On the interaction of a solitary wave and a submerged dike

The unsteady, two-dimensional Navier–Stokes equations and the exact free surface boundary conditions were solved to study the interaction of a solitary wave and a submerged dike. A piston-type wavemaker was set up in the computational domain to produce the incident solitary waves. The incident wave and the associated boundary layer flow in a wave tank with a flat bed were compared with the analytical solutions to verify the accuracy of this numerical scheme. Effects of the incident wave height and the size of the dike on the wave transformation, the flow fields, and the drag forces on the dike were discussed. Our numerical results showed that even though the induced local shear stress on the top surface of the dike is large at some particular locations, the resultant pressure drag is much larger than the friction drag. The primary vortex generated at the lee side of the dike and the secondary vortex at the right toe of the dike may scour the bottom and cause a severe problem for the dike.     

Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.     

Dynamic pressure distribution on a cylinder due to wave diffraction

The experimental investigations on the dynamic pressure distribution around a large vertical cylinder resting on a flume bed and piercing the free surface subjected to regular waves have been carried out in a 4-m wide wave flume in a constant water depth of 2.5 m at Ocean Engineering Centre, Indian Institute of Technology, Madras, India. The cylinder of diameter 400 mm was fixed with diaphragm type pressure transducers at eight different locations below the still water level along with one at the still water level. In addition to this, to study the effect of nonlinearity, one pressure transducer was located above the still water level. The experimental results pertaining to mostly deep water conditions are compared with MacCamy and Fuchs theory and the agreement is found to be good. In order to account for the effects of nonlinearities the above said theory has been modified the results of which are found to be in better agreement.     

Breaking wave loads at vertical seawalls and breakwaters

This paper presents recent advances in knowledge on wave loads, based on experimental work carried out in the CIEM/LIM large flume at Barcelona within the framework of the VOWS (Violent Overtopping by Waves at Seawalls) project. Both quasi-static and impact wave forces from the new data set have been compared with predictions by empirical and analytical methods. The scatter in impact forces has been found to be large over the whole range of measurements, with no existing method giving especially good predictions. Based on general considerations, a simple and intuitive set of prediction formulae has been introduced for quasi-static and impact forces, and overturning moments, giving good agreement with the new measurements. New prediction formulae have been compared with previous measurements from physical model tests at small and large scale, giving satisfactory results over a relatively wide range of test conditions. The time variation of wave impacts is discussed, together with pressure distribution up the wall, which shows that within experimental limitations the measured pressures are within existing limits of previous study.     

Breaking wave prediction with boundary elements and finite volumes for use with small boat capsize studies: Convergence and resource requirements

The prediction of extreme breaking waves forms the foundation of many fields of research. The authors have recently completed a study in the capsize and re-righting of sailing yachts using breaking wave prediction to enhance experimental results. As breaking wave prediction is only the beginning of any research program a prediction method is required to be both accurate and computationally inexpensive. This paper describes the investigation of two methods varying in computational demand. It has been concluded that a non-linear free surface boundary element method is immediately realisable with application to a research program requiring a large number of predicted waves. A finite volume approach is realisable, but its engineering application across numerous waves is difficult.     

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depth

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.     

Comparative Study of Different SPH Schemes on Simulating Violent Water Wave Impact Flows

Free surface flows are of significant interest in Computational Fluid Dynamics（CFD）. However, violent water wave impact simulation especially when free surface breaks or impacts on solid wall can be a big challenge for many CFD techniques. Smoothed Particle Hydrodynamics（SPH） has been reported as a robust and reliable method for simulating violent free surface flows. Weakly compressible SPH（WCSPH） uses an equation of state with a large sound speed, and the results of the WCSPH can induce a noisy pressure field and spurious oscillation of pressure in time history for wave impact problem simulation. As a remedy, the truly incompressible SPH（ISPH） technique was introduced, which uses a pressure Poisson equation to calculate the pressure. Although the pressure distribution in the whole field obtained by ISPH is smooth, the stability of the techniques is still an open discussion. In this paper, a new free surface identification scheme and solid boundary handling method are introduced to improve the accuracy of ISPH. This modified ISPH is used to study dam breaking flow and violent tank sloshing flows. On the comparative study of WCSPH and ISPH, the accuracy and efficiency are assessed and the results are compared with the experimental data.     

Effects of Topography and Current on Horizontal Irrotational Waves in Shallow Water

Based on the Boussinesq assumption,derived are couple equations of free surface elevationand horizontal velocities for horizontal irrotational flow,and analytical expressions of the correspondingpressure and vertical velocity.After the free surface elevation and horizontal velocity at a certain depth areobtained by numerical method,the pressure and vertical velocity distributions can be obtained by simplecalculation.The dispersion at different depths is the same at the O(ε)approximation.The waveamplitude will decrease with increasing time due to viscosity,but it will increase due to the matching ofviscosity and the bed slope.thus,flow is unstable.Numerical or analytical results show that the waveamplitude.velocity and length will increase as the current increases along the wave direction.but theamplitude will increase.and the wave velocity and length will decrease as the water depth decreases.     

Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter

Phase control may substantially increase the power absorption in point-absorber wave energy converters. This study deals with validation of dynamic models and latching control algorithms for an oscillating water column (OWC) inside a fixed vertical tube of small circular cross-section by small-scale testing. The paper describes experimental and numerical results for the system's dynamics, using simple and practical latching control techniques that do not require the prediction of waves or wave forces, and which will be relevant to any type of point-absorbing devices.In the experimental set-up, the upper end of the tube was equipped with an outlet duct and a shut-off valve, which could be controlled to give a latching of the inner free surface movement. The pressure drop through the open valve is used as a simplified measure of the energy extraction. The control was realized by using the real-time measurement signals for the inner and outer surface displacement.A mathematical model of the system was established and applied in numerical simulation. In the case the OWC's diameter is much smaller than the wavelength and the wave amplitude much smaller than the draft, the free surface movement inside the tube can be described as an oscillating weightless piston. For this hydrodynamic problem an analytical solution is known. In addition, the mathematical model includes the effects of viscous flow losses, the air compressibility inside the chamber and the pressure drop across the valve. Experimental results were used to calibrate some of the model parameters, and the total model was formulated as a coupled system of six non-linear, first-order differential equations. Time-domain integration was used to simulate the system in order to test the control strategies and compare with experimental results.     

Experimental validation of a CFD model using a narrow wave flume

Induced swell is characterized in an experimental wave flume that is used to validate the corresponding computational model. The experiments and the numerical simulations are performed in water at several depths (h [m] of 0.2, 0.1, and 0.07), using a piston-type wave maker at set amplitudes (0.015 < A_p [m] < 0.15), accelerations-decelerations (0.3 < a_p < 1.0) and average velocities (0.03 < U [m/s] < 0.3) that control the propagation velocity, the period and the wavelength of the waves. The physical effects are modelled with a 2D computational model (STAR-CCM + v11.02) with a mesh of around 630,000 cells of different adaptive sizes, depending on the region under consideration. The physical model is based on a two-phase Eulerian “Volume of Fluid” unsteady model, accounting for gravity and surface tension, that characterizes turbulence with a k-ε model. A user-defined function, based on the period and the amplitude of the vertical paddle in the wave maker, describes the cyclic motion of the linear induction motor. Both the experimental and the computational results are analyzed taking the validity limits of various wave theories as a reference (Le Méhauté). As a result, the experiments are classified within the intermediate water depth regime that corresponds to the second-order Stokes’ wave theory. In addition, both the wave propagation velocity and the period are represented as a function of the wavelength and compared with the analytical solutions from the wave theories. The experimental and the computational test campaign yielded results that confirmed the validity of the computational model and that defined the most appropriate conditions for a high-quality CFD simulation.     

Regular waves onto a truncated circular column: A comparison of experiments and simulations

Accurate prediction of hydrodynamic forces on offshore structures is critical for safe and cost effective design of fixed and floating offshore structures exposed to a harsh environment. In the present paper, nonlinear interactions between regular waves and a single surface-piercing truncated circular column have been investigated using a frequency domain potential flow solver (DIFFRACT) and a full CFD solver in OpenFOAM for direct comparisons. Both the predicted free surface elevation around the column and the total force acting on the column have been analysed and compared with experimental data from MOERI. The degree of non-linearity and the contribution of each harmonic to the free surface run-up and wave forces have been examined, and evaluations of the accuracy and computational efficiency of the potential flow solver and the full CFD solver are provided and compared in the paper. Also of note are the local forms of the scattered waves around the column in numerical simulations, which are consistent with the Type-1 and Type-2 patterns identified in physical experiments at Imperial College.     

Simulating nonlinear waves on the free surface in surf zones with two-dimensional sloping beach

Unsteady nonlinear wave motions on the free surface in shallow water and over slopes of various geometries are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier–Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. Either linear or Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with various wave periods and sea bottom slopes in surf zone. The results are compared with other existing computational and experimental results. Agreement between the experimental data and the computation results is good.     

Large eddy simulation of spilling and plunging breakers

A Navier–Stokes solver with a free surface model is used for simulating wave breaking, undertow, and turbulence in breaking waves. The free surface model is based on the Volume of Fluid concept. Turbulence scales larger than the grid scale are simulated directly while turbulence scales smaller than the grid scale are represented by a sub-grid scale model. Two different approaches for the sub-grid scale model have been applied, which are the Smagorinsky model and a model based on a k-equation for the sub-grid scale turbulence. The waves approach the shore in shore-normal direction and break on a plane constant sloping beach. Periodic spilling and plunging breakers are simulated for 20 and 16 wave periods, respectively. The set-up, undertow, and turbulence levels are compared to experimental results. Despite the rather coarse resolution of the computational domain, satisfactory results for the wave height decay and undertow have been obtained. However, the turbulence levels are over-predicted when using the standard values of the model parameters and a complete answer to this problem has not been found. Furthermore, the evolution of vorticity over the wave period has been studied. It shows that at the initial breaking point vorticity is generated around the vertical as well as around the transverse axis. Later vorticity around the longitudinal axis (offshore–onshore direction) is generated, probably through deformation of vorticity around the other axis.     

RANS modelling applied to random wave interaction with submerged permeable structures

This paper is the second part of the work presented by Garcia et al. [Garcia, N., Lara, J.L., Losada, I.J., 2004. 2-D numerical analysis of near-field flow at low-crested breakwaters. Coastal Engineering 51 (10), 991–1020]. In the mentioned paper, flow conditions at low-crested rubble-mound breakwaters under regular wave attack were examined, using a combination of measured data of free surface, bottom pressure and fluid velocities from small-scale experiments and numerical results provided by a VOF-type model (COBRAS) based on the Reynolds-Averaged Navier–Stokes (RANS) equations. This paper demonstrates the capability of the COBRAS model to reproduce irregular wave interaction with submerged permeable breakwaters. Data provided by the numerical model are compared to experimental data of laboratory tests, and the main processes of wave–structure interaction are examined using both experimental and numerical results. The numerical model validation is carried out in two steps. First, the procedure of irregular wave generation is verified to work properly, comparing experimental and numerical data of different cases of irregular wave trains propagating over a flat bottom. Next, the validation of the numerical model for wave interaction with submerged rubble-mound breakwaters is performed through the simulation of small-scale laboratory tests on different incident wave spectra. Results show that the numerical model adequately reproduces the main aspects of the interaction of random waves with submerged porous breakwaters, especially the spectral energy decay at the structure and the spectrum broadening past the structure. The simulations give good results in terms of height envelopes, mean level, spectral shape, root-mean-square height for both free surface displacement and dynamic pressure inside the breakwater. Moreover, large-scale simulations have been conducted, on both regular and irregular incident wave conditions. The overall pattern of the wave interaction with a large-scale submerged breakwater is adequately reproduced by the numerical model. The processes of wave reflection, shoaling and breaking are correctly captured. The good results achieved at a near prototype scale are promising regarding the use of the numerical model for design purposes.     

容器固有频率对液体晃荡的影响

针对矩形容器内液体晃荡问题,采用了时域高阶边界元方法建立自由水面满足完全非线性边界条件的数学模型。求解中采用混合欧拉-拉格朗日方法追踪流体瞬时水面,运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过将计算得到的波面结果与实验数据、解析解和已发表结果对比,吻合良好,验证了本方法的准确性。进而采用谱分析方法分析了波面时间历程,得到容器各阶固有频率对液体晃荡的影响。研究发现,基频对液体晃荡的影响最大,且非线性越强,更高阶容器固有频率的影响越大。     

Wave loads on a stationary floating bottomless cylindrical body with finite wall thickness

This paper aims at presenting a method for solving the linearised diffraction problem of the interaction between regular sinusoidal, small amplitude incident waves and a bottomless cylindrical floating body with a vertical symmetry axis and finite wall thickness, through the idealisation of the flow field around the structure using ring elements. The horizontal and vertical excitation forces, the rolling moment, the resulting wave motion inside the cylinder, as well as the pressure distribution on the wetted surface of the structure are obtained by solving the diffraction boundary-value problem through the implementation of the Galerkin method. The analytical predictions are compared with other analytical results and pertinent experimental data. Finally, the influence of the wall thickness on the wave loads and the fluid motion inside the pond is examined.     

Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.     

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.     

改进波浪发电浮标性能的试验研究

为了改进波浪发电浮标为性能，以及推广使用，使之能适用于波浪周期短波高小的海区，对上海航标厂的波浪发电浮标为浮体进行了试验研究。试验测量了气室压力、内波高、浮体升沉等物理量。通过输出功率的比较，提出了浮体设计方案的建议。     

A time-dependent numerical model of the mild-slope equation

On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time-dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin’s model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin’s model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin’s model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real-time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research an d engineering applications about the wave propagation in a biggish area.