Numerical study of vegetation damping effects on solitary wave run-up using the nonlinear shallow water equations

Vegetation damping effects on propagating water waves have been investigated by many researchers. This paper investigates the effects of damping due to vegetation on solitary water wave run-up via numerical simulation. The numerical model is based on an implementation of Morison's formulation for vegetation induced inertia and drag stresses in the nonlinear shallow water equations. The numerical model is solved via a finite volume method on a Cartesian cut cell mesh. The accuracy of the numerical scheme and the effects of the vegetation terms in the present model are validated by comparison with experiment results. The model is then applied to simulate a solitary wave propagating on a plane slope with vegetation. The sensitivity of solitary wave run-up to plant height, diameter and stem density is investigated by comparison of the numerical results for different patterns of vegetation. The numerical results show that vegetation can effectively reduce solitary wave propagation velocity and that solitary wave run-up is decreased with increase of plant height in water and also diameter and stem density.     

Numerical study for vegetation effects on coastal wave propagation by using nonlinear Boussinesq model

The vegetation has important impacts on coastal wave propagation. In the paper, the sensitivities of coastal wave attenuation due to vegetation to incident wave height, wave period and water depth, as well as vegetation configurations are numerically studied by using the fully nonlinear Boussinesq model. The model is based on the implementation of drag resistances due to vegetation in the fully nonlinear Boussinesq equation where the drag resistance is provided by the Morison’s formulation for rigid structure induced drag stresses. The model is firstly validated by comparing with the experimental results for wave propagation in vegetation zones. Subsequently, the model is used to simulate waves with different height, period propagating on vegetation zones with different water depth and vegetation configurations. The sensitivities of wave attenuation to incident wave height, wave period, water depth, as well as vegetation configurations are investigated based on the numerical results. The numerical results indicate that wave height attenuation due to vegetation is sensitive to incident wave height, wave period, water depth, as well as vegetation configurations, and attenuation ratio of wave height is increased monotonically with increases of incident wave height and decreases of water depth, while it is complex for wave period. Moreover, more vegetation segments can strengthen the interaction of vegetation and wave in a certain range.     

Laboratory and numerical studies of wave damping by emergent and near-emergent wetland vegetation

Wetlands protect mainland areas from erosion and damage by damping waves. Yet, this critical role of wetland is not fully understood at present, and a means for reliably determining wave damping by vegetation in engineering practice is not yet available. Laboratory experiments were conducted to measure wave attenuation resulting from synthetic emergent and nearly emergent wetland vegetation under a range of wave conditions and plant stem densities. The laboratory data were analyzed using linear wave theory to quantify bulk drag coefficients and with a nonlinear Boussinesq model to determine numerical friction factors to better represent wetland vegetation in engineering analysis.     

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.     

Laboratory study on wave dissipation by vegetation in combined current–wave flow

Coastal wetlands such as salt marshes and mangroves provide valuable ecosystem services including coastal protection. Many studies have assessed the influence of plant traits and wave conditions on vegetation-induced wave dissipation, whereas the effect of tidal currents is often ignored. To our knowledge, only two studies investigated wave dissipation by vegetation with the presence of following currents (current velocity is in the same direction as wave propagation) (Li and Yan, 2007; Paul et al., 2012). However, based on independent experiments, they have drawn contradictive conclusions whether steady currents increase or decrease wave attenuation. We show in this paper that this inconsistency may be caused by a difference in ratio of imposed current velocity to amplitude of the horizontal wave orbital velocity. We found that following currents can either increase or decrease wave dissipation depending on the velocity ratio, which explains the seeming inconsistency in the two previous studies. Wave dissipation in plant canopies is closely related to vegetation drag coefficients. We apply a new approach to obtain the drag coefficients. This new method eliminates the potential errors that are often introduced by the commonly used method. More importantly, it is capable of obtaining the vegetation drag coefficient in combined current–wave flows, which is not possible for the commonly used calibration method. Based on laboratory data, we propose an empirical relation between drag coefficient and Reynolds number, which can be useful for numerical modeling. The characteristics of drag coefficient variation and in-canopy velocity dynamics are incorporated into an analytical model to help understand the effect of following currents on vegetation-induced wave dissipation.     

A coupled model of submerged vegetation under oscillatory flow using Navier–Stokes equations

This work presents a new model for wave and submerged vegetation which couples the flow motion with the plant deformation. The IH-2VOF model is extended to solve the Reynolds Average Navier–Stokes equations including the presence of a vegetation field by means of a drag force. Turbulence is modeled using a k–ε equation which takes into account the effect of vegetation by an approximation of dispersive fluxes using the drag force produce by the plant. The plant motion is solved accounting for inertia, damping, restoring, gravitational, Froude–Krylov and hydrodynamic mass forces. The resulting model is validated with small and large-scale experiments with a high degree of accuracy for both no swaying and swaying plants. Two new formulations of the drag coefficient are provided extending the range of applicability of existing formulae to lower Reynolds number.     

A Practical bi-parameter formula of gas transfer velocity depending on wave states

The parameter that describes the kinetics of the air-sea exchange of a poorly soluble gas is the gas transfer velocity which is often parameterized as a function of wind speed. Both theoretical and experimental studies suggest that wind waves and their breaking can significantly enhance the gas exchange at the air-sea interface. A relationship between gas transfer velocity and a turbulent Reynolds number related to wind waves and their breaking is proposed based on field observations and drag coefficient formulation. The proposed relationship can be further simplified as a function of the product of wind speed and significant wave height. It is shown that this bi-parameter formula agrees quantitatively with the wind speed based parameterizations under certain wave age conditions. The new gas transfer velocity attains its maximum under fully developed wave fields, in which it is roughly dependent on the square of wind speed. This study provides a practical approach to quantitatively determine the effect of waves on the estimation of air-sea gas fluxes with routine observational data.     

基于抛物型缓坡方程模拟近岸植被区波浪传播

植被对波浪传播运动有重要影响。考虑近岸波浪在植被区传播中的折射、绕射、破碎及植被引起的波能耗损效应,基于抛物型缓坡方程建立了模拟近岸植被区波浪传播的数学模型,对模型进行了数值模拟验证,采用数值模拟试验分析了植被对波浪传播的影响。数值模拟结果表明,波浪在近岸植被区传播时,随着植被密度和植被高度的增加,波浪传播中的波高衰减增大,波能耗损增加;不同周期波浪在植被区传播中的波高衰减过程也明显不同。     

Drag force on a vegetation field due to long-crested and short-crested nonlinear random waves

This paper provides a practical method for estimating the drag force on a vegetation field exposed to long-crested (2D) and short-crested (3D) nonlinear random waves. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (1999), in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process. Effects of nonlinear waves are included by adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D random waves.     

木本植被覆盖岸坡上波浪爬升过程的数值模拟研究

近岸木本植物构成的生态缓冲带作为新型的海岸软防护结构,兼具功能性和生态友好性,在沿海工程建设中愈发受到关注,如何深入开展其防护效果的机理研究是目前亟待解决的问题。本文采用数值模拟方法,在N-S方程中分别考虑树枝和树干的拖曳力影响,提出了木本植被作用下波浪沿斜坡爬升的表面波衰减的连续介质等效模型,并采用MAC法来跟踪自由曲面上的水颗粒轨迹。本文以波浪沿1/30的斜坡爬升为算例,对比讨论了有无植被作用下波浪的传播过程,并将算例结果与以往试验结果规律进行对照,验证了数值模型的有效性。最后,分别讨论了植物枝干的高度、密度、树枝倾斜角度等植被特性和波浪因素对植被消浪效果的影响,得到植被消浪的基本规律。文中的计算结果也可为实际的护岸工程和生态景观设计提供参考。     

Numerical simulation of solitary and randomwave propagation through vegetation based on VOFmethod

A vertical two-dimensional numerical model has been applied to solving the Reynolds Averaged Navier- Stokes （RANS} equations in the simulation of current and wave propagation through vegetated and non- vegetated waters. The k-e model is used for turbulence closure of RANS equations. The effect of vegeta- tion is simulated by adding the drag force of vegetation in the flow momentum equations and turbulence model. To solve the modified N-S equations, the finite difference method is used with the staggered grid system to solver equations. The Youngs＇ fractional volume of fluid （VOF） is applied tracking the free sur- face with second-order accuracy. The model has been tested by simulating dam break wave, pure current with vegetation, solitary wave runup on vegetated and non-vegetated channel, regular and random waves over a vegetated field. The model reasonably well reproduces these experimental observations, the model- ing approach presented herein should be useful in simulating nearshore processes in coastal domains with vegetation effects.     

Nonlinear random wave-induced drag force on a vegetation field

This paper provides a practical method by which the drag force on a vegetation field beneath nonlinear random waves can be estimated. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (Mendez, F.J., Losada, I.J., Losada, M.A., 1999. Hydrodynamics induced by wind waves in a vegetation field. J. Geophys. Res. 104 (C8), 18383–18396). Effects of nonlinear waves are included by using Stokes second order wave theory where the basic harmonic motion is assumed to be a stationary Gaussian narrow–band random process. An example of calculation is also presented.     

聚焦波作用下平面网衣结构的水动力特性研究

由于沿海区域的限制以及愈加严重的环境污染,渔业养殖正从近海走向深远海。深远海海域的海况更加恶劣,给养殖装备的设计与性能评估带来新的挑战。为解决该问题,对极端波浪与养殖装备网衣结构的相互作用开展研究。基于waves2Foam建立数值波浪水池,极端波浪模拟采用基于NewWave理论的聚焦波模型,网衣结构模拟采用多孔介质模型,并通过与Morison模型计算的网衣受力等效分析,获得多孔介质模拟网衣结构阻力系数的直接估计方法。然后将多孔介质模型嵌入waves2Foam中,开展聚焦波与网衣结构相互作用的数值模拟,同时开展水槽试验,验证数值模拟的准确性。基于数值模拟结果,系统地分析了不同网衣密实度及不同波浪参数下网衣结构的升阻力特性以及网衣结构对波浪场的扰动规律。研究表明：聚焦波波峰幅值和网衣密实度对网衣结构的升阻力影响较大,且升力峰值出现在阻力为0的时刻;网衣结构对聚焦波的时空演化特性有影响,改变了聚焦波波形。     

Non-hydrostatic finite element model for coastal wave processes

This paper presents the application of the depth-integrated non-hydrostatic finite element model, CCHE2D-NHWAVE (Wei and Jia, 2014), for simulating several types of coastal wave processes. Specifically, the model is applied to (1) predict the swash zone hydrodynamics involving wave bore propagation, (2) resolve wave propagation, breaking, and overtopping in fringing reef environments, (3) study the vegetation effect on wave height reduction through both submerged and emergent vegetation zones using the drag force term technique, and (4) simulate tsunami wave breaking in the nearshore zone and inundation in the coastal area. Satisfactory agreement between numerical results and benchmark data shows that the non-hydrostatic model is capable of modeling a wide range of coastal wave processes. Furthermore, thanks to its simple numerical formulation, the non-hydrostatic model also demonstrates a better computation efficiency when comparing with other numerical models.     

Generation of 3D regular and irregular waves using Navier–Stokes equations model with an internal wave maker

Due to their capability of correctly representing wave characteristics, the number of numerical models based on Navier–Stokes equation (NSE) models has recently increased remarkably. One of the key challenges of this type of wave model, however, is to minimize the wave re-reflection from the incident boundary. Many numerical techniques have been developed to deal with this problem, and previous studies have reported on internal wave makers that employ NSE. Research on generation and transformation of irregular waves using a three-dimensional NSE model, however, has begun very recently, and few studies have yet been reported. In this study, a three-dimensional numerical model was applied to generate irregular waves, and transformation of irregular waves was simulated in a numerical wave tank. The model was first verified by applying it to simple numerical tests in two dimensions. The model was then used to generate directional monochromatic and irregular waves in three dimensions. The numerical results were compared with the analytical solutions, and good agreement was observed. Finally, the model was applied to simulate the transformation of irregular waves over an uneven bottom geometry in a wave tank.     

Wave-induced drag force on vegetation under shoaling random waves

This paper provides a practical method for estimating the drag force on a vegetation field in shoaling conditions beneath non-breaking and breaking random waves. This is achieved by using a simple drag formula based on two empirical drag coefficients given by Méndez et al. (1999) and Méndez and Losada (2004), respectively, in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process and propagating in shallow waters. The effects of shoaling and breaking waves are included by adopting the Méndez et al. (2004) wave height distribution. Results are presented and discussed for different slopes, and an example of calculation is also provided to demonstrate the application of the method.     

Quasi-linear model of interaction of surface waves with strong and hurricane winds

A quasi-linear model for determining the aerodynamic drag coefficient of the sea surface and the growth rate of surface waves under a hurricane wind is proposed. The model explains the reduction (stabilization) in the drag coefficient during hurricane winds. This model is based on the solution of the Reynolds equations in curvilinear coordinates with the use of the approximation of the eddy viscosity, which takes into account the presence of the viscous sublayer. The profile of the mean wind velocity is found with consideration for nonlinear wave stresses (wave momentum flux), whereas wave disturbances induced in air by waves on the water surface are determined in the context of linear equations. The model is verified by comparing the calculation results with experimental data for a wide range of wind velocities. The growth rate and drag coefficient for hurricane winds are calculated both with and without consideration for the shortwave portion of the windwave spectrum. On the basis of calculations with the quasi-linear model, a simple parametrization is proposed for the drag coefficient and the growth rate of surface waves during hurricane winds. This model is convenient for use in models of forecasting winds and waves.     

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.     

A rapid assessment method for calculating the drag coefficient in wave attenuation by vegetation

Vegetation in wetlands is a large-scale nature-based resource that can provide multiple benefits to human beings and the environment,such as wave attenuation in coastal zones.Traditionally,there are two main calibration approaches to calculate the attenuation of wave driven by vegetation.The first method is a straightforward one based on the exponential attenuation of wave height in the direction of wave transmission,which,however,overlooks the crucial drag coefficient (C_D).The other method is in accordance with more complicate equations for predicting the damping factor,which is regarded as a function of C_D.In this study,a new relation,combining these above two conventional approaches,is proposed to predict the C_D in an operative approach.Results show that values yielded by the new assessment method perform a strong linear relationship with a collection of historical observations,with a promising R~2 value of 0.90.Besides,the linear regression derives a new predictive equation for the bulk drag coefficient.Additionally,a calibrated value of 4 for the empirical plant drag coefficient(C_P) is revealed.Overall,this new equation,with the superiority of the convenient exponential regression,is expected to be a rapid assessment method for calculating wave attenuation by vegetation and predicting the drag coefficient.     

New model to determine forces at on-bottom slender pipelines

The present paper proposes a numerical model to determine horizontal and vertical components of the hydrodynamic forces on a slender submarine pipeline lying at the sea bed and exposed to non-linear waves plus a current. The new model is an extension of the Wake II type model, originally proposed for sinusoidal waves (Soedigdo et al., 1999) and for combined sinusoidal waves and currents (Sabag et al., 2000), to the case of periodic or random waves, even with a superimposed current. The Wake II type model takes into account the wake effects on the kinematic field and the time variation of drag and lift hydrodynamic coefficients. The proposed extension is based on an evolutional analysis carried out for each half period of the free stream horizontal velocity at the pipeline. An analytical expression of the wake velocity is developed starting from the Navier–Stokes and the boundary layer equations. The time variation of the drag and lift hydrodynamic coefficients is obtained using a Gaussian integration of the start-up function. A reduced scale laboratory investigation in a large wave flume has been conducted in order to calibrate the empirical parameters involved in the proposed model. Different wave and current conditions have been considered and measurements of free stream horizontal velocities and dynamic pressures on a bottom-mounted pipeline have been conducted. The comparison between experimental and numerical hydrodynamic forces shows the accuracy of the new model in evaluating the time variation of peaks and phase shifts of the horizontal and vertical wave and current induced forces.