Numerical simulation of pollutant transport acted by wave for a shallow water sea bay

A numerical model of pollutant transport acted by water waves on a shallow‐water mild‐slope beach is established in this study. The numerical model is combined with a wave propagation model, a multiple wave‐breaking model, a wave‐induced current model and a pollutant convection–dispersion model. The wave propagation model is based on the higher‐order approximation of parabolic mild‐slope equation which can be used to simulate the wave refraction, diffraction and breaking in a large area of near‐shore zone combined with the wave‐breaking model. The wave‐induced current model is established using the concept of the radiation stress and considering the effect of bottom resistance caused by waves. The numerical model is verified by laboratory experiment results of regular and irregular waves over two mild beaches with different slopes. The numerical results agree well with experimental results. The numerical model has been applied in the near‐shore zone of Bohai bay in China. It is concluded that pollutant transport parallel to the shoreline due to the action of waves, which will induce serious pollution on the beach. Copyright © 2005 John Wiley & Sons, Ltd.     

水平层状岩体边坡动力响应中的结构面效应研究

根据应力波传播原理分析了水平层状岩体边坡中应力波传播特征,建立了应力波在该类边坡中传播的模型。利用离散元软件UDEC分析了不同频率垂向压缩应力波作用下边坡动力响应规律中的结构面效应。结果表明:边坡中的水平层面对坡顶的动力响应有明显影响。低频应力波作用下,水平层状岩体边坡坡顶的垂向峰值速度较均质坡体相同部位的峰值速度的增加值随坡高增加而增大。较高频率应力波作用时,边坡顶部靠近坡面的垂向峰值速度高于无结构面边坡相同部位的峰值速度,远离坡面时情况相反; 坡顶垂向峰值速度大小呈周期性变化,输入应力波频率越大该变化频次越高。研究结果将有助于进一步揭示各种不同岩体结构类型边坡在动力荷载作用下损伤机理及破坏模式。     

Godunov‐type adaptive grid model of wave–current interaction at cuspate beaches

This paper presents a second‐order accurate Godunov‐type numerical scheme for depth‐ and period‐averaged wave–current interaction. A flux Jacobian is derived for the wave conservation equations and its eigensystem determined, enabling Roe's approximate Riemann solver to be used to evaluate convective fluxes. Dynamically adaptive quadtree grids are used to focus on local hydrodynamic features, where sharp gradients occur in the flow variables. Adaptation criteria based on depth‐averaged vorticity, wave‐height gradient, wave steepness and the magnitude of velocity gradients are found to produce accurate solutions for nearshore circulation at a half‐sinusoidal beach. However, the simultaneous combination of two or more separate criteria produces numerical instability and interference unless all criteria are satisfied for mesh depletion. Simulations of wave–current interaction at a multi‐cusped beach match laboratory data from the United Kingdom Coastal Research Facility (UKCRF). A parameter study demonstrates the sensitivity of nearshore flow patterns to changes in relative cusp height, angle of wave incidence, bed roughness, offshore wave height and assumed turbulent eddy viscosity. Only a small deviation from normal wave incidence is required to initiate a meandering longshore current. Nearshore circulation patterns are highly dependent on the offshore wave height. Reduction of the assumed eddy viscosity parameter causes the primary circulation cells for normally incident waves to increase in strength whilst producing rip‐like currents cutting diagonally across the surf zone. Copyright © 2004 John Wiley & Sons, Ltd.     

Mesoscale calculations of the dynamic behavior of a granular ceramic

Mesoscale calculations have been conducted in order to gain further insight into the dynamic compaction characteristics of granular ceramics. The primary goals of this work are to numerically determine the shock response of granular tungsten carbide and to assess the feasibility of using these results to construct the bulk material Hugoniot. Secondary goals include describing the averaged compaction wave behavior as well as characterizing wave front behavior such as the strain rate versus stress relationship and statistically describing the laterally induced velocity distribution. The mesoscale calculations were able to accurately reproduce the experimentally determined Hugoniot slope but under predicted the zero pressure shock speed by 12%. The averaged compaction wave demonstrated an initial transient stress followed by asymptotic behavior as a function of grain bed distance. The wave front dynamics demonstrate non-Gaussian compaction dynamics in the lateral velocity distribution and a power-law strain rate–stress relationship.     

凹边坡参数对边坡稳定性的影响

抽象出凹边坡的几何模型,采用量纲分析的方法,给出凹边坡几何参数和物理力学参数对边坡稳定系数的影响通式．在FLAC定义的边坡稳定系数意义下,经过数万次计算,采用二次回归的方法,确定了通式中的影响指数,形成经验公式．结果表明,受Mohr-Coulomb和拉应力两个强度准则控制的材料,形成的凹边坡的稳定性受无量纲粘聚力、边坡角、内摩擦角的控制．凹形边坡有利于边坡的稳定,边坡稳定性与岩土的抗拉强度关系不大．这一稳定系数公式对于形状规则均匀性好且符合Mohr-Coulomb破坏准则的凹边坡可以给出精度高的估计．对于其它边坡的稳定性评价还需要做有针对性的工作．     

清管载荷作用下输气管道安全落差研究

山地天然气管道局部落差和坡度大,在清管过程中易在清管器冲击载荷作用下发生屈曲和应力超限。基于有限元方法研究了考虑管-土耦合作用的大落差管段清管过程非线性动力学特征,分析了清管器运行速度、管道坡度、清管器-管内壁间摩擦系数对管道受力和位移的影响,得到了不同坡度、摩擦系数条件下极限清管运行速度和最大高程差。结果表明:清管器运行速度、管道坡度的增加会引起管道应力、位移的增加,运行速度的影响效果更为显著;随着清管器-管内壁间摩擦系数的增加,清管冲击载荷先减小后增加;针对Φ813mm×11mm的X70输气管道,在管道坡度为30°~70°、落差不超过340m~691m范围内的清管作业是安全的。     

随机波浪作用下近岸波流场的数值模拟

结合近岸波浪抛物型缓坡模型和近岸波流场模型,对近岸不规则波浪及其破碎后所产生的流场进行了数值模拟. 在不规则波浪场的模拟中,采用JONSWAP波浪谱对入射单向不规则波浪要素按等分频率法进行离散,应用考虑波浪不规则性和破碎效应的抛物型缓坡方程对波浪场进行数值模拟,并基于抛物型缓坡方程中的波浪势函数等参数计算波浪辐射应力,以波浪辐射应力为主要动力因素基于近岸流数学模型对近岸波浪破碎所产生的近岸流场进行数值模拟,并对数值模拟结果进行了验证. 模拟结果表明该模型可有效地用于研究波浪破碎产生的近岸波流场.      

Higher order Boussinesq-type equations for water waves on uneven bottom

Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain. The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation. Taking the velocities on half relative water depth as the fundamental unknowns, terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution, with which the problem was closed. With enhancements of the finite order Taylor expansion for the velocity field, the application range of the present model was extended to the slope bottom which is not so mild. For linear properties, some validation computations of linear shoaling and Booij' s tests were carried out. The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents. All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.     

Over-reflection and instabilities in shear flows of shallow water with bottom friction

In a two-dimensional shear flow of shallow water, the bottom friction relates uniquely the spanwise profile of the depth-averaged velocity to the bottom topography. If the basic flow varies weakly in the spanwise direction, the local analysis of stability at every spanwise position gives the region of the flow parameters for which the classic hydraulic instability due to the bottom friction cannot occur. In this region, the linear analyses of the waves scattering and instability due to the lateral shear can be performed effectively by means of the frictionless linearized equations if both the bottom slope and friction are equally small.The energy of the total perturbed flow can be split into three main parts that correspond to the basic flow, small amplitude wave motion and induced mean flow. The waves can be either amplified or damped near the critical layers, where their streamwise phase velocity equals the velocity of the basic flow. Two physical mechanisms of this amplification exist. The first one is similar to that suggested by Takehiro and Hayashi for a linear frictionless shallow water flow. The incident and transmitted waves carry energy of opposite signs, which results in an increase in the amplitude of the reflected wave compared to that of the incident one. This mechanism of over-reflection operates for any combination of the flow parameters. The other mechanism is similar to Landau damping in plasma flows; it is related to the energy exchange between the waves and fluid particles at the critical layers due to the velocity synchronism. It may lead to either additional amplification or damping of the waves for different flow conditions. In particular, its significance can be reduced by stronger bottom friction. If the basic flow has uniform potential vorticity, Landau damping is negligible, and over-reflection always occurs. If the feed-back is provided by another critical layer, the net over-reflection results in the formation of trapped modes.     

非均匀水流水域波浪的传播变形

将两个不同的、考虑波流相互作用和能量耗散项的、依赖时间变化的双曲型缓坡方程分别化 为一组等价的控制方程组，具体分析了底摩阻项对相对频率和波数矢的影响，从而选择了合 适的数学模型. 将所选择的缓坡方程化为依赖时间变化的抛物型方程，并用ADI法进 行数值求解，建立了缓变水深水域非均匀水流中波浪传播的数值模拟模型. 通过和波流共线 的解析解的比较，说明数值解和解析解相一致. 结合Arthur(1950)水流这一经典算例，定 量地讨论了考虑联合折射-绕射作用后的波数和仅考虑折射作用的波数的差别及其对波高分 布的影响. 在基本同样的条件下, 本文的数值解与他人的计算结果一致.     

波浪作用下直立结构物附近强湍动掺气流体运动的数值模拟

波浪破碎卷入气体易对建筑物受力产生压力振荡, 了解波浪作用下建筑物附近掺气水流的运动特性是精确计算建筑物受力的前提. 基于OpenFOAM开源程序包和修正速度入口造波方法建立三维数值波浪水槽, 模型采用S-A IDDES湍流模型进行湍流封闭, 并采用修正的VOF 方法捕捉自由液面, 数值模拟了规则波在1:10的光滑斜坡上与直立结构物的相互作用过程, 重点分析了结构物附近的水动力和掺气水流运动特性. 结果表明, 建立的数值模型能精确地捕捉波浪作用下直立结构物附近的自由液面的变化以及气泡输运过程, 较好地描述气体卷入所形成的气腔形态以及多气腔之间的融合、分裂等过程; 波浪与直立结构物相互作用产生强湍动掺气水流, 其运动过程十分复杂; 掺气流体输运过程中水气界面周围一直伴随着涡的存在, 其中, 气泡的分裂与周围正负涡量剪切作用密切相关, 且其输运轨迹主要受周围流场的影响; 研究揭示了结构物附近湍动能与掺气特性的关系, 发现波浪作用下直立结构物附近湍动能的分布与掺气水流特征参数(气泡数量、空隙率)整体呈现一定的线性关系.      

Slopes of small-scale wind waves and their relation to mass transfer rates

A technique is described which measures the time-varying slope of a wavy air-water interface. New results are presented for statistical and spectral properties of slopes of wind generated waves in a rectangular flow channel. Previous measurements of oxygen absorption in the same facility are reviewed in light of these results in order to relate surface structure to mass transfer rates. Measurements of mass transfer rates and RMS wave slopes are found to agree for facilities with a large range of sizes when comparisons are made at the same friction velocities.This work was supported by the Department of Energy under grant DOE DEF G02 86ER 13556 and the National Science Foundation under grant NSF CTS-09877.     

爆炸下球壳变形空间周期分布的理论计算方法

早期研究提出了对振动叠加应变增长现象的解剖式分析方法，进而发现爆炸加载下带扰动源球壳上的弯曲波和壳体变形呈空间周期分布的规律。参考Timoshenko梁的弯曲理论，基于平截面假定和壳体发生较小的弯曲变形的假设，推导出球壳上弯曲波波速和波长的关系，计算得到最短弯曲波和与膜振动频率相近的弯曲波的波速，还结合早期研究提出的壳体变形分布周期与弯曲波波速的关系，计算得到了壳体变形空间分布的周期。结果表明:（1）理论计算结果与数值仿真结果基本吻合，其中弯曲波波速的计算结果与数值仿真结果相差在15%以内，壳体变形空间分布周期的计算结果与数值仿真结果相差在12%以内；（2）弯曲波波长越短，波速越快，当波长无限短时，波速趋于极限值，约为声速的0.574倍。本计算方法为解剖式分析方法提供了一定的理论依据。     

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.     

沿岸流不稳定多模式运动的理论分析

目前对沿岸流不稳定研究比较成熟的理论基础是线性不稳定理论,该理论假定增长率最大的不稳定模式决定着沿岸流的波动特性,但实验分析结果表明对有些情况下该假定难以解释实验中观测到的情况.利用沿岸流不稳定运动的多模式理论分析了实验中观测到的情况.结果表明沿岸流速度剖面对于沿岸流不稳定运动模式影响很大,特别是速度剖面的变化会导致不稳定模式出现多个模式的情况,即增长率曲线出现多于两个峰的情况.用解析的速度剖面分析了速度剖面前剪切和后剪切同时变化及单独变化对于沿岸流不稳定多模式运动的影响.结果表明对于坡度为1:100的平直斜坡的情况用前剪切不稳定理论可以解释其观测到的现象.      

A numerical investigation of wall effects in three‐dimensional,laminar flow over a backward facing step with a constant aspect and expansion ratio

The wall effects are investigated in the three‐dimensional laminar flow over a backward‐facing step. For this purpose, a numerical experiment is designed under actual laboratory conditions. The aspect ratio of the computational domain is 1:40 and the expansion ratio is 1:2. The Reynolds number ranges from 100 to 950. The governing equations are the steady state, isothermal and incompressible Navier–Stokes equations for Newtonian fluids. They are solved with a homemade Galerkin finite element code. The computations are validated with data from available laboratory and numerical experiments. The results focus on the variation of both velocity profiles and lengths of eddies along the lower and upper wall in the spanwise direction. Calculated streamlines in the streamwise and transverse direction show how the flow is distorted near the lateral wall and how it develops up to the plane of symmetry. The study of skin friction lines along the top and bottom wall of the domain reveals a flow that takes place in the spanwise direction. This spanwise component of the flow becomes more dominant with increasing Reynolds number and is impossible to be sustained at steady state for Reynolds numbers higher than 950 for this particular geometry. Copyright © 2012 John Wiley & Sons, Ltd.     

黄茅海波-流共同作用下的三维悬沙数值模拟

针对黄茅海河口区波流相互作用显著、三维空间结构明显及泥沙运动复杂等特点,联合第3代海浪模式SWAN,建立了波流共同作用下的三维悬沙数学模型.在水流计算中,考虑了波浪产生的辐射应力影响,波浪依赖的表面风应力影响及波浪影响下的底部剪切应力,并采用k-kl紊流闭合模型提供垂向涡粘系数和垂向扩散系数.悬沙扩散方程中的源函数利用切应力法确定,泥沙沉降速度考虑絮凝作用,从而提高黄茅海悬沙场数值模拟精度.通过含沙量实测资料验证,模拟值与实测值符合较好.在模型验证的基础上,讨论了不考虑波浪与考虑波浪两种情况下黄茅海的悬沙分布特征,为工程实际研究提供了依据.     

渤、黄海的底摩擦系数

利用伴随法，根据32个验潮站的水位观测资料来优化渤、黄海的底摩擦系数．所作的一系列数值模拟实验表明；利用伴随方法优化渤、黄海的底摩擦系数能够有效地减少数值模拟结果与观测结果的差异．     

Fiber-optic probe measurements of void fraction and bubble size distributions beneath breaking waves

Experiments were performed to determine the accuracy of single-tip fiber-optic probes for making simultaneous measurements of the void fraction and bubble size distributions under breaking waves. Tests in a vertical bubble column showed that the normalized RMS error in the void fraction measurements was ∼10%. The relationship between bubble rise time and bubble velocity was investigated in a unidirectional flow cell. Similar to previous studies the rise time and bubble velocity were found to be related by a power law equation. The probes can provide mean bubble velocities accurate to ±10% when a minimum of ∼15 individual bubble velocities are averaged. The fiber-optic probes were deployed beneath a plunging breaking wave in a laboratory wave channel. The slope and shape of the bubble cord length size distribution measured with the probes was found to agree closely with the size distribution measured from digital video recordings. The probes were then positioned in the splash-up zone of a plunging breaker and the resulting cord length distribution had a shape and slope that was in agreement with previous measurements. These results demonstrate that single-tip fiber optic probes can provide accurate simultaneous measurements of the void fraction and bubble sizes inside the dense bubble clouds entrained by breaking waves.