Implementation and evaluation of alternative wave breaking formulas in a coastal spectral wave model

This paper describes methods and results of research for incorporating four different parameterized wave breaking and dissipation formulas in a coastal wave prediction model. Two formulations assume the breaking energy dissipation to be limited by the Rayleigh distribution, whereas the other two represent the breaking wave energy by a bore model. These four formulations have been implemented in WABED, a directional spectral wave model based on the wave action balance equation with diffraction, reflection, and wave–current interaction capabilities. Four parameterized wave breaking formulations are evaluated in the present study using two high-quality laboratory data sets. The first data set is from a wave transformation experiment at an idealized inlet entrance, representing four incident irregular waves in a slack tide and two steady-state ebb current conditions. The second data set is from a laboratory study of wave propagation over a complex bathymetry with strong wave-induced currents. Numerical simulation results show that with a proper breaking formulation the wave model can reproduce laboratory data for waves propagating over idealized or complicated bathymetries with ambient currents. The extended Goda wave breaking formulation with a truncated Rayleigh distribution, and the Battjes and Janssen formulation with a bore model produced the best agreement between model and data.     

Simulation of nearshore wave processes by a depth-integrated non-hydrostatic finite element model

This paper presents CCHE2D-NHWAVE, a depth-integrated non-hydrostatic finite element model for simulating nearshore wave processes. The governing equations are a depth-integrated vertical momentum equation and the shallow water equations including extra non-hydrostatic pressure terms, which enable the model to simulate relatively short wave motions, where both frequency dispersion and nonlinear effects play important roles. A special type of finite element method, which was previously developed for a well-validated depth-integrated free surface flow model CCHE2D, is used to solve the governing equations on a partially staggered grid using a pressure projection method. To resolve discontinuous flows, involving breaking waves and hydraulic jumps, a momentum conservation advection scheme is developed based on the partially staggered grid. In addition, a simple and efficient wetting and drying algorithm is implemented to deal with the moving shoreline. The model is first verified by analytical solutions, and then validated by a series of laboratory experiments. The comparison shows that the developed wave model without the use of any empirical parameters is capable of accurately simulating a wide range of nearshore wave processes, including propagation, breaking, and run-up of nonlinear dispersive waves and transformation and inundation of tsunami waves.     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

Numerical modelling of deformation of multi-directional random waves over a varying topography

Two numerical formulations of the breaking phenomenon were implemented in a numerical model for random wave propagation based on the elliptic formulation of the mild-slope equation. The randomness of the wave field was simulated based on a spectral component method, in which the 3-D spectrum is discretised in components of equal energy. One of the breaking process formulations is based on the concept of breaking each independent spectral component. The other is based on the distribution of the local amount of energy dissipated through the independent spectral components. The model based on the concept of breaking each independent spectral component produces the best estimates of the wave field, when the numerical results are compared with laboratory data.     

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.     

An empirical model to estimate the propagation of random breaking and nonbreaking waves over vegetation fields

In this work, a model for wave transformation on vegetation fields is presented. The formulation includes wave damping and wave breaking over vegetation fields at variable depths. Based on a nonlinear formulation of the drag force, either the transformation of monochromatic waves or irregular waves can be modelled considering geometric and physical characteristics of the vegetation field. The model depends on a single parameter similar to the drag coefficient, which is parameterized as a function of the local Keulegan–Carpenter number for a specific type of plant. Given this parameterization, determined with laboratory experiments for each plant type, the model is able to reproduce the root-mean-square wave height transformation observed in experimental data with reasonable accuracy.     

Improved representation of breaking wave energy dissipation in parametric wave transformation models

An improved formulation to describe breaking wave energy dissipation is presented and incorporated into a previous parametric cross-shore wave transformation model [Baldock, T.E., Holmes, P., Bunker, S., Van Weert, P., 1998. Cross-shore hydrodynamics within an unsaturated surf zone. Coastal Engineering 34, 173–196]. The new formulation accounts for a term in the bore dissipation equation neglected in some previous modelling, but which is shown to be important in the inner surf zone. The only free model parameter remains the choice of γ, the ratio of wave height to water depth at initial breaking, and a well-established standard parameter is used for all model runs. The proposed model is compared to three sets of experimental data and a previous version of the model which was extensively calibrated against field and laboratory data. The model is also compared to the widely used model presented by Thornton and Guza (1983) [Thornton, E.B., Guza, R.T., 1983. Transformation of wave height distribution. Journal of Geophysical Research 88 (No.C10), 5925–5938].     

The Relative Trough Froude Number for initiation of wave breaking: Theory,experiments and numerical model confirmation

It is important to accurately locate the wave breaking region for the calculation of nearshore hydrodynamics. Energy from breaking waves drives hydrodynamic phenomena such as wave set-up, set-down, wave run-up, longshore currents, rip currents, and nearshore circulation. Numerous studies have been undertaken to describe when and where wave breakings occurs. Recent development of computer resources permits the use of phase-resolving numerical models for the study of wave propagation, transformation, and nearshore hydrodynamics. This requires new types of wave breaking criteria for the numerical model. The Relative Trough Froude Number (RTFN) is a new wave breaking criterion. This model is based on the moving hydraulic jump concept, therefore it satisfies properly posed boundary-value conditions. It has been experimentally proved that a critical RTFN at the initiation of wave breaking is consistent with and without the presence of an opposing current, but previous efforts did not investigate the theory for the critical value. This paper provides a theoretical analysis and a numerical analysis to demonstrate why the RTFN theory works as a wave breaking initiation (trigger) index. The theoretical analysis provides a universal constant for the initiation of wave breaking for all water depths assuming the Miche formula properly describes the wave breaking condition. A subroutine for wave breaking in a numerical model, FUNWAVE was modified to include the RTFN trigger. The numerical model was calibrated with data from wave tank experiments, and it was found that the critical condition is very close to the theoretical number, CTFN = 1.45. A second paper (in preparation) provides details of the theory and experiments for a second criterion for termination of wave breaking. The time scale for the establishment of the breaking region i.e., between the initiation position and termination position, depends upon the additional momentum present under turbulent condition within the breaking wave. This subject is not considered herein.     

Large Eddy Simulation for Plunge Breaker and Sediment Suspension

Breaking waves are a powerful agent for generating turbulence that plays an important role in many fluid dynamical processes, particularly in the mixing of materials. Breaking waves can dislodge sediment and throw it into suspension, which will then be carried by wave-induced steady current and tidal flow. In order to investigate sediment suspension by breaking waves, a numerical model based on large-eddy-simulation (LES) is developed. This numerical model can be used to simulate wave breaking and sediment suspension. The model consists of a free-surface model using the surface marker method combined with a two-dimensional model that solves the flow equations. The turbulence and the turbulent diffusion are described by a large-eddy-simulation (LES) method where the large turbulence features are simulated by solving the flow equations, and a subgrid model represents the small-scale turbulence that is not resolved by the flow model. A dynamic eddy viscosity subgrid scale stress model has been used for the     

Experimental study on suspended sediment concentration and its vertical distribution under spilling breaking wave actions in silty coast

In this paper,flume experiments are focused on sediment transport inside and outside the surf zone.According to the energy dissipation balance principle of sediment-laden flow and the similarity between energy dissipation of spilling breaking wave and hydraulic jump,formulas are proposed to predict time averaged suspended sediment concentration under both non-breaking and breaking waves.Assuming that the sediment diffusion coefficient,which is related with energy dissipation,is proportional to water depth,formulas are proposed to predict close-to-bed suspended sediment concentration and vertical distribution of suspended sediment under spilling breaking waves,and the prediction shows a good agreement with the measurement.     

基于InterDyMFoam的潜礁孤立波传播数值模拟

建立了基于OpenFOAM动边界的类fixedValuePointPatchVectorField继承的仿物理造波数值波浪水槽。对孤立波在三种不同潜礁地形上的行进、爬坡以及破碎等典型过程进行数值模拟,模拟结果与Boussinesq模型及物理模型试验所得结果进行了对比分析。结果表明,采用动边界进行仿物理造波更适合处理波高水深比较大的孤立波传播问题,可以较好地模拟孤立波在潜礁上传播引起的波浪破碎、水跃等现象。     

Numerical Study of Dam-Break Induced Tsunami-Like Bore with A Hump of Different Slopes

Numerical simulation of dam-break wave, as an imitation of tsunami hydraulic bore, with a hump of different slopes is performed in this paper using an in-house code, named a Constrained Interpolation Profile (CIP)-based model. The model is built on a Cartesian grid system with the Navier Stokes equations using a CIP method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of solid body boundary. A more accurate interface capturing scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) scheme, is adopted as the interface capturing method. Then, the CIP-based model is applied to simulate the dam break flow problem in a bumpy channel. Considerable attention is paid to the spilling type reflected bore, the following spilling type wave breaking, free surface profiles and water level variations over time. Computations are compared with available experimental data and other numerical results quantitatively and qualitatively. Further investigation is conducted to analyze the influence of variable slopes on the flow features of the tsunami-like bore.     

斜坡平台波浪破碎数值模拟

波浪在斜坡地形上破碎,破波后稳定波高多采用物理模型试验方法进行研究,利用近岸波浪传播变形的抛物型缓坡方程和波能流平衡方程,导出了适用于斜坡上波浪破碎的数值模拟方法。首先根据波能流平衡方程和缓坡方程基本型式分析波浪在破波带内的波能变化和衰减率,推导了波浪传播模型中波能衰减因子和破波能量流衰减因子之间的关系;其次,利用陡坡地形上的高阶抛物型缓坡方程建立了波浪传播和波浪破碎数学模型;最后,根据物理模型试验实测数据对数值模拟的效果进行验证。数值计算与试验资料比较表明,该模型可以较好地模拟斜坡地形的波浪传播波高变化。     

Modelling of waves and currents around submerged breakwaters

Recent experimental data collected during the DELOS project are used to validate two approaches for simulating waves and currents in the vicinity of submerged breakwaters.The first approach is a phase-averaged method in which a wave model is used to simulate wave transformation and calculate radiation stresses, while a flow model (2-dimensional depth averaged or quasi-3D) is used to calculate the resulting wave driven currents. The second approach is a phase resolving method in which a high order 2DH-Boussinesq-type model is used to calculate the waves and flow.The models predict wave heights that are comparable to measurements if the wave breaking sub-model is properly tuned for dissipation over the submerged breakwater. It is shown that the simulated flow pattern using both approaches is qualitatively similar to that observed in the experiments. Furthermore, the phase-resolving model shows good agreement between measured and simulated instantaneous surface elevations in wave flume tests.     

Shock-capturing Boussinesq-type model for nearshore wave processes

This paper describes the formulation and validation of a nearshore wave model for tropical coastal environment. The governing Boussinesq-type equations include the conservative form of the nonlinear shallow-water equations for shock capturing. A Riemann solver supplies the inter-cell flux and bathymetry source term, while a Godunov-type scheme integrates the evolution variables in time. The model handles wave breaking through momentum conservation with energy dissipation based on an eddy viscosity concept. The computed results show very good agreement with laboratory data for wave propagation over a submerged bar, wave breaking and runup on plane beaches as well as wave transformation over fringing reefs. The model accurately describes transition between supercritical and subcritical flows as well as development of dispersive waves in the processes.     

波浪作用下方块石护面稳定性研究

护面是海堤和护岸的重要结构,直接抵御波浪作用,可采用人工块体、块石等,种类繁多。采用紧密排列方块石作为护面结构是一种景观性较好的型式,依据方块石厚度不同能抵御不同大小的波浪作用。干砌条石及干砌块石护面曾有一些规范给出过计算方法,但现行规范没有相关内容可供设计参考,已有计算方法的理论分析还存在不足。当波浪与斜坡堤相互作用时,方块石护面出现位移或脱落可能发生在波浪回落最低阶段、波浪破碎打击阶段及破后爬高水流作用阶段,通过研究得到了不同阶段波浪对方块石护面作用力的计算方法。在波浪回落最低阶段,考虑了护面及其下方垫层渗透性影响,通过理论分析建立了低渗透护面浮托压强计算模型,采用物模试验将计算结果与试验测量值进行了对比分析,结果表明总体趋势符合,量值接近;在波浪破碎冲击阶段,基于射流冲击作用原理,提出了波浪在斜坡面破碎冲击压强计算方法,通过试验分析了波浪破碎水深波高比与破波相似参数的关系,利用浅水波理论计算了波浪破碎冲击水流流速;在爬高水流作用阶段,提出了水流引起的方块石护面垂直浮托力及水平拖曳力的计算方法,通过试验结果拟合了浮托力系数和拖曳力系数,验证了水流作用下护面的受力特征。最后,针对方块...     

Incompressible SPH flow model for wave interactions with porous media

The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications.     

Verification of a VOF-based two-phase flow model for wave breaking and wave–structure interactions

The objective of the present study is to develop a volume of fluid (VOF)-based two-phase flow model and to discuss the applicability of the model to the simulation of wave–structure interactions. First, an overview of the development of VOF-type models for applications in the field of coastal engineering is presented. The numerical VOF-based two-phase flow model has been developed and applied to the simulations of wave interactions with a submerged breakwater as well as of wave breaking on a slope. Numerical results are then compared with laboratory experimental data in order to verify the applicability of the numerical model to the simulations of complex interactions of waves and permeable coastal structures, including the effects of wave breaking. It is concluded that the two-phase flow model with the aid of the advanced VOF technique can provide with acceptably accurate numerical results on the route to practical purposes.     

Wave dissipation by vegetation with layer schematization in SWAN

The energy of waves propagating through vegetation is dissipated due to the work done by the waves on the vegetation. Dalrymple et al. (1984) estimated wave dissipation by integrating the force on a cylinder over its vertical extent. This was extended by Mendez and Losada (2004) to include varying depths and the effects of wave damping due to vegetation and wave breaking for narrow-banded random waves. This paper describes the wave dissipation over a vegetation field by the implementation of the Mendez and Losada formulation in a full spectrum model SWAN, with an extension to include a vertical layer schematization for the vegetation. The present model is validated with the original equation and results from Mendez and Losada (2004). The sensitivity of the model to the shape of the frequency spectrum, directional spreading and layer schematization are investigated. The model is then applied to field measurements by using a vegetation factor. This model has the ability to calculate two-dimensional wave dissipation over a vegetation field including some important aspects such as breaking and diffraction as used in SWAN model.