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.     

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.     

On Radiation Boundary Conditions and Wave Transformation Across the Surf Zone

The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary conditions. With wave breaking and energy dissipation expressed in a direct form in the equation, the proposed model could provide an efficient numerical scheme and accurate predictions of wave transformation across the surf zone. The radiation boundary conditions are iterated in the model without use of approximations. The numerical predictions for wave height distributions across the surf zone are compared with experimental data over typical beach profiles. In addition, tests of waves scattering around a circular pile show that the proposed model could also provide reasonable improvement on the radiation boundary conditions for large incident angles of waves.     

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.     

粤东后江湾涨落潮下的碎波带波能与滩面地形时空变化分析

利用涌浪和处于陡滩面、滩面下陡坎和深槽海滩地形条件下的海滩碎波带压力波和滩面地形资料,对碎波带中的入射总波能、长重力波能及两者比值随潮位涨落的变化关系,碎波带动力因子与滩面地形之间的作用关系及典型相关和多维偏交叉谱关系等作了初步分析。结果表明,碎波带中的入射总波能与潮位涨落呈现出一致的变化规律;而碎波带中的长重力波能变化与潮位涨落变化趋势相反;碎波带各动力因子、滩面潜水位和碎波带波浪、潮位及滩面地形引起的滩面陡坎处破波点位置变动等因素的耦合作用,对滩面向海发育和滩面地形变化有重要影响。     

Calculations of wave transformation across the surf zone

The accuracy of predicting wave transformation in the nearshore is very important to wave hydrodynamics, sediment transport and design of coastal structures. An efficient numerical model based on the time-dependent mild-slope equation is presented in this paper for the estimation of wave deformation across the surf zone. This model incorporates an approximate nonlinear shoaling formula and an energy dissipation factor due to wave breaking to improve the accuracy of the calculation of wave height deformation prior to wave breaking and also in the surf zone. The model also computes the location of first wave breaking, wave recovery and second wave breaking, if physical condition permits. Good agreement is found upon comparison with experimental data over several one-dimensional beach profiles, including uniform slope, bar and step profiles.     

A parabolic equation extended to account for rapidly varying topography

In this paper, following the procedure outlined by Li (1994. An evolution equation for water waves. Coastal Engineering, 23, 227-242) and Hsu and Wen (2000. A study of using parabolic model to describe wave breaking and wide-angle wave incidence. Journal of the Chinese Institute of Engineers, 23(4), 515–527) and Hsu and Wen (2000) the extended refraction–diffraction equation is recasted into a time-dependent parabolic equation. This model, which includes higher-order bottom effect terms, is extended to account for a rapidly varying topography and wave energy dissipation in the surf zone. The importance of the higher-order bottom effect terms is examined in terms of the relative water depth. The present model was tested for wave reflection in a number of different environments, namely from a plane slope with different inclinations, from a patch of periodic ripples. The model was also tested for wave height distribution around a circular shoal and wave breaking on a barred beach. The comparison of predictions with other numerical models and experimental data show that the validity of the present model for describing wave propagation over a rapidly varying seabed is satisfactory.     

Morphodynamics of a bar-trough surf zone

A field study was made of the distinguishing morphodynamic processes operating in a surf zone which perennially exhibits accentuated bar-trough topography (the “longshore-bar-trough” and “rhytmic-bar-and-beach” states as described by Wright and Short, 1984). Characteristic features of the morphology include a shallow bar with a steep shoreward face, a deep trough, and a steep beach face. This morphology, which is favored by moderate breaker heights and small tidal ranges, strongly controls the coupled suite of hydrodynamic processes. In contrast to fully dissipative surf zones, the bar-trough surf zone is not at all saturated and oscillations at incident wave frequency remain dominant from the break point to the subaerial beach. The degree of incident wave groupiness does not change appreciably across the surf zone. Infragravity standing waves which, in dissipative surf zones, dominate the inshore energy, remain energetically secondary and occur at higher frequencies in the bar trough surf zone. Analyses of the field data combined with numerical simulations of leaky mode and edge wave nodal—antinodal positions over observed surf-zone profiles, indicate that the frequencies which prevail are favored by the resonant condition of antinodes over the bar and nodes in the trough. Standing waves which would have nodes over the bar are suppressed. Sediment resuspension in the surf zone appears to be largely attributable to the incident waves which are the main source of bed shear stress. In addition, the extra near-bottom eddy viscosity provided by the reformed, non-breaking waves traversing the trough significantly affects the vertical velocity profile of the longshore current. Whereas the bar is highly mobile in terms of onshore—offshore migration rates, the beach face and inner regions of the trough are remarkably stable over time.     

Transformation model of wave height distribution on planar beaches

A new probability density function (pdf) for the transformation of depth-limited wave height distributions is presented. Assuming the bore approach for modeling the energy dissipation in the inner surf zone to be valid, an analytical expression for the transformation of wave height distribution including shoaling and breaking on a planar beach is obtained. The resulting expression for the pdf is formulated with a single function and only one shape parameter, which is calibrated as a function of the local root-mean-square (rms) wave height-to-water depth ratio and the local Iribarren number. The transformed pdf is able to reproduce the shape of field and laboratory measured wave height histograms and the sharp change in the shape of the wave height distribution in depth-limited breaking conditions for low exceedance probability. Results show that the theory is appropriate to represent wave height distribution transformation over shallow foreshores or in the surf zone. Alternatively, a combination of the new model with existing state-of-the-art wave energy propagation models allows the complete definition of the wave height distribution transformation on a planar beach.     

平直斜坡上破波带内质量输移流对污染物输移影响的数值研究

破波带内外都有质量输移流存在,其对破波带内污染物输移有怎样的影响,需要进一步深入研究。本文基于实验以及考虑质量输移流的对流扩散数学模型研究了平直斜坡上破波带内质量输移流对污染物输移影响。数学模型包括波浪模型、近岸流模型以及对流扩散模型。首先建立了破波带内污染物输移数学模型,其中波浪场基于波能守恒方程来计算,波导流场基于Longuet-Higgins提出的辐射应力模拟,污染物对流扩散方程中考虑了质量输移流的影响,并利用算例验证该数学模型。其次简要介绍了平直斜坡上破波带内污染物输移实验,并分析了污染物输移特性。连续投放污染物会形成污染带,本文分析了两种波况下不同时刻污染带与岸线夹角的变化,以及污染物在垂直岸线和沿岸线方向的输移速度,结果表明对两种波况来说在初始10-40s污染团向岸线方向输移速度分别约为0.05m/s、0.017m/s,之后速度分别减小为0.001m/s、0.011m/s。数值模拟结果与实验结果比较表明：考虑质量输移流的模拟结果与实验更为吻合。因而,通过实验以及数模研究表明破波带内质量输移流对破波带内污染物在垂直岸线方向的输移有重要影响,而对沿岸方向的输移则影响较小。     

Large Eddy Simulation for Wave Breaking in the Surf Zone

In this paper, (he large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads lo the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale mode! is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this pape     

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.     

Comparing a quasi-3D to a full 3D nearshore circulation model: SHORECIRC and ROMS

Predictions of nearshore and surf zone processes are important for determining coastal circulation, impacts of storms, navigation, and recreational safety. Numerical modeling of these systems facilitates advancements in our understanding of coastal changes and can provide predictive capabilities for resource managers. There exists many nearshore coastal circulation models, however they are mostly limited or typically only applied as depth integrated models. SHORECIRC is an established surf zone circulation model that is quasi-3D to allow the effect of the variability in the vertical structure of the currents while maintaining the computational advantage of a 2DH model. Here we compare SHORECIRC to ROMS, a fully 3D ocean circulation model which now includes a three dimensional formulation for the wave-driven flows. We compare the models with three different test applications for: (i) spectral waves approaching a plane beach with an oblique angle of incidence; (ii) monochromatic waves driving longshore currents in a laboratory basin; and (iii) monochromatic waves on a barred beach with rip channels in a laboratory basin. Results identify that the models are very similar for the depth integrated flows and qualitatively consistent for the vertically varying components. The differences are primarily the result of the vertically varying radiation stress utilized by ROMS and the utilization of long wave theory for the radiation stress formulation in vertical varying momentum balance by SHORECIRC. The quasi-3D model is faster, however the applicability of the fully 3D model allows it to extend over a broader range of processes, temporal, and spatial scales.     

Cross-shore hydrodynamics within an unsaturated surf zone

This paper concerns the hydrodynamics induced by random waves incident on a steep beach. New experimental results are presented on surface elevation and kinematic probability density functions, cross-shore variation in wave heights, the fraction of broken waves and velocity moments. The surf zone is found to be unsaturated at incident wave frequencies, with a significant proportion of the incident wave energy remaining at the shoreline in the form of bores. Wave heights in both the outer and inner surf zones are best described by a full Rayleigh distribution [Thornton, E.B., Guza, R.T., 1983. Transformation of wave height distribution. J. Geophys. Res. 88, 5925–5938], rather than a truncated Rayleigh distribution as used by Battjes and Janssen (1978) [Battjes, J.A, Janssen, J.P., 1978. Energy loss and setup due to breaking of random waves. Proc. 16th Int. Conf. Coastal Eng. ASCE, New York, pp. 569–588]. A new parametric wave transformation model is outlined which provides explicit expressions for the fraction of broken waves and the energy dissipation rate within the surf zone. On steep beaches, the model appears to offer improved predictive capabilities over the original Battjes and Janssen model. Cross-shore variations in the velocity variance and velocity moments are best described using Linear Gaussian wave theory, with less than 20% of the velocity variance in the inner surf zone due to low frequency energy.     

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.     

华南水东湾波控、中等潮差岬湾海滩地形动力分类

海滩地形动力分类在国外的海岸地貌研究中已经被广泛接受。本文使用了华南粤西水东湾切线带、过渡带和遮蔽带海滩连续16个月32次大潮期间同步获取的波浪、潮汐、泥沙和海滩地形数据,分别按照无量纲沉降参数、相对潮差参数和无量纲海湾尺度参数对这一岬湾海滩不同岸段的海滩类型进行了研究,研究发现：（1）水东湾切线带海滩的主要状态为有裂流的低潮台地状态和沙坝型海滩状态,过渡带海滩主要状态是低潮沙坝/裂流海滩和沙坝消散型状态,遮蔽带海滩主要状态是有或无沙坝的消散型状态;（2）海湾不同岸段海滩状态的顺序变化与差异体现了岬湾海滩状态的时空变化性,与现场观测的海滩地形的变化基本一致,说明了对波控中到强潮海滩进行研究时,需要考虑潮汐的影响。同时,本文主要给出了海滩状态研究的一个框架体系,由于海滩不同的状态伴随不同的侵蚀模式,要求我国今后需加强在这一方面研究,以进一步丰富我国海滩地形演变、海滩地形动力过程和海滩防侵蚀的理论基础。     

Numerical experiments of swash oscillations on steep and gentle beaches

A weakly non-linear Boussinesq model with a slot-type shoreline boundary is used to simulate swash oscillations on beaches. Numerical simulations of swash were compared with laboratory measurements and in general good agreement found (less than 15% root-mean-square error of surface elevation except in regular waves). A series of numerical experiments on shoreline movement were then performed for a range of beach slopes and incident wave conditions. The resulting swash characteristics are then discussed in terms of their physical nature and spectral properties. On steep slopes, both individual bores and infragravity waves are equally significant in driving the swash while infragravity waves alone drive them on mild slopes. Swash excursions on any given slope are found to be highest when individual bores from a partially saturated surf zone ride on top of low-frequency waves. This is confirmed by the relationship found between swash excursion and wave groupiness in the surf zone. Swash excursions increase with increasing incident wave energy, even in fully saturated surf zones. However, a poor correlation is found between swash excursion and the surf similarity parameter due to the involvement of infragravity wave energy in the swash.     

北戴河海滩泥沙捕获实验及其初步结果分析

介绍了利用泥沙捕获器观测破波带泥沙垂直分布结构的现场实验方法和基本程序，以及利用实验结果计算泥沙通量的方法。研究表明，近岸带泥沙运移通量及其在垂向上的分布受破波带相对位置和海滩地形变化的影响。在破波点附近，波浪的搅动和流场作用强，泥沙运移通量增大，泥沙在波浪的作用下可以大量进入垂直水体以悬移和跃移的方式运移。在本实验中，破波点附近的泥沙在距海底100cm的垂直水体中运移，通量垂向向上逐渐减小。远离破波点，泥沙运移通量和进入垂直水体的高度明显下降。在地形变化复杂的有坝海滩，沙坝顶部的泥沙运移通量最大，泥沙进入垂直水体运移的机率增加，而在沙坝问的沟槽内，波浪和海流作用减弱，泥沙通量和垂向进入水体运移的比例下降。     

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.     

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.