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 …     

新型高阶Boussinesq水波方程

从经典的Boussinesq方程出发，引入两个参数并对方程中的部分项进行替换，通过严格的数学推导给出量级为O(εμ2)的高阶非线性项，得到一种新型的高阶Boussinesq方程。该方程的色散关系比经典Boussinesq方程提高了一阶，变浅作用性能也得到了改善，方程的适用范围由浅水达到中等水深。利用Crank-Nicloson格式的有限差分法对方程进行数值模型在一维方向上进行离散计算，建立了高阶Boussinesq方程的数值模型。为验证数值模型的正确性，将数值计算结果与Zou等(2001)的物模试验结果以及Beji与Nadaoka方程的数值结果进行对比，本文的数值结果与试验结果吻合程度较好，表明本文方程可适于模拟变水深下的波浪场数值模拟。     

数字波浪槽在防波堤预设计中的应用

传统的以物理模型进行的防波堤断面实验被以计算机进行的数字波浪槽代替,边界造波为Bretschneider/Mit-suyasu波浪谱,防波堤断面根据海港水文规范(简称“规范”)设计。以改进的Boussinesq波浪方程,通过引入波浪反射项以数值模拟实现了波浪在水槽中传播的全过程。通过数值水槽获得了波浪在本文防波堤断面前0.45的反射系数,将数值模拟的结果和规范中的反射系数进行了对比得出,数字波浪水槽有满意的精度以及在规范中使用了一定的安全系数,表明数字波浪槽在防波堤的预设计中有重要作用。     

新型透空组合板式防波堤结构型式及消浪特性分析

为提高透空式防波堤的消浪性能并减小结构受力,在前人研究基础上提出了一种新型透空组合板式防波堤,比较分析了该型式的防波堤(模型c)与另外两种型式的防波堤(模型a和模型b)的结构特点。通过物理模型试验,探讨了模型c在不同影响因素下的消浪特性,并对比分析了模型a与模型c的透射系数、反射系数和能量耗散系数在不同相对堤宽下的变化关系,比较了两种模型的消浪效果。分析得出,由于模型c兼具开孔水平板式防波堤和开孔挡板式防波堤的作用,模型c的波浪反射小于模型a,消浪效果优于模型a,且模型c这种结构能有效减小防波堤结构受力;当模型宽度和相对间隙比同时较大时消浪效果更好,防波堤出水后的消浪性能要优于淹没状态下的防波堤。     

Numerical study on flow structure near two impermeable trapezoid submerged breakwaters on slop bottoms

Studying on hydrodynamic characteristics in water waves propagating over two impermeable trapezoid submerged breakwaters is of great significance to research design and construction of this type of submerged breakwaters. The turbulent characteristics are discussed with cnoidal waves in the wave flume with 1:20 smooth slope.The governing equations of the vertical 2D model are the Reynolds-averaged Navier-Stokes equations. The Reynolds stress terms are closed by a nonlinear (anisotropic) k − ε turbulence transportation model. Using a VOF method for tracking the free surface and source function wave generating method. Furthermore, the supplementary discussion is made by means of numerical results.

     

EXPERIMENTAL STUDY ON A NEW KIND OF OPEN TYPE BREAKWATERS

A new kind of open type breakwaters was proposed based on the concept of wave energy conversion. The excellent feature of the structure is that it can absorb and utilize the wave energy to dissipate waves. The effects of some factors, such as the configuration insides, the geometrical parameters and the relative width (the ratio of the width to the wave length), on the performance of the breakwater were discussed based on a series of regular wave tests in the wave flume. The hydrodynamic characteristics of the new open type breakwater were analyzed in detail, and the structure was optimized to improve the performance of the breakwater to effectively dissipate the waves with long period. The variation of the coefficients of wave transmission and reflection along with attenuation with respect to relative width was examined. The results of the physical model tests indicate that the transmission coefficient significantly decreases by about twenty percent at the range of relative width from 0. 1 to 0.2, compared with the traditional open type breakwaters.     

应用Boussinesq方程对非线性Stem波的数值研究

本文应用具有四阶频散特征的新型Ｂｏｕｓｓｉｎｅｓｑ方程，采用空间差分为交错Ｓｈｕｍａｎ格式，时间层为ＡＤＩ的有限差分格式，对非线性Ｓｔｅｍ波进行了数值模拟研究。其结果表明，这种组合式差分格式能有效地模拟非线性Ｓｔｅｍ波的演变规律。同时由计算结果也发现当入射波质的角大于某临界值时，Ｓｔｅｍ波动场向Ｇｅｎｕｓ－２波系转化并呈现出较稳定的六角形波型双周期结构，在入射波系的入射角小于某一临界值时，沿墙发展     

ALTERNATIVE MODEL FOR NONLINEAR WATER WAVES OVER ARBITRARY DEPTHS

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Design formulas of transmission coefficients for permeable breakwaters

New empirical formulas of the transmission coefficient for permeable breakwaters were suggested based on available experimental data regarding the low-crest structure(LCS), including the permeable rubble mound breakwater and pile-type breakwater. The rationality of the present formulas was verified by their comparison with existing empirical and analytical formulas. Numerical flume results were obtained by solving the modified Boussinessq-type wave equations(MBEs), and a new expression relating the friction coefficient α to the relative submerged depth t sR H was also derived. Comparative analysis shows that the results of the present formulas agree with the numerical flume results as well as available experimental data, and the present formulas are superior to the existing empirical and analytical expressions in estimating the transmission coefficient. The present formulas can provide references for estimation of the transmission coefficient in engineering practice.     

波浪传播的数值模拟与物理模拟耦合模型

此文对于二维波浪的传播建立了数值模拟与物理模拟的耦合模型。模型中,数值模拟采用基于改进Boussinesq方程的三角形网格有限元模型,物理模拟采用推板式造波机。模型的求解采用空间五点的拉格朗日插值和时间的四阶Runge-Kutta格式。通过波浪模拟实验研究了耦合模型在不同波浪要素下的适应性。进一步针对于规则波和不规则波分别建立了实时修正由于造波机造波性能所引起的模拟误差的方法。波浪模拟实验结果表明,耦合边界附近数模结果与物模结果吻合很好,实时修正方法能很好修正由于造波机造波性能所引起的模拟误差,耦合模型和实时修正方法能有效建立起数模与物模的确定性联合。     

浮式防波堤研究进展

浮式防波堤与其他传统防波堤相比,可适应水深较大、地基软弱、大潮差和引入水体交换等情况,在港口海岸工程、海洋工程以及海水养殖等诸多领域具有广阔应用前景。对国内外浮式防波堤的主要研究成果和进展进行了综述,从理论推导、经验公式和数值计算3个方面归纳和总结了浮式防波堤波浪透射系数的计算方法。介绍了浮式防波堤结构型式的研究进展,重点分析了浮箱式、浮筒式、浮筏式及其相应改进结构等不同型式浮式防波堤的消浪原理和消浪效果,分析比较了不同结构型式浮式防波堤的优缺点。最后介绍了浮式防波堤在国内外的工程应用,并分析了限制浮式防波堤应用的主要原因,指出了目前浮式防波堤研究方面的不足,以及推广应用浮式防波堤需要进一步研究的内容。     

废旧轮胎浮式防波堤模型试验

依据水弹性相似理论设计小比尺的废旧轮胎浮式防波堤模型,该模型试验结果与原型结果吻合较好,验证了废旧轮胎浮式防波堤模型试验所取的相似关系是合理的,试验技术是可行的。研究废旧轮胎浮式防波堤结构衰减波能量的机理,探讨结构相对堤宽、锚链拖地长度、锚链刚度对废旧轮胎浮式防波堤消浪性能及锚链力的影响。在该试验范围内,当堤宽大于0.6倍波长时,透射系数小于0.5,锚链刚度和锚链拖地长度对透射系数的影响不明显。     

水平斜插板透空式防波堤消波性能数值模拟

通过改进已有的防波堤模型，建立了一种新型水平斜板透空式防波堤模型。基于VOF方法建立了波浪与水平斜板防波堤相互作用的数值模型。经数值模拟研究了该新型水平斜板防波堤结构对波浪透射系数的影响，主要考虑了斜板角度、波陡、相对板间距、相对板宽和相对出水高度等因素对防波堤消波效果的影响。模拟结果显示:①水平斜插板透空式防波堤比水平板透空式防波堤的消波效果好。在斜插板作用下，随着斜板角度增大，透射系数逐渐增大，但增幅逐渐减小；②随着波陡增大，透射系数先减后增；③随着水平板间距增加，透射系数增大；④随着防波堤相对板宽的增大，透射系数逐渐减小；⑤随着防波堤出水高度增加，透射系数先减后增。结果表明，该新型结构防波堤的消波效果显著，可以很好地消减波浪，应用前景良好。     

Revisiting study on Boussinesq modeling of wave transformation over various reef profiles

To better understand the complex process of wave transformation and associated hydrodynamics over various fringing reef profiles, numerical experiments were conducted with a one-dimensional （1D） Boussinesq wave model. The model is based on higher-order Boussinesq equations and a higher-accuracy finite difference method. The dominant energy dissipation in the surf zone, wave breaking, and bottom friction were considered by use of the eddy viscosity concept and quadratic bottom friction law, respectively. Numerical simulation was conducted for a wide range of wave conditions and reef profiles. Good overall agreement between the computed results and the measurements shows that this model is capable of describing wave processes in the fringing reef environment. Numerical experiments were also conducted to track the source of underestimation of setup for highly nonlinear waves. Linear properties （including dispersion and shoaling） are found to contribute little to the underestimation; the low accuracy in nonlinearity and the ad hoc method for treating wave breaking may be the reason for the problem.     

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.     

Numerical study of edge waves using extended Boussinesq equations

An edge wave numerical model was developed based on extended Boussinesq equations with the internal wave-generation method. The form of edge waves near a seawall was chosen as the input signal in order to avoid treatment of the moving shoreline on a sloping beach. As there was an energy transfer between different edge wave modes, not only the target mode but also other modes appeared in the simulations. Due to the nonlinear effect, the simulation results for mode-0 edge waves were slightly modulated by mode-1 and mode-2 waves. As the magnitudes of these higher-mode waves are not significantly related to those of the target mode, the internal wave-generation method in Boussinesq equations can produce high-quality edge waves. The numerical model was used to investigate the nonlinear properties of standing edge waves, and the numerical results were in strong agreement with theory.     

NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP

Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.     

各种扰动源产生孤立子波的研究

本文就四种不同形式的扰动在浅水中生成孤立子波的问题进行了研究。这里采用的理论基础是Boussinesq型非线性色散长波模型。非线性偏微分方程组按初-边值问题用有限差分法数值求解,这里包括对开边界条件的近似处理。 数值计算实例给出了四种不同扰动源生成孤立子波的条件和规律。由对计算结果的分析比较,可以发现当外界与流体间有一定方式的质量、动量或能量(动能、位能)交换时,只要满足一定的条件均能生成孤立子波。     

BOUSSINESQ MODELLING OF NEARSHORE WAVES UNDER BODY FITTED COORDINATE

A set of nonlinear Boussinesq equations with fully nonlinearity property is solved numerically in generalized coordinates,to develop a Boussinesq-type wave model in dealing with irregular computation boundaries in complex nearshore regions and to facilitate the grid refinements in simulations.The governing equations expressed in contravariant components of velocity vectors under curvilinear coordinates are derived and a high order finite difference scheme on a staggered grid is employed for the numerical implementation.The developed model is used to simulate nearshore wave propagations under curvilinear coordinates,the numerical results are compared against analytical or experimental data with a good agreement.     

Effects of the wave directionality on wave transformation

A numerical model is proposed based on the time domain solution of the Boussinesq equations using the finite element method in this paper. The typical wave diffraction through a breakwater gap is simulated to validate the numerical model. Good agreements are obtained between the numerical and experimental results. Further, the effects of the wave directionality on the wave diffraction through a breakwater gap and the wave transformation on a planar bathymetry are numerically investigated. The results show that the wave directional spreading has a significant effect on the wave diffraction and refraction. However, when the directional spreading parameter s is larger than around 40, the effects of the wave directional spreading on the wave transformation can be neglected in engineering applications.