Three-dimensional structure of wave-induced momentum flux in irrotational waves in combined shoaling-refraction conditions

In the paper, the three-dimensional structure of the wave-induced momentum flux in irrotational waves propagating over a two-dimensional, irregular bathymetry is analyzed. The expansion method developed by de Vriend and Kitou [de Vriend, H.J., Kitou, N., 1990a. Incorporation of wave effects in a 3D hydrostatic mean current model. Delft Hydraulics Report H-1295. de Vriend, H.J., Kitou, N., 1990b. Incorporation of wave effects in a 3D hydrostatic mean current model. Proc. 22nd Int. Coast. Eng. Conf. ASCE, 1005–1018.] for unidirectional waves has been extended to derive expressions for velocity components in three-dimensional waves over sloping bottom. The vertical wave-induced momentum flux resulting from this solution has been shown to be vertically-varying (contrary to the 2D-V case) and to act as a counterbalance for the vertical variability of the other wave forcing terms in the momentum equations. Thus, the total wave forcing remains depth-invariant, but—contrary to the ‘traditional’ solution based on the radiation stress concept—it does not depend explicitly on the direction of wave propagation and is a simple function of gradients of wave energy and water depth only. One of the most important consequences of this fact is the lack of the longshore-current-generating force in the case of non-dissipative waves approaching a shore with a bottom profile uniform in the along-shore direction. To illustrate the meaning of the new solution, the wave forcing due to waves approaching a barred beach has been analysed in detail. Also, the present solution has been shown to give the same results as the one obtained by extending of the approach by Rivero and Arcilla [Rivero, F.J., Arcilla, A.S., 1995. On the vertical distribution of 〈ũw˜〉. Coast. Eng. 25, 137–152.] to three dimensions.     

Wave-induced sediment transport and onshore sandbar migration

The 25-m onshore migration of a nearshore sandbar observed over a 5-day period near Duck, NC, is simulated with a simplified, computationally efficient, wave-resolving single-phase model. The modeled sediment transport is assumed to occur close to the seabed and to be in phase with the bottom stress. Neglected intergranular stresses and fluid–granular interactions, likely important in concentrated flow, are compensated for with an elevated (relative to that appropriate for a clear fluid) model roughness height that gives the best fit to the observed bar migration. Model results suggest that when mean-current-induced transport is small, wave-induced transport leads to the observed onshore bar migration. Based on the results from the simplified phase-resolving model, a wave-averaged, energetics-type model (e.g., only moments of the near-bottom velocity field are required) with different friction factors for oscillatory and mean flows is developed that also predicts the observed bar migration. Although the assumptions underlying the models differ, the similarity of model results precludes determination of the dominant mechanisms of sediment transport during onshore bar migration.     

基于间断有限元方法的三维近岸波生流数值模型建立

在三维水动力模型中引入三维辐射应力,水滚影响以及波浪附加紊动效应,并基于间断有限元方法建立了非结构化网格三维波生流数值模型。采用实验室内斜坡地形条件下正向入射波在破波带附近产生的近底回流和斜向入射波产生的沿岸流对模型进行了验证。结果表明,计算值与实测值吻合程度较好,该模型可以较好地描述三维近岸波生流。     

Random wave-induced scour at the trunk section of a breakwater

This paper provides a stochastic method by which the random wave-induced scour depth at the trunk section of vertical-wall and rubble-mound breakwaters can be derived. Here the formulas for regular wave-induced scour depth provided by Xie [Xie, S.L., 1981. Scouring patterns in front of vertical breakwaters and their influence on the stability of the foundations of the breakwaters. Report. Department of Civil Engineering, Delft University of Technology, Delft, The Netherlands, September, 61 pp.] for vertical-wall breakwater and Sumer and Fredsøe [Sumer, B.M., Fredsøe, J., 2000. Experimental study of 2D scour and its protection at a rubble-mound breakwater. Coast. Eng. 40, 59–87] for rubble-mound breakwater are used. These formulas are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the random wave-induced scour depth. Comparisons are made between the present method and the Sumer and Fredsøe [Sumer, B.M., Fredsøe, J., 2000. Experimental study of 2D scour and its protection at a rubble-mound breakwater. Coast. Eng. 40, 59–87.] random wave scour data for rubble-mound breakwater, as well as the Hughes and Fowler [Hughes, S.A., Fowler, J.A., 1991. Wave-induced scour predictions at vertical walls. ASCE Proc. Conf. Coastal Sediments vol. 91, 1886–1899] random wave scour data and formula for vertical-wall breakwater. A tentative approach to random wave-induced scour at a vertical impermeable submerged breakwater is also suggested.     

Numerical Modeling of the Undertow Structure and Sandbar Migration in the Surfzone

A process-based 3D numerical model for surfzone hydrodynamics and beach evolution was established. Comparisons between the experimental data and model results proved that the model could effectively describe the hydrodynamics, sediment transport feature and sandbar migration process in the surfzone with satisfactory precision. A series of numerical simulations on the wave breaking and shoaling up to a barred beach were carried out based on the model system. Analyzed from the model results, the wave-induced current system in the surfzone consists of two major processes, which are the phase-averaged undertow caused by wave breaking and the net drift caused by both of the nonlinear wave motion and surface roller effect. When storm waves come to the barred beach, the strong offshore undertow along the beach suppresses the onshore net drift, making the initial sandbar migrate to the seaside. Under the condition of calm wave environment, both the undertow and net drift flow to the shoreline at the offshore side of the sandbar, and then push the initial sandbar to the shoreline. The consideration of surface roller has significant impact on the modeling results of the sandbar migration. As the roller transfer rate increases, the sandbar moves onshore especially under the storm wave condition.     

Quasi-three-dimensional modelling of the morphology of longshore bars

A morphological quasi-three-dimensional (Q3D) area model for barred coasts has been developed. The model combines a two-dimensional depth integrated model for wave-driven currents with a model for undertow circulation currents. The combined model makes a simultaneous simulation of the bar-forming processes associated with the undertow and the horizontal wave-driven circulation currents, which may cause instabilities of the bar and the formation of rip channels. Situations with normal and oblique wave incidence are considered. Compared to the depth integrated approach the Q3D model produces less pronounced alongshore irregularities for obliquely incident waves. For normal incident waves the Q3D model produces a crescentic bar while the depth integrated model predicts almost straight sections of the bar interrupted by rip channels. The sensitivity to variation of wave angle and beach slope is further investigated.     

Numerical Simulation of the Three-Dimensional Wave-Induced Currents on Unstructured Grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three-dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.     

A phase-resolving cross shore sediment transport model for beach profile evolution

A phase-resolving wave transformation module is combined with an intra-wave sediment transport module to calculate the on-/offshore sediment transport rates. The wave module is based on the Boussinesq equations extended into the surf zone. The vertical variation of the mean undertow and the intra-wave sediment concentrations are calculated. The net sediment transport rates are calculated, and the equation for conservation of sediment is solved to predict the beach profile evolution. The results of the present paper showed that the undertow contribution to the sediment transport rates is not dominating in all parts of the surf zone, even for eroding beaches, suggesting that other contributions should not be neglected. The present model also showed that for the same offshore wave energy the time series of the oscillatory motion is important and that the effect of wave groups cannot be disregarded.     

The vertical structure of combined wave–current flow

A simple numerical model, based on the Reynolds stress equations and k–ε turbulence closure scheme, is developed for the coastal wave and current bottom boundary layer. The current friction velocity is introduced to account for the effect of currents on waves. The implicit Crank–Nicolson finite difference method discretizes the governing equations. Vertical changing step grids with the constant ratio for two adjacent spatial steps are used together with the equal time steps in the modeling. Vertical profiles of mean current velocity and wave velocity amplitude are obtained. These modeled results are compared with the laboratory experimental data of Van Doorn [1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands]. It has been shown that modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands) mean velocity profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands) wave velocity amplitude profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled wave velocity amplitudes are in good agreement with the laboratory experimental data of Van Doorn [1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands].     

Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications

Regional Ocean Modeling System (ROMS v 3.0), a three-dimensional numerical ocean model, was previously enhanced for shallow water applications by including wave-induced radiation stress forcing provided through coupling to wave propagation models (SWAN, REF/DIF). This enhancement made it suitable for surf zone applications as demonstrated using examples of obliquely incident waves on a planar beach and rip current formation in longshore bar trough morphology (Haas and Warner, 2009). In this contribution, we present an update to the coupled model which implements a wave roller model and also a modified method of the radiation stress term based on Mellor (2008, 2011a,b,in press) that includes a vertical distribution which better simulates non-conservative (i.e., wave breaking) processes and appears to be more appropriate for sigma coordinates in very shallow waters where wave breaking conditions dominate. The improvements of the modified model are shown through simulations of several cases that include: (a) obliquely incident spectral waves on a planar beach; (b) obliquely incident spectral waves on a natural barred beach (DUCK'94 experiment); (c) alongshore variable offshore wave forcing on a planar beach; (d) alongshore varying bathymetry with constant offshore wave forcing; and (e) nearshore barred morphology with rip-channels. Quantitative and qualitative comparisons to previous analytical, numerical, laboratory studies and field measurements show that the modified model replicates surf zone recirculation patterns (onshore drift at the surface and undertow at the bottom) more accurately than previous formulations based on radiation stress (Haas and Warner, 2009). The results of the model and test cases are further explored for identifying the forces operating in rip current development and the potential implication for sediment transport and rip channel development. Also, model analysis showed that rip current strength is higher when waves approach at angles of 5° to 10° in comparison to normally incident waves.     

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...     

NearCoM-TVD — A quasi-3D nearshore circulation and sediment transport model

The newly developed nearshore circulation model, SHORECIRC, using a hybrid finite-difference finite-volume TVD-type scheme, is coupled with the wave model SWAN in the Nearshore Community Model (NearCoM) system. The new modeling system is named NearCoM-TVD and the purpose of this study is to report the capability and limitation of NearCoM-TVD for several coastal applications. For tidal inlet applications, the model is verified with the semi-analytical solution of Keulegan (1967) for an idealized inlet-bay system. To further evaluate the model performance in predicting nearshore circulation under intense wave–current interaction over complex bathymetry, modeled circulation patterns are validated with measured data during RCEX field experiment (MacMahan et al., 2010). For sediment transport applications, two sediment transport models are applied to predict three sandbar migration events at Duck, NC, during August to October 1994 (Gallagher et al., 1998). The model of Kobayashi et al. (2008) incorporates wave-induced onshore sediment transport rate as a function of the standard deviation of wave-induced horizontal velocities. The modeled beach profile evolution for two offshore events and one onshore event agrees well with the measured data. The second model investigated here combines two published sediment transport models, namely, the total load model driven by currents under the effect of wave stirring (Soulsby, 1997) and the wave-driven sediment transport model due to wave asymmetry/skewness (van Rijn et al., 2011). The model study with limited field data suggests that the parameterization of wave stirring is appropriate during energetic wave conditions. However, during low energy wave conditions, the effect of wave stirring needs to be re-calibrated.     

Velocity predictions for shoaling and breaking waves with a Boussinesq-type model

In this paper, the performance of a 1-D Boussinesq model is evaluated against laboratory data for its ability to predict surf zone velocity moments. Wave evolution over a plane beach and a complex bathymetry both extending into the surf-zone is examined for six cases. For the plane beach, these comprise two cases, a spilling and a plunging cnoidal wave. For the complex bathymetry, these comprise four cases of longer and short wavelengths (spilling and plunging breakers), with regular and irregular periodicity. The model evaluation places emphasis on parameters of the wave field that could be used for the prediction of sediment transport; orbital velocity, undertow, velocity skewness, kurtosis and asymmetry. It is found that, despite an overestimation of the depth-averaged horizontal velocity in the regular waves cases, the predicted higher order velocity moments and undertow are in good agreement with the laboratory data. A bispectral analysis demonstrates that the nonlinear transfers of energy amongst the low order harmonics are well reproduced, but energy exchanges with the higher harmonics are less well predicted. As a result, the model handles velocity moments better in the shorter wave tests than in the long wave cases where triad interactions are stronger. Of the four parameters describing wave breaking, the model behaviour is most sensitive to the critical wave front slope φ_B, especially with regard to velocity skewness and kurtosis predictions. It is also found that increasing the thickness of the surface roller for the case of plunging breakers improves the model's performance.     

Evolution of waves and currents over a submerged laboratory shoal

The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal.     

Field and model data analysis of sand transport patterns in Texel Tidal inlet (the Netherlands)

Texel inlet, the largest inlet in the Dutch Wadden Sea, has undergone drastic changes in the morphology of basin, ebb-tidal delta and adjacent coastlines after closure of a major part of its back-barrier basin. Despite intensive monitoring and analysis, present observation-based conceptual models lack the subtle physics necessary to explain the sand exchange between inlet, ebb-tidal delta and adjacent coastlines.Fundamental understanding of the inlet dynamics and evolution is obtained by integrating field and model data analysis. The state-of-the-art process-based model Delft3D Online Morphology has been used to generate synoptic data of high spatial and temporal resolution over the inlet domain. It is shown that the Delft3D Online Morphology model is capable of the quasi real-time simulation of the dominant flow and transport patterns over a 3-month period on the scale of the inlet. The high-resolution numerical model results prove to be a valuable tool in identifying the main transport patterns and mechanisms in the inlet domain. Qualitative transport patterns in Texel Inlet and its associated ebb-tidal delta are derived by integration of the observations and model results.The present ebb-tidal delta developments are best described as a second-stage self-organizing phase of redistribution and recirculation of sediments to obtain a natural dynamic equilibrium state, adapted to the changed configuration of the main-ebb channels. Sand is transported from the abandoned ebb-delta front (western margin of Noorderhaaks) and along the adjacent coastlines into the basin where it partly settles. Ebb-tidal currents redistribute sand back from the basin mainly onto the southern ebb-tidal delta shoals. Large gross transport rates, but small morphological changes, point to sediment recirculation. Sediment import into the basin results from net flood dominated transport due to tidal asymmetry, landward directed wind- and wave-driven flow, and larger flood transport capacities due to wave effects (e.g. enhanced bed shear stresses and stirring of sediment) that exceed the net ebb-dominated tidal residual transports.     

Investigation and Discussion on the Beach Morphodynamic Response Under Storm Events Based on A Three-Dimensional Numerical Model

A well-established 3D phase-averaged beach morphodynamic model was applied to investigate the morphodynamics of a typical artificial beach,and a series of discussions were made on the surfzone hydro-sedimentological processes under calm and storm events.Model results revealed that the nearshore wave-induced current presents a significant 3D structure under stormy waves,where the undertow and longshore currents exist simultaneously,forming a spirallike circulation system in the surfzone.Continuous longshore sediment transport would shorten the sediment supply in the cross-shore direction,subsequently suppress the formation of sandbars,showing that a typical recovery profile under calm waves does not necessarily develop,but with a competing process of onshore drift,undertow and longshore currents.Sediment transport rate during storms reaches several hundreds of times as those under calm waves,and two storm events contribute approximately 60%to the beach erosion.Sediment transport pattern under calm waves is mainly bed load,but as the fine sands underneath begin to expose,the contribution of suspended load becomes significant.     

琼州海峡汽车轮渡港区泥沙运动数值模拟研究

采用Delf t3D软件建立了琼州海峡汽车轮渡改扩建工程海区风浪、潮流和泥沙耦合计算数学模型,并采用实测潮位、流速、含沙量和地形变化资料对模型进行了率定。在数值计算成果与实测资料达到精度要求后,首先对潮流场分布进行了分析,然后对工程前后工程海域含沙量分布及变化进行了研究,最后给出了工程区域地形冲淤变化。     

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.     

黄河口滨海区冲淤演变与潮流不对称

涨落潮不对称是河口滨海区流场的重要特征,在泥沙输运和地貌演变过程中扮演着重要的角色.本文基于实测水深地形、沉积物粒度、水文泥沙观测等资料,分析了黄河口滨海区的冲淤变化、泥沙输运和沉积物特征.同时,本文利用Delft 3D模型模拟了黄河口滨海区的流场,并计算了不同条件下涨落潮流速的不对称分布,结合上述分析,探讨了黄河口滨...     

A Three-Dimensional Nearshore Hydrodynamic Model with Depth-Dependent Radiation Stresses

For the simulation of the three-dimensional (3D) nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-depeedent radiation stresses in the Cartsian coordinates are introduced on the basis of the linear wave theory,and then vertical variations of depth-dependent radiation stresses are discussed.The 3D hydrodynamic model of EICIRC (Eulerian-Lagrangian CIRCulation) is extended by adding the terms of the depth-dependent or depth-averaged radiation stresses in the momentum equations.The wave set-up,set-down and undertow are simulated by the extended ELCIRC model based on the wave fields provided by the experiment or the REF/DIF wave model.The simulated results with the depth-dependent and depth-averaged radiation stresses both show good agreement with the experimental data for wave set-up and set-down.The undertow profiles predicted by the model with the depth-dependent radiation stresses are also consistent with the experimental results,while the model with the depth-averaged radiation stresses can not reflect the vertical distribution of undertow.