Energy dissipation in oscillatory flow over rippled beds

Measurements of energy dissipation have been made with an oscillating tray apparatus similar to that of Bagnold (1946). Two different bed profiles were examined: one was sinusoidal and the other consisted of fins projecting perpendicularly fromthe plate in a regular two-dimensional pattern. The tests with the sinusoidal profile showed that significant variation in energy dissipation coefficient with Reynolds number occurs near the point at which vortex formation first starts to take place. It is suggested that Bagnold did not observe this effect because of the particular profile used in his tests. The tests with the finned beds showed that even when vortex formation is fully developed there is still some variation in energy dissipation coefficient with Reynolds number, at constant a/k_s, at high Reynolds numbers.     

Numerical simulation of fluid–structure interaction using a combined volume of fluid and immersed boundary method

In this work, a combined immersed boundary (IB) and volume of fluid (VOF) methodology is developed to simulate the interactions of free-surface waves and submerged solid bodies. The IB method is used to account for the no-slip boundary condition at solid interfaces and the VOF method, utilizing a piecewise linear interface calculation, is employed to track free surfaces. The combined model is applied in several case studies, including the propagation of small-amplitude progressive waves over a submerged trapezoidal dike, a solitary wave traveling over a submerged rectangular object, and wave generation induced by a moving bed. Numerical results depicting the free-surface evolutions and velocity fields are in good agreement with either experimental data or numerical results obtained by other researchers. In addition, the simplification of the initial free-surface deformation used in most tsunami earthquake source study is justified by the present model application. The methodology presented in the paper serves as a good tool for solving many practical problems involving free surfaces and complex boundaries.     

Numerical modeling investigation on turbulent oscillatory flow over a plane rough bed composed by randomly arrayed particles

A three-dimensional numerical model is established to simulate the turbulent oscillatory boundary layer over a fixed and rough bed composed by randomly arrayed solid spheres based on the lattice Boltzmann method and the large eddy simulation model.The equivalent roughness height,the location of the theoretical bed and the time variation of the friction velocity are investigated using the log-fit method.The time series of turbulent intensity and Reynolds stress are also investigated.The equivalent roughness height of cases with Reynolds numbers of 1×10~4–6×10~4 is approximately 2.81 d(grain size).The time variation of the friction velocity in an oscillatory cycle exhibits sinusoidal-like behavior.The friction factor depends on the relative roughness in the rough turbulent regime,and the pattern of solid particles arrayed as the rough bed in the numerical simulations has no obvious effect on the friction factor.     

Wave boundary layer over a stone-covered bed

This paper summarizes the results of an experimental investigation on wave boundary layers over a bed with large roughness, simulating stone/rock/armour block cover on the sea bottom. The roughness elements used in the experiments were stones the size of 1.4cm and 3.85cm in one group of experiments and regular ping-pong balls the size 3.6cm in the other. The orbital-motion-amplitude-to-roughness ratio at the bed was rather small, in the range a/k_s = 0.6–3. The mean and turbulence properties of the boundary-layer flow were measured. Various configurations of the roughness elements were used in the ping-pong ball experiments to study the influence of packing pattern, packing density, number of layers and surface roughness of the roughness elements. The results show that the friction factor seems to be not extremely sensitive to these factors. The results also show that the friction factor for small values of the parameter a/k_s does not seem to tend to a constant value as a/k_s → 0 (contrary to the suggestion made by some previous investigators). The present friction-factor data indicates that the friction factor constantly increases with decreasing a/k_s. An empirical expression is given for the friction factor for small values of a/k_s. The results further show that the phase lead of the bed friction velocity over the surface elevation does not seem to change radically with a/k_s, and found to be in the range 12°–23°. Furthermore the results show that the boundary-layer turbulence also is not extremely sensitive to the packing pattern, the packing density, the number of layers and the surface roughness of the roughness elements. There exists a steady streaming near the bed in the direction of wave propagation, in agreement with the existing work. The present data indicate that the steady streaming is markedly smaller in the case where the ping-pong balls are aligned at 45° to the wave direction than in the case with 90° alignment. Likewise, it is found that the steady streaming is relatively smaller in the case of the one-layer ping-pong-ball roughness than in the case of the two-layer situation.     

Horizontal circulations caused by the bottom oscillatory boundary layer in a bay with a sloping bed

The horizontal circulations caused by the combined effect of the bottom oscillatory boundary layer (Stokes layer) and a sloping bed have been investigated both theoretically and experimentally. The generating mechanism is analogous to that for horizontal circulation induced by wind or by density variation. This horizontal circulation can account for a part of the tidal residual current observed in a tidal hydraulic model.     

Numerical simulation of stably stratified turbulent flows over flat and urban surfaces

Stably stratified turbulent flows over surfaces with explicit roughness elements simulating an urban built-up area have been calculated using an LES model. A method of conducting numerical experiments allowing turbulent flows with specified values of the Obukhov scale L to reach a quasisteady state at the surface has been proposed. It has been shown that, to calculate both temperature and wind-velocity profiles over such objects, one can use the same universal dependences that are used for a flat surface. It has been found that stable stratification does not affect the roughness parameter z _0u and the displacement height D.     

Threshold conditions for sand movement on a rippled bed

Flume experiments have been carried out to determine the threshold of grain movement on a rippled bed. The results indicate a form drag component of between 5 and 12 times the skin friction. The threshold of motion on the rippled sand bed can be represented by = 70D ^0.3 in whichD > 0.09 cm.     

基于IDDES方法的冲刷地形海底管道绕流数值模拟

近年来,海底管道对于近海油气工业中碳氢化合物的运输十分重要,预测海底管道周围水动力特征对于研究管道损坏机理具有重要意义。基于Spalart-Allmaras改进延迟分离涡模拟(improved detached eddy simulation,简称IDDES)湍流模型,利用开源OpenFOAM求解器计算单管冲刷过程中4个特征阶段管道周围水动力特征。在数值模拟中先计算了无圆管时均匀来流充分发展后的流场,依据该流场中进口流速分布设定有管道时的边界层及进口边界条件。通过将最终模拟结果与前人试验数据及数值模拟结果进行对比,表明了该模型计算结果相对于k-ε模型及LES模型更加贴合试验结果,验证了定义边界层方法的可靠性及IDDES模型在预测管道周围流场的适用性。模型计算结果显示,随着冲刷坑深度的逐渐增加,管道下游回流区会经历一个大幅缩减又逐渐扩大的过程,且逐渐关于圆管中心所在水平线对称;通过对不同冲刷阶段尾涡形态的分析表明,冲刷前期并没有涡脱产生,中期已经有产生涡脱的趋势,后期出现了明显的且较为稳定的涡脱。     

An experimental investigation of the velocity field under cnoidal waves over the asymmetric rippled bed

1 IntroductionIn coastal areas a ubiquitous phenomenon is theformation of ripples in the seabed. It is now widelyaccepted that the flow and sediment transport overseabed are vital in relation to erosion, surface wavedissipation and pollution dispersion et…     

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.     

Numerical simulation of unsteady free-surface motions using a boundary integral formulation

A numerical time simulation method is described to solve fluid flow problems including unsteady free surface motion. The method is based on potential flow theory. At every time step, the problem is solved using a boundary integral formulation of the fluid domain. The linearized free surface conditions are integrated in time and the solution is marched forward. Computational results simulating the free surface motion for the cases of a linear progressive wave, wave propagating into a region of calm water and the wave maker motion are presented. Comparison with theoretical results demonstrate the feasibility of the proposed simulation scheme.     

Numerical simulation of a quasi-tropical cyclone over the Black Sea

The paper describes results of numerical experiments on the simulation of a mesoscale quasi-tropical cyclone, a rare event for the Black Sea, with the MM5 regional atmospheric circulation model. General characteristics of the cyclone and its evolution and physical formation mechanisms are discussed. The balances of the momentum components have been estimated, and sensitivity experiments have been performed. It is shown that, according to its main physical properties and energy supply mechanisms, the cyclone can be related to quasi-tropical cyclones.     

Propagation of water waves over permeable rippled beds

Unsteady two-dimensional Navier-Stokes equations and Navier-Stokes type model equations for porous flow were solved numerically to simulate the propagation of water waves over a permeable rippled bed. A boundary-fitted coordinate system was adopted to make the computational meshes consistent with the rippled bed. The accuracy of the numerical scheme was confirmed by comparing the numerical results concerning the spatial distribution of wave amplitudes over impermeable and permeable rippled beds with the analytical solutions. For periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. The trajectories of the fluid particles that are initially located close to the ripples were also determined. One of the main results herein is that under the action of periodic water waves, fluid particles on an impermeable rippled bed initially moved back and forth around the ripple crest, with increasing vertical distance from the rippled wall. After one or two wave periods, they are then lifted towards the next ripple crest. All of the marked particles on a permeable rippled bed were shifted onshore with a much larger displacement than those on an impermeable bed. Finally, the flow fields and the particle motions close to impermeable and permeable beds induced by a solitary wave are elucidated.     

Numerical simulation of impact loads using a particle method

The violent free-surface motions interacting with structures are investigated using the moving particle semi-implicit (MPS) method, which was originally proposed by Koshizuka and Oka (1996) for incompressible flow simulation. In the present numerical method, a more efficient algorithm for Lagrangian moving particles is used for solving various highly nonlinear free-surface problems without using the Eulerian approach or the grid system. Therefore, the convection terms and time derivatives in the Navier–Stokes equation can be calculated more directly without any numerical diffusion, instabilities, or topological failure. In particular, the MPS method is applied to the simulation of liquid-entry and slamming problems, such as wet-drop (liquid–liquid collision) tests in an LNG tank and slamming loads (solid–liquid collision) on rigid plates with various incident angles. The numerical results are in good agreement with available experimental data.     

Numerical simulation of wave damping over porous seabeds

This paper presents a study of wave damping over porous seabeds by using a two-dimensional numerical model. In this model, the flow outside of porous media is described by the Reynolds Averaged Navier–Stokes equations. The spatially averaged Navier–Stokes equations, in which the presence of porous media is considered by including additional inertia and nonlinear friction forces, is derived and implemented for the porous flow. Unlike the earlier models, the present model explicitly represents the flow resistance dependency on Reynolds number in order to cover wider ranges of porous flows. The numerical model is validated against available theories and experimental data. The comparison between the numerical results and the theoretical results indicates that the omission or linearization of the nonlinear resistance terms in porous flow models, which is the common practice in most of analytical models, can lead to significant errors in estimating wave damping rate. The present numerical model is used to simulate nonlinear wave interaction with porous seabeds and it is found that the numerical results compare well with the experimental data for different wave nonlinearity. The additional numerical tests are also conducted to study the effects of wavelength, seabed thickness and Reynolds number on wave damping.     

The instability of viscous two-layer oscillatory flows

The instability of oscillatory flows in a two-layer fluid where the two layers differ in density and viscosity has been analysed using a perturbation method for long waves with special interest on effects of viscosity, time scale, density and depth of the fluid. The flow of a fluid with homogeneous density can be unstable, when the kinematic viscosity of the upper fluid layer is different from that of the lower one. Viscosity stratification results in unstable oscillatory flows. Two limiting cases of single-layer flow are also considered.     

胶州湾潮汐潮流动边界数值模拟

基于普林斯顿海洋模式,通过干湿网格判别法引入潮汐潮流的漫滩过程,考虑M₂,S₂,K₁,O₁,M₄和MS₄六个主要分潮,建立了胶州湾潮汐潮流数值模拟和预报模型,研究了该海域潮汐潮流特征,并讨论了漫滩对潮流模拟的影响。与实测资料的对比验证表明,该模式能够对胶州湾的潮汐和潮流做出较为合理的预测。给出了胶州湾潮汐、潮流、余流等分布特征,模拟的潮流场以及余流场涡旋等现象与观测符合良好;计算了潮波能通量,从能量角度探讨了潮波的传播特性;对潮位与潮流场演变规律,以及潮能通量的分析表明,胶州湾内的潮波以驻波为主。通过数值试验发现,漫滩过程的引入对胶州湾潮流速度的模拟至关重要,不考虑漫滩过程的模式会夸大或者低估潮流流速。对于滩涂面积广阔的海域来说,潮流数值模式中考虑漫滩的影响是必要的。     

基于格子Boltzmann方法的斜坡堤越浪数值模拟研究

准确确定越浪量对于斜坡堤设计有重要意义。利用格子Boltzmann方法(LBM),并采用主动吸收式速度入口造波、出流边界消波、VOF方法追踪自由表面以及静态Smagorinsky模型模拟紊流运动,建立二维数值波浪水槽,对光滑斜坡堤上规则波与不规则波越浪进行数值模拟。模拟结果与试验值及其他数值模型结果比较表明,二维LBM数值波浪水槽具有模拟斜坡堤越浪的能力,但对于破碎较为剧烈的越浪过程模拟,该模型还存在一定的不足,未来可从提高自由表面模型精度等方面进一步改善其性能。     

基于局部时间步长方法的潮流数值模型研究及应用

为了准确快速地模拟潮流过程,将局部时间步长(LTS)方法应用于基于黎曼近似解通量——有限体积法的浅水模型。LTS方法和传统整体最小时间步长方法的计算性能对比表明,两种方法的计算结果定量差异远小于模拟值与实测值之间相对误差;但由于LTS方法对每个网格采用了与稳定性条件相适应的尽可能大的时间步长,计算效率大幅度提高。本模型计算所得渤海、黄海、东海的潮流传播过程、潮汐调和常数的空间分布、无潮点位置,以及长江口和杭州湾区域的潮流过程与已有认识和实测资料吻合良好。     

基于MPS方法模拟低雷诺数方柱绕流问题

柱体绕流问题是流体力学领域一个非常经典的问题。当流体流经柱体时,由于黏性的存在,会发生许多复杂的流动现象,如流动分离、涡旋周期性生成与脱落等,经常被作为标准验证算例。同时,柱体绕流广泛存在于实际工程中,并在一定工况下可能对工程产生巨大危害,因此对柱体绕流进行深入研究具有重要意义。研究中,拟将一种无网格类方法——半隐式移动粒子方法(moving particle semi-implicit method,简称MPS)引入到柱体绕流问题的数值研究中,并对不同雷诺数下二维方柱绕流问题进行数值模拟。首先,使用基于MPS方法自主开发的MLParticle-SJTU求解器,结合入口边界条件和出口边界条件,模拟了雷诺数Re分别为40、200和1 000时均匀来流条件下的方柱绕流。随后,将模拟的绕流结果与文献中试验和数值计算结果进行了对比,结果吻合较好,并且在雷诺数为200和1 000时,可以清晰地捕捉到方柱尾流中的卡门涡街现象,验证了MPS方法在柱体绕流问题模拟上的有效性和适用性。