Modeling the interaction of solitary waves and semi-circular breakwaters by using unsteady reynolds equations

A vertical 2 -D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid( VOF) method was used to reconstruct the free surface. The model was verified by experimental data. Then the model was used to simulate solitary wave interaction with submerged, alternative submerged and emerged semi-circular breakwaters. The process of velocity field, pressure field and the wave surface near the breakwaters was obtained. It is found that when the semi-circular breakwater is submerged, a large vortex will be generated at the bottom of the lee side wall of the breakwater ; when the still water depth is equal to the radius of the semi-circular breakwater, a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting, but the velocity near the bottom of the lee side wall of the breakwater is always relatively small. When the semi-circular breakwater is emerged, and solitary wave cannot overtop it, the solitary wave surface will run up and down secondarily during reflecting from the breakwater. It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.     

均匀水流冲击下扭王字块断裂失稳过程的数值模拟研究

扭王字块是一种重要的港口防波堤护面块体,其断裂失稳过程与所受水流冲击力密切相关。文章以基于连续介质力学的离散元方法(CDEM)为基础,通过引入FVM算法及半弹簧-半棱联合接触模型,分别实现了大位移下单元变形的准确计算及单元接触的快速更新。基于改进后的CDEM方法,通过在扭王字块表面施加按流速方向逐渐增加的动态面力,对均匀水流冲击下单扭王字块的断裂过程及扭王字块群的失稳滑移过程进行了数值分析。通过分析,不同方向水流冲击下单扭王字块的主要断裂模式为沿着根部的折断,其断裂流速约为21~25m/s;不同吨位下扭王字块群的失稳模式为扭王字块单体从群体中跳出,其失稳流速约为4~11m/s。     

海岛渔港防波堤建设的潮动力响应

摘要：潮流场．通过计算舟山大岙渔港防波堤工程建造前后潮流场、潮位及纳潮量的变化,分析了海岛渔港防波堤建设的潮动力响应．结果表明防波堤工程的建造,对港内的纳潮量和潮波影响不大,但却改变了进出渔港的潮流流路和流速．尤其在渔港进出口断面,尽管断面面积缩小,但断面平均流速却未随之增大,反而有较大幅度的减小,最大流速减小约0．35m·s^-1     

应用SBFEM研究波浪与薄板的相互作用问题

应用比例边界有限元法(SBFEM)求解了频域下波浪与刚性薄板防波堤相互作用问题。求解中将整个计算区域分为薄板周围的有限子域和直到无限远处的无限子域。有限子域的比例中心设置在薄板的下端,这时薄板的两侧为侧边面,而无限子域的比例中心设置在无限子域与有限子域的交界上,同时将水底和自由水面做为平行侧边面。应用加权余量法在每个子域内推导出比例边界有限元方程,然后在有限子域与无限子域交界上匹配求解。通过与解析解的对比,证明了这种方法的精确性,而后对不同类型的薄板防波堤进行了计算,并给出了反射和透射系数的变化规律。     

潜堤对波浪在直立式防浪墙上爬高的影响

对直立式防浪墙前潜堤的空间布置对波浪在直墙上爬高的影响进行了研究.建立简化模型,即直立式防浪墙前海床设计为平底,潜堤设计为直立薄板. 改变潜堤高度及其与防浪墙之间距,研究不同的潜堤布置对波浪在直墙上爬高的影响. 针对线性波浪场,利用数值波浪水槽模拟了潜堤作用下直墙上波浪的爬高现象. 同时建立了理论模型,系统地分析了潜堤布置形式对直墙上波浪爬高的影响. 研究结果表明潜堤相对于水深的高度越大,对波浪在直墙上爬高的影响越大,而在一定的相对高度条件下,潜堤与直立墙之间距对波浪爬高的影响呈现出一定的规律性.      

Wave interaction with a new type perforated breakwater

In this study examined is the wave interaction with a new modified perforated breakwater, consisting of a perforated front wall, a solid back wall and a wave absorbing chamber between them with a two-layer rock-filled core. The fluid domain is divided into three sub-domains according to the components of the breakwater. Then by means of the matched eigenfunction expansion method, an analytical solution is obtained to assess the hydrodynamic performance of the new structure. An approach based on a step approach method is introduced to solve the complex dispersion equations for water wave motions within two-layer porous media. Numerical results of the present model are compared with previous limiting cases. The effects of rock fill on the reflection coefficient and the horizontal wave force are discussed. The project supported by the Program for Changjiang Scholars and Innovative Research Teams in Universities (IRT0420). The English text was polished by Keren Wang.     

Propagation and scattering of waves by dense arrays of impenetrable cylinders in a waveguide

A coupled numerical scheme, based on modal expansions and boundary integral representations, is developed for treating propagation and scattering by dense arrays of impenetrable cylinders inside a waveguide. Numerical results are presented and discussed concerning reflection and transmission, as well as the wave details both inside and outside the array. The method is applied to water waves propagating over an array of vertical cylinders in constant depth extended all over the water column, operating as a porous breakwater unit in a periodic arrangement (segmented breakwater). Focusing on the reflection and transmission properties, a simplified model is also derived, based on Foldy–Lax theory. The latter provides an equivalent index of refraction of the medium representing the porous structure, modeled as an inclusion in the waveguide. Results obtained by the present fully coupled and approximate models are compared against experimental measurements, collected in wave tank, showing good agreement. The present analysis permits an efficient calculation of the properties of the examined structure, reducing the computational cost and supporting design and optimization studies.     

Large Motions of a Moored Floating Breakwater Modeled as an Impact Oscillator

Two-dimensional motions of a floating breakwater moored to thesea floor by two cables are considered. The breakwater is modeled bothas a point mass and as a rigid body. The mooring lines are assumed tohave no effect on the breakwater when they are slack, and to provide aninstantaneous impulsive force when they become taut, analogous to animpact oscillator or a ball bouncing on a rigid surface. The axialcomponent of the velocity is reduced at this instantaneous tautcondition. Fluid inertia and damping are not included, and the waveforces are assumed to be harmonic. A critical force is defined, and theeffects of the forcing frequency, the coefficient of restitution, andthe shape and size of the body on the critical force are examined.Trajectories of the motion are plotted and the impact velocities arecomputed and analyzed. Knowledge of the number and magnitude of theseimpacts is useful in assessing fatigue of the mooring lines.     

Numerical simulations of wave interactions with vertical wave barriers using the SPH method

This paper focuses on the fluid boundary separation problem of the conventional dynamic solid boundary treatment (DSBT) and proposes a modified DSBT (MDSBT). Classic 2D free dam break flows and 3D dam break flows against a rectangular box are used to assess the performance of this MDSBT in free surface flow and violent fluid–structure interaction, respectively. Another test, water column oscillations in a U‐tube, is specially designed to reveal the applicability of dealing with two types of particular boundaries: the wet–dry solid boundary and the large‐curvature solid boundary. A comparison between the numerical results and the experimental data shows that the MDSBT is capable of eliminating the fluid boundary separation, improving the accuracy of the solid boundary pressure calculations and preventing the unphysical penetration of fluid particles. Using a 2D SPH numerical wave tank with MDSBT, the interactions between regular waves and a simplified vertical wave barrier are simulated. The numerical results reveal that the maximum horizontal force occurs at the endpoint of the vertical board, and with the enlargement of the relative submerged board length, the maximum moment grows linearly; furthermore, the relative average mass transportation under the breakwater initially increases to 11.14 per wave strike but is later reduced. The numerical simulation of a full‐scale 3D wave barrier with two vertical boards shows that the wave and structure interactions in the practical project are far more complicated than in the simplified 2D models. The SPH model using the MDSBT is capable of providing a reference for engineering designs. Copyright © 2014 John Wiley & Sons, Ltd.     

Wave reflection by a submerged cycloidal breakwater in presence of a beach with different depth profiles

In this work, formulas for the reflection and transmission coefficients of one-dimensional linear water waves propagating over a submerged structure with a cycloidal cross section in presence of a sloping beach are determined. In the specialized literature, the previous coefficients are obtained mainly for the limit of linear water waves, considering that the water depth upstream and downstream of the structure is flat. For the analysis, we have obtained an approximate analytical solution to the dimensionless Modified Mild-Slope Equation, which models the interactions of a wide range of water waves, from short waves to long waves. The results shown that the presence of small breakwaters not always generate increments on the reflection coefficients, but on the contrary case they contribute to the reflection of the waves decreasing, which is due to the interference of energy that exists between the inclined beach and the structure. To validate the approximate analytical solution, we present a comparison against analytical solutions reported in the specialized literature, obtained with the aid of linear long wave theory, and a numerical solution, all the solutions adjust properly. Results of this study are expected to be used by coastal engineers for preliminary feasibility and desk design of submerged cycloidal breakwaters.