COMPARISON BETWEEN BOUSSINESQ EQUATIONS AND MILD-SLOPE EQUATIONS MODEL

1. INTRODUCTIONWave transformation,one of the most i mpor-tant near-shore hydrodynamic processes , has closerelations to human activities as well as i mpact on o-ceanic environment , resources and engineeringstructures .So it is of greater i mportance to …     

岛礁地形抛石护岸稳定性试验研究

岛礁地形是一种特殊的海岸形式,国内外学者对波浪在岛礁地形上的传播变形研究较多,但对于岛礁地形上的护岸工程研究较少,缺乏对关键设计参数的研究。以马尔代夫机场岛护岸工程为例,通过比例尺为1:10的波浪水槽物理模型试验,分析研究了3种不同岸坡宽度、4种不同水深和波浪组合工况下的护面块石稳定性。结果表明,前沿岸坡宽度,即护岸坡脚至礁缘之间的距离是影响抛石护岸稳定性的重要因素。在同样水深、波况及护岸块石质量条件下,护面块石的失稳率随岸坡宽度的增加而减小。进一步分析发现,为保障护岸安全,抛石护岸外坡坡脚宜布置于波浪破碎点之后,且与破碎点之间距离不应小于浅水波长的26%,即0.26T$ \sqrt{g h_{\mathrm{e}}}$。     

基于Boussinesq方程的陡峭礁坪上波浪传播变形数值模拟

为了探究应用基于二阶完全非线性Boussinesq方程开发的Funwave-TVD波浪模型模拟波浪在陡峭礁坪上传播变形的可行性,在采用试验及已有文献成果进行可行性验证的基础上,利用该模型模拟了波浪在陡峭礁坪上的传播变形过程,分析了不同波浪要素及不同水深情况下波浪在陡峭礁坪上的传播规律。结果表明:当波高与水深的比值超过一定值时,波浪发生破碎,波高迅速减小;对于深水情况下的陡峭礁坪地形,当波浪离开礁坪坡脚的水平距离为4倍入射波长及更远时,礁坪上的平均波高可降低为稳定值。     

Surf-zone dynamics derived from basin-scale experiments

Surf-zone hydrodynamics forced by oblique wave shoaling and breaking on beach slopes were investigated. The results showed that in wave-basin experiments with incident angles in the range of 15°–30°, wave breaking was initiated at a breaker coefficient of around 0.67, which was significantly less than that predicted from empirical relations based on normally incident waves for a given beach slope and deep-water wave steepness. The measurements also showed that subsequent saturated breaking occurred at a breaker coefficient of around 0.47 that was independent of beach slope in the range of 1:10 to 1:100. This result is likely applicable to both oblique and normally incident waves. It is shown that the measured wave heights and longshore velocity profiles in wave-basin studies can be reasonably well predicted by theory with proper adjustments to the process parameters. Best-match formulations were identified for quantifying bottom friction, eddy viscosity, and energy loss due to surface rollers.     

Boussinesq方程波浪数学模型在港池波浪计算中的应用

简要介绍了Boussinesq方程的形式和特点,参考丹麦Abbott等人提出的改进的该方程的形式及解法,初步建立了考虑底摩擦效应、波浪破碎效应的Boussinesq方程波浪数学模型,将其应用于港池波浪计算,并与海港水文规范的计算结果进行对比分析。     

综合考虑多种变形因素的近岸多向不规则波传播数学模型-I.模型的建立

根据线性波动的叠加原理和波浪方向谱理论,作者在综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射的近岸规则波传播基本方程的基础上,推导出了综合考虑多种变形因素的近岸多向不规则波传播变形的基本方程。使用有限差分作为数值方法,给出了波浪破碎和障碍物后边界的处理方法,建立了综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射、波浪破碎、障碍物影响的近岸多向不规则波传播变形数学模型。该模型以组成波的谱值及波向为变量,在实数域内求解,适合大面积海区波场计算。     

沙坝海岸上裂流的数值模拟

建立了基于二阶完全非线性Boussinesq水波方程的二维波浪破碎数值模型,对沙坝海岸上产生的裂流进行了数值模拟研究。首先将文献[1]中给出的一组二阶完全非线性Boussinesq方程进行扩展,在动量方程中引入紊动粘性项模拟波浪破碎引起的能量耗散,采用窄逢法处理海岸动边界问题,并考虑了混合子网格效应以及水底摩擦。然后,在矩形网格上离散控制方程,采用有限差分方法和混合四阶Adams-Bashforth-Moulton预报矫正格式建立了数值模型。应用所建立模型对一带沟槽沙坝海岸上产生裂流的实验进行数值模拟,将计算的波高、增减水、时均流速、时均流场等与实验数据进行了比较。数值结果与实验结果吻合较好,这说明建立的数值模型是准确有效的,为下一步应用该模型模拟实际海岸上的裂流提供了研究基础。     

SENSITIVITY STUDY OF THE EFFECTS OF WAVE-INDUCED VERTICAL MIXING ON VERTICAL EXCHANGE PROCESSES

The hydrodynamic model COHERENS-SED, developed by the present authors through introducing wave-enhanced bottom stress, wave dependent surface drag coefficient, wave-induced surface mixing, SWAN to COHERENS, is modified to account for wave-induced vertical mixing. The COHERENS-SED model can also be used for one-dimensional, two-dimensional, three-dimensional current and salinity calculations. One-dimensional model and three-dimensional model are used to study the effects of the wave-induced vertical mixing. The horizontal current velocity profiles obtained by the model are in good agreement with the analytical velocity profiles under the same input conditions. Numerical results show that higher wave height would generally generate larger vertical eddy viscosity and lower horizontal velocity. The results for fresh water in Yellow River Delta show that the wave-induced vertical mixing increases the momentum of fresh water transferring ability downwards to seabed and salt water's mixing with upper fresh water. Fresh water flume length is compressed considerably.     

基于有限体积法的三维波生近岸流数值模型

波浪破碎产生近岸流是近岸浅水区域一个重要的水动力现象。该文利用辐射应力的概念,并考虑辐射应力沿水深的变化、波浪破碎引起的水滚以及波流共同作用下的水底剪应力,建立了基于有限体积法的三维波生近岸流数值模型。运用建立的数值模型模拟了两个实验室实验,并同实验的实测结果进行了对比。结果表明,建立的数值模型能够较好地模拟波浪破碎产生的近岸流。     

Numerical simulation of wave transformation,breaking and runup by a contravariant fully non-linear Boussinesq equations model

In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations(FNBE) in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-finite difference scheme. A high-order upwind weighted essentially non-oscillatory(WENO) finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations(NSWE). On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento(Italy).     

TESTS AND APPLICATIONS OF A BOUSSINESQ MODEL WITH AMBIENT CURRENT

A new type Boussinesq model is proposed and applied for wave propagation in a wave flume of uniform depth and over a submerged bar with current present or absent, respectively. Firstly, for the propagation of monochromatic incident wave with current absent, the Boussinesq model is tested in its complete form, and in a form without the introduction of utility velocity variables. It is validated that the introduction of utility velocity variables can improve the characteristics of velocity field, dispersion and nonlinearity. Both versions of the Boussinesq models are of higher accuracy than the fully-nonlinear fourth-order model, which is one of the best forms among the existing traditional Boussinesq models that do not incorporate breaking mechanism in one dimension. Secondly, the Boussinesq model in its complete form is applied to simulating the propagation of bichromatic incident waves with current present or absent, respectively, and the modeled results are compared to the analytical ones or the experimental ones. The modeled results are reasonable in the case of inputting bichromatic incident waves with the strong opposing current present.     

A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

A total variation diminishing-weighted average flux(TVD-WAF)-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer(HLL) Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourthorder monotone upstream-centered scheme for conservation laws(MUSCL). The time marching scheme based on the third-order TVD RungeKutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.     

单排三角锥透空圆孔礁坝保滩促淤的试验研究

借助波浪水槽断面模型试验,开展了不同设计水位下的单排三角锥透空圆孔礁坝对波浪的消减作用及对砂质岸滩地形演变和底层水质点运动轨迹影响的研究。由试验资料分析可知:人工礁坝对波高消减、波面形态及波浪爬高有较大影响;人工礁坝会削弱掩护区的水动力强度,减弱波浪挟沙能力,促使超饱和悬沙在礁后落淤,且通过对水质点水平运动离岸流速的阻减,防止底层泥沙产生离岸亏损。本试验研究在一定程度上揭示了人工礁坝的消浪阻流特征及砂质岸滩地形的响应规律,可为人工礁坝在砂质海滩防护中的应用提供依据。     

NUMERICAL STUDY OF WAVE EFFECTS ON SURFACE WIND STRESS AND SURFACE MIXING LENGTH BY THREE-DIMENSIONAL CIRCULATION MODELING

1. INTRODUCTION Coastal and continental shelf regions are characterized by intensive interaction between wave and current. These regions are of great economic significance to mankind. Therefore, the modeling of wave and current as well as their mutual int…     

LARGE EDDY SIMLIATION WAVE BREAKING OVER MUDDY SEABED

The Large Eddy Simulation (LES) of the wave breaking over a muddy seabed is carried out with a Coupled Level Set and Volume Of Fluid (CLSVOF) method to capture the interfaces.The effects of the mud on the wave breaking are studied.The existence of a mud layer beneath an otherwise rigid bottom is found to have a similar effect as an increase of the water depth.As compared with the case of a simple rigid bottom,the inception of the wave breaking is evidently delayed and the breaking intensity is much reduced.The dissipation of the wave energy is shown to have very different rates before,during and after the breaking.Before and after the breaking,the mud plays an important role.During the breaking,however,the turbulence as well as the entrainment of the air also dissipate a large amount of energy.     

考虑底摩阻损耗的波浪传播与衰减计算的边界元法

边界元法在势流计算中具有使问题降低一维的优点。为了将边界元法与基于粘性流体理论的底部波能损耗结合起来，本文采用一种包含底摩阻系数的底部边界条件，可以在考虑底摩阻损耗的情况下计算极平缓岸坡上波浪的传播与衰减。数值结果得到了物模实验数据的验证。     

一种扩展型缓坡方程的时域计算模式

该文通过引入有效波面函数,把考虑海底摩擦、波浪破碎、陡变和快变地形等因素影响的扩展型缓坡方程,化为最简形式的时间双曲型缓坡方程.基于此方程和非线性振幅频散关系,建立了波浪传播的数值模拟模型,并对数值格式进行了误差分析,结果表明由于耗散项的引入,数值格式的稳定性较文献[1]得到了提高.数值解与物理模型实验值和解析解吻合良好,表明模型可以对近岸波浪传播过程中折射、绕射、反射、浅水变形、海底摩擦、波浪破碎和弱非线性等因素的影响进行较好地预测.     

NUMERICAL SIMULATIONS OF WATER WAVE DYNAMICS BASED ON SPH METHODS

A numerical model was established for simulating water wave dynamic problems by adopting the Smoothed Particle Hydrodynamics (SPH) methods of iterative solution of Poisson's equation for pressure field, and meanwhile the sub-grid turbulence model was applied in the simulation so as to more accurately describe the turbulence characteristics at the time of wave breaking. In this article, simulation of the problem of the dam collapsing verifies the compoting accuracy of this method, and its results can be identical with the results of VOF method and the experimental results by comparison. Numerical simulations of the course of solitary wave and cnoidal wave run-up breaking on beaches were conducted, and the results are basically consistent with experimental results. This indicates that the SPH method is effective for the numerical simulation of the complex problems of water wave dynamics.     

Modeling of fully nonlinear wave evolution over a submerged bar

A three-dimensional fully nonlinear numerical wave tank (NWT) is developed by using a time-domain higher-order boundary element method (HOBEM). The source generation of waves is adopted to generate input waves. The mixed Eulerian-Lagrangian (MEL) method is utilized to track and refresh the free surface. The model is applied to three examples of wave evolution and harmonic decomposition during propogation over a submerged bar and numerical results are compared with the experimental data and the solutions of Boussinesq model. It shows that the present model agrees better with the measurements than the Boussinesq model and are more adaptable for stronger nonlinear waves.

     

DISSIPATION OF WAVE ENERGY ON VERY MILD SLOPE

1.　INTRODUCTIONOffshoreareasarewherepeoplefrequentlyengagevariouskindsofhumanactivities,forexamples,portbuilding.seawallconstruction,installationofoildrillingplatformandseashorepowerstation,etc.Whenstructuresplacedinshallowwateraredesigned,thedesignwaveheightalwaystakesthecriticalwaveheight-breakingwaveheight.ThecriticalwaveheightadoptedinChineseCodeisdeterminedbyGoda′smethod,whichiswidelyusedinmanycountries.Thismethodisbasedonthestudyofregularwavesonbottomslopei≥1/50.Themaximumwavehe…