacional de Engenharia Civil), UA (Universidade de Aveiro) and UALG (Universidade do Algarve), in the scope of Projecto BRISA (Breaking Waves and Induced SAnd Transport), which was supported by Fundação para a Ciência e a Tecnologia (FCT) (BRISA, 21b,a). 6

7 The main goal of this campaign was to obtain hydrodynamic and morphological data, in order to test and validate numerical models, study breaking dynamics and its influence on sediment transport. Several types of instruments attached to H-profiles were used in the acquisition of field data, such as pressure transducers (PT), electromagnetic current meters (ECM) and acoustic Doppler velocimeters (ADV). Free-surface elevation (measured by PTs) and current velocity measurements, in both horizontal and vertical directions (measured by ECMs and ADVs), were obtained along a cross-shore profile inside the surf-zone. Furthermore, a pressure transducer was positioned, roughly, 5 m away from the shore line, in order to measure the free-surface elevation in the deepest waters of the domain (Rocha, 211) Field data Bathymetry A bathymetric survey was carried out during the ebb tide of the first day of the campaign. The survey consisted in one longshore and sixteen cross-shore transects, the last separated by 5 m from each one. During the ebb tide of the following day, a topographic survey was conducted along nine cross-shore transects and the H-shaped profiles were positioned along one of those nine cross-shore transects..7 PT1 PT Hm (m) /5 8:3 13/5 8:3 14/5 8:3 (a) Spectral estimate of the significant wave height, H m, along periods of 3 minute duration. Data collected by PT (postitioned offshore) and PT1 (positioned inside the surf-zone). 15 ECM1 ADV_UALG 3 ECM1 ADV_UALG VL(cm/s) 7.5 VC(cm/s) 15 12/5 8:3 13/5 8:3 14/5 8:3 (b) Mean of the longshore currents along 3 minute periods, v C. Data collected by ECM1 LNEC and ADV UALG (both positioned inside the surf-zone) /5 8:3 13/5 8:3 14/5 8:3 (c) Mean of the cross-shore currents along 3 minute periods, v C. Data collected by ECM1 LNEC and ADV UALG (both positioned inside the surf-zone). Figure 4: Processed field data regarding the spectral estimate of the significant wave height, variation of the mean water level and longshore currents measured at a specific height of the water column Processing data collected by the instruments In order to compare measured field data with numerical results, field data was divided in several 3 minute duration periods over the entire field campaign. The goal of this procedure is to obtain stationary processes and hence obtain the spectral estimate of the significant wave height, H m, and the average value of longshore and cross-shore currents, v L and v C respectively, along those periods, which might be considered stationary. As an example, the spectral analysis carried out for PT and PT1 is shown in Figure 4a. Both time series suggest that, from the 12 th of May until the nighttime tide of the 14 th of May, the significant wave height, H m, has no relevant changes, in contrast with the daytime tide of the 14 th of May during which a new wave field entered the domain with a greater significant wave height. Also, the higher values of H m measured by PT1 (positioned inside the surfzone) in comparison with PT (positioned offshore) show the shoalling effect in the nearshore waters. The mean longshore and cross-shore currents, measured at a specific height of the water colmun, are presented in Figure 4b and Figure 4c, respectively. The distribution of the longshore currents, Figure 4b, confirms the presence of 7

8 two different wave fields, the second starting after the nighttime high-tide of the 14th of May with a higher H m, in comparison with the first. Under the influence of the first wave field, longshore currents have no significant activity, as its magnitude remains close to cm/s for the first three high-tides of the campaign. Also, the similar values collected by ECM1 LNEC and ADV UALG, during the nighttime high-tide of the 14 th of May, might be explained due to the short distance that separates both of them, 2 m. Finally, the difference between the currents measured during the daytime tide of the 14 th of May reflect the higher level reached by the daytime high-tide of the 14 th of May in comparison with the previous high-tide, which ended up positioning ECM1 LNEC in a more offfshore part of the surf-zone, where weaker longshore currents are felt Model settings Delft3D-WAVE In the same way as done in the laboratory study case, the incident wave field was imposed along the offshore boundary, oriended SW. A high-resolution grid of 1 m and 5 m in the longshore and cross-shore directions was set up in the region of interest, which measures 8 m and 7 m in the longshore and cross-shore directions, respectively. In the same way as it was done in the laboratory study case, the wave grid had to be extended 2 m updrift and downdrift the real domain. This was achieved by setting up a second coarser grid, with cells measuring 2 m in both long- and cross-shore directions. The coarser grid was also extended offshore, which will be discussed in the following subsection Delft3D-FLOW In comparison to the methodology described in the previous chapter, it was necessary to take into account the variation of bathymetry near the lateral boundaries (Neumann type). Therefore, the hydrodynamic grid was also extended 1 m updrift and downdrift the real domain in order to create a uniform bathymetry near the Neumann boundaries, which impose an alongshore gradient of the water level, η x =. Moreover, it was also necessary to define the water level in the offshore boundary (Dirichlet type), in the same way as done in the laboratory case. However, as mentioned before, the water level was not measured during the field campaign and hence it was necessary to extend the domain 5 m offshore, with a straight bottom, so as to guarantee that the water level condition (which equals the tidal level) is far from the breaking zone and no set-up/set-down occurs. Also, a logarithmic distribution of 15 horizontal layers was used so as to take energy dissipation due to bottom friction into account. In comparison with the laboratory study case, higher values of the background horizontal eddy viscosity, ν back H = 1.2 m 2 /s, were indispensable so as to provide valid results, which is in agreement with the value used by Hsu et al. (28) for a field application. Increasing this parameter was found to lead to a stationary field of currents, after 6 min of computation, whereas the cross-shore distribution tended to be more uniform. Consequently, it was necessary to reach a optimal trade-off between those two effects of the horizontal background viscosity Analysis of the results Computational runs were carried out for three specific periods, with one hour spacing between two consecutive periods. Figure 5 suggests that the spectral estimate of the significant wave height is well represented by the model, particularly for the first two periods, where no significant overestimation or underestimation is noticed. Regarding the last period, 4:3, there is a slight overestimation of the field data inside the breaking zone. Also, in all the three figures it is clear that the cross-shore distribution of H m follows the bottom profile, as it was expected. The direction of the waves used to force the wave module was obtained after carrying out a sensitivity analysis, as there was no field data regarding this physical parameter. As it can be seen from Figure 6, the computed cross-shore distribution of the longshore currents well-reproduces the general trend of the field data for all the three periods, with a slight underestimation of the value collected by ADV UALG (second red square, from the left to the right) for the first and third periods, Figure 6a and 6c, respectively. Furthermore, it is also clear that the distribution of the longshore currents is asymptotically tending to zero in the offshore part of the domain, where there is no depth-induced wave breaking occurring. Figures 7b and 7c suggest that the distribution of the cross-shore currents is excessively directed towards the shore although the qualitative trend is well described. Regarding the first period, Figure 7a, the model seems to well predict the general trend of the currents, despite marginally overestimating the field data. However, the system seems to generate unrealistic values, for both long- and cross-shore currents, at shallow waters. The same conclusion was drawn by Hsu et al. (26), who suggests that, at shallow waters, the amount of dissipated roller energy is too high, resulting in too high velocities. The same authors found that increasing the threshold depth in relation to its default value, from.1 m to.2 m, led to a reduction of the peak near the shoreline without affecting the distribution of the currents 8

9 far from the shoreline. This might be explained by the fact that roller stresses are stopped at a depth of two times de threshold depth. In the present work, increasing the threshold depth was also found to lead to a reduction of the current peak near the shoreline..6.6 Hm(m).4.2 Hm(m) (a) 14 th of May, 2: (b) 14 th of May, 3:3.6 Hm(m) (c) 14 th of May, 2:3. Figure 5: Cross-shore distribution of the H m for the three analysed periods. The blue line displays the numerical results and the red squares represent the experimental measurements. 1 5 vl(cm/s) 1 vl(cm/s) (a) 14 th of May, 2: (b) 14 th of May, 3:3 1 vl(cm/s) (c) 14 th of May, 2:3. Figure 6: Cross-shore distribution of the longshore currents for the three analysed periods. The blue line displays the numerical results and the red squares represent the experimental measurements. 9

10 vc(cm/s) (a) 14 th of May, 2:3. vc(cm/s) (b) 14 th of May, 3:3 vc(cm/s) (c) 14 th of May, 2:3. Figure 7: Cross-shore distribution of the cross-shore currents for the three analysed periods. The blue line displays the numerical results and the red squares represent the experimental measurements. 5. Acknowledgements The fourth chapter of this study was developed within the scope of the project BRISA (BReaking waves and Induced SAnd Transport), PTDC/ECM/67411/26, financially supported by Fundação para a Ciência e Tecnologia. 6. Conclusions The hydrodynamic module Delft3D-FLOW is based on the RANS (Reynolds-Averaged Navier-Stokes) equations, under the Boussinesq and shallow-water assumptions. Furthermore, the theory of radiation stress, proposed by Longuet-Higgins and Stewart (1962), is complemented with the roller theory, which was found to provide good results regarding the spectral estimate of the significant wave height, variation of the mean water level and longshore currents. In the second chapter, it should be stressed out that the discrepancies between laboratory and numerical data might be due to, not only, numerical errors but also due to physical modelling errors. The modelling technique included a recirculation system, powered by pumps and turbines, and a tuning process so as to define the most proper distribution of the longshore currents. In both laboratory a field study cases, the model was capable of describing the general trend of the distribution of the spectral estimate of significant wave height and both distributions of the longshore and cross-shore currents. Regarding the variation of the mean water level, this variable was qualitatively well simulated by the model in the laboratory study case. References Booij, N., Ris, R., and Holthuijsen, L. (1999). A third-generation wave model for coastal regions. Journal of Geophysical Research, 14: BRISA (21a). Relatório da Campanha BRISA II, Costa da Caparica, 11 a 15 de Maio de 21. Technical Report 3/21, Laboratório Nacional de Engenharia Civil. BRISA (21b). Relatório de Campo - Universidade do Algarve, Projecto BRISA - Campanha Costa da Caparica (Praia da Saúde) (11 a 15 de Maio de 21). Technical report, Universidade do Algarve. Broomans, P. (23). Numerical Accuracy in Solutions of the Shallow-Water Equations. Master of science dissertation, Technical University of Delft. 1

11 Deltares (211). Delft3D-FLOW. Simulation of multi-dimensional hydrodynamic flows and transport phenomena, including sediments. Delft. Hamilton, D. G. and Ebersole, B. A. (21). Establishing uniform longshore currents in a large-scale sediment transport facility. Coastal Engineering, 42: Hamilton, D. G., Ebersole, B. A. E., Smith, E. R., and Wang, P. (21). Development of a Large-Scale Laboratory Facility for Sediment Transport Research. US Aramy Corps of Engineers, Coastal and Hydraulics Laboratory, U.S Army Engineer Research and Development Center, 399 Halls Ferry Road, Vicksburg, MS , 1st edition. Holthuijsen, L. H. (27). Waves in Oceanic and Coastal Waters. Cambridge University Press. Hsu, Y. L., Dykes, J. D., Allard, R. A., and Kaihatu, J. M. (26). Evaluation of Delft3D Performance in Nearshore Flows. Technical Report NRL/MR/ , Naval Research Laboratory. Hsu, Y. L., Dykes, J. D., Allard, R. A., and Wang, D. W. (28). Validation Test Report for Delft3D. Technical Report NRL/MR/ , Naval Research Laboratory. Longuet-Higgins, M. S. and Stewart, R. W. (1962). Radiation stress and mass transport in gravity waves, with applications to surf beats. Journal of Fluid Mechanics, 13: Rocha, M. V. (211). Numerical modelling of groin impact on nearshore hydrodynamics. Master of science dissertation, Universidade de Aveiro. Svendsen, I. (1984). Wave heights and set-up in a surf zone. Coastal Engineering, 8: Svendsen, I. A., Qin, W., and A.Ebersole, B. (23). Modelling waves and currents at the LSTF and other laboratory facilities. Coastal Engineering, 5: Treffers, R. (29). Wave-Driven Longshore Currents in the Surfzone. Master of Science dissertation, Delft University of Technology. 11