波浪增减水的实用数学模型及其数值模拟

提出了一种模拟近岸区波浪增减水的实用数学模型.首先采用考虑波能损失的抛物型缓坡方程数值模拟波浪破碎引起的波浪复振幅变化,接着根据计算得到的波浪复振幅,采用一种新的辐射应力公式计算辐射应力分量,然后采用深度平均方程计算波浪破碎产生的增减水.采用该模型对规则波和不规则波破碎引起的增减水进行了数值模拟,数值模拟结果与实验结果吻合良好,表明该模型可有效模拟近岸区由于波浪破碎引起的增减水.     

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。     

近岸波浪破碎区不规则波浪的数值模拟

基于近岸不规则波浪传播的抛物型缓坡方程和两类波浪破碎能量损耗因子,对近岸波浪破碎区不规则波浪的波高分布进行了数值模拟,并结合实验结果对数值模拟结果进行了验证分析,结果表明采用两类波浪破碎能量损耗因子所模拟的破碎区波高与实测值均吻合良好,波浪破碎能量损耗因子及波浪破碎指标对破碎区波浪波高分布影响较明显。     

近岸较大区域波浪数值模型的比较

将适用于近岸较大区域波浪传播变形的三种模型,即基于抛物型缓坡方程的不规则波模型、引入浅水波浪谱 TMA 谱的 SWAN(simulating waves nearshore)模型以及采用默认 JONSWAP 谱的 SWAN模型应用于特拉华大学(University of Delaware)圆形浅滩实验进行比较.结果显示,抛物型缓坡方程和SWAN 的模拟结果与实验所测数据符合都比较好; SWAN 在非线性作用较强的浅滩中心及靠后部效果更佳,而抛物型缓坡方程由于没有考虑非线性作用,模拟得到的最大波高较实测值偏高,且波高变化较为剧烈.     

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。     

多方向不规则波传播变形数值模拟

在推广的缓坡方程数学模型基础上建立了多方向不规则波数学模型,综合考虑了波浪折射、绕射、反射、底摩擦和风能输入等因素。基于线性波浪理论,将波浪方向谱在频率和方向上按等能量分割法离散后,分别计算各组成波的传播变形,再计算合成波要素。缓坡方程数学模型采用改进的ADI法求解,计算效率高,稳定性好。采用椭圆形浅滩不规则波模型试验结果和单突堤不规则波绕射理论解对数学模型进行了验证,数值模拟结果和试验值及理论解符合良好。利用该模型进行了某港港内波浪折射、绕射和反射的联合数值模拟,给出了合理的港内波高分布。     

Boussinesq方程与抛物型缓坡方程2种波浪模型的比较分析

波浪破碎的模拟对于波浪模拟的准确性十分重要。为了解波浪破碎模型的问题,本文对抛物型缓坡方程和Boussinesq方程这2种波浪模型所采用的破碎方法进行比较和分析。运用基于Boussinesq方程的Funwave模型和基于抛物型缓坡方程的REF/DIF模型,分别对特拉华大学的未破碎圆形浅滩试验和作者于实验水槽进行的Undertow试验这2个物理模型进行波高模拟、比较与分析。模拟结果表明:Funwave和REF/DIF这2种波浪模型都能准确的模拟出波高随水深的变化情况,但对于波浪破碎后的情况,REF/DIF模型模拟的更为精确一些。     

考虑边界波浪方向的缓坡方程自适应求解模型

缓坡方程是描述近岸波浪运动较好的数学模型之一。在发展的自适应有限元求解缓坡方程的基础上,采用迭代求解的方法,确定波浪相对于边界的入射方向,从而对边界条件进行改进,建立了求解缓坡方程的数值计算模型。典型算例表明,考虑波浪相对于边界的入射角度后,模型可以更好地模拟吸收波浪边界,同时对多向波对双突堤的绕射进行了模拟研究,与试验结果比较表明,所建立的数值计算模型能够适用于多向不规则波传播过程的模拟研究。     

结合椭圆型缓坡方程模拟近岸波流场

波浪向近岸传播的过程中,由波浪破碎效应所产生的近岸波流场是近岸海域关键的水动力学因素之一.结合近岸波浪场的椭圆型缓坡方程和近岸波流场数学模型对近岸波浪场及由斜向入射波浪破碎后所形成的近岸波流场进行了数值模拟.计算中考虑到波浪向近岸传播中由于波浪的折射、绕射、反射等效应使局部复杂区域波向不易确定,采用结合椭圆型缓坡方程所给出的波浪辐射应力公式来计算波浪产生的辐射应力,在此基础上耦合椭圆型缓坡方程和近岸波流场数学模型对近岸波流场进行数值模拟,从而使模型综合考虑了波浪的折射、绕射、反射等效应且避免了对波向角的直接求解,可以应用于相对较复杂区域的近岸波流场模拟.     

用抛物型方程求解波浪折射的数值计算

据微幅波理论导出的波动方程是椭圆型的，数值计算比较复杂，但若以抛物型方程近似取代椭圆型的波方程，那么数值计算将会简单得多。本文将就抛物型方程建立波浪折射的数值计算模型式。     

Determination of wave energy dissipation factor and numerical simulation of wave height in the surf zone

Based on the time-dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation. The wave height of regular and irregular waves is numerically simulated by use of the parabolic mild slope equation considering the energy dissipation due to wave breaking. Comparison of numerical results with experimental data shows that the expression for the energy dissipation factor is reasonable. The effects of the wave breaking coefficient on the breaking point and the distribution of wave height after breaking are discussed through the study of a specific experimental topography.     

港域波浪数学模型的改进与验证

通过物理模型对改进的港内波浪传播变形数学模型进行验证。该数学模型以推广的时变缓坡方程为控制方程,采用含松弛因子的ADI法求解,并对波浪反射和透射边界模拟方法进行改进。先通过物理模型试验确定斜向浪入射条件下抛石防波堤前的波浪反射系数,作为数学模型中部分反射边界模拟的依据。然后进行了一个典型港口内波浪折射、绕射和反射的模型试验,测量港内波浪分布。对比模型试验和数学模型计算的结果表明,数学模型可较好地模拟港内复杂地形和边界条件下规则波和不规则波的传播变形。     

波浪作用下近岸区污染物输移扩散的数学模型及其实验验证

在近岸缓坡浅水海岸,波浪破碎产生沿岸流是近岸海域流场的重要组成部分,它对污染物输移扩散规律的影响重大,在高阶近似抛物化缓坡方程求解大面积波浪场基础上,建立了波浪作用下污染物输移扩散数学模型.计算结果与不同坡度均匀斜坡地形上具有不同波高、周期的规则波及不规则波浪作用下污染物输移扩散实验结果进行了比较,分析了各种因素对波浪作用下沿岸流分布规律影响,所得结论认为地形坡度及入射波高对污染物输移扩散的影响较大,波浪作用将使缓坡海滩上污染物的输移扩散平行岸线方向.     

Verification of A Numerical Harbour Wave Model

A numerical model for wave propagation in a harbour is verified by use of physical models.The extended time-dependent mild slope equation is employed as the governing equation,and the model is solved by use of ADI method containing the relaxation factor.Firstly,the reflection coefficient of waves in front of rubble-mound breakwaters under oblique incident waves is determined through physical model tests,and it is regarded as the basis for simulating partial reflection boundaries of the numerical model.Then model tests on refraction,diffraction and reflection of waves in a harbour are performed to measure wave height distribution.Comparative results between physical and numerical model tests show that the present numerical model can satisfactorily simulate the propagation of regular and irregular waves in a harbour with complex topography and boundary conditions.     

Numerical study of wave and longshore current interaction

Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole（2001） and Reniers and Battjes（1997） were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.     

Numerical Simulation of Wave Height and Wave Set-Up in Nearshore Regions

Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and then a practical method for the simulation of wave height and wave set-up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions.     

On the modeling of wave propagation on non-uniform currents and depth

By transforming two different time-dependent hyperbolic mild slope equations with dissipation term for wave propagation on non-uniform currents into wave-action conservation equation and eikonal equation, respectively, shown are the different effects of dissipation term on the eikonal equation in the two different mild slope equations. The performances of intrinsic frequency and wave number are also discussed. Thus the suitable mathematical model is chosen in which the wave number vector and intrinsic frequency are expressed both more rigorously and completely. By using the perturbation method, an extended evolution equation, which is of time-dependent parabolic type, is developed from the time-dependent hyperbolic mild slope equation which exists in the suitable mathematical model, and solved by using the alternating direction implicit (ADI) method. Presented is the numerical model for wave propagation and transformation on non-uniform currents in water of slowly varying topography. From the comparisons of the numerical solutions with the theoretical solutions of two examples of wave propagation, respectively, the results show that the numerical solutions are in good agreement with the exact ones. Calculating the interactions between incident wave and current on a sloping beach [Arthur, R.S., 1950. Refraction of shallow water waves. The combined effects of currents and underwater topography. EOS Transactions, August 31, 549–552], the differences of wave number vector between refraction and combined refraction–diffraction of waves are discussed quantitatively, while the effects of different methods of calculating wave number vector on numerical results are shown.