Wave runup on a concentric twin perforated circular cylinder

The regular wave interaction with a twin concentric porous circular cylinder system consisting of an inner impermeable cylinder and an outer perforated cylinder was studied through physical model and numerical model studies. The experiments were carried out on the twin concentric cylinder model in a wave flume to study the wave runup and rundown at the leading and trailing edges of the perforated cylinder. It was found that the maximum wave runup on the perforated cylinder is almost same as the incident wave height. The experimental results were used to develop the predictive formulae for the wave runup and rundown on the perforated cylinder, which can be easily used for design applications. The wave runup profiles around the perforated cylinder for different values of ka and porosities were studied numerically using Green's Identity Method. The results of the numerical study are presented and compared with the experimental measurements.     

The effect of water depth on the performance of a small surging wave energy converter

The effect of water depth on the performance of a small surging wave energy converter (WEC) is investigated analytically, numerically and experimentally. It is shown that although the average annual incident wave power is significantly reduced by water depth, a large proportion of this reduction is due to the dissipation of highly energetic, but largely unexploitable seas. It is also shown that the power capture is related more closely to incident wave force than incident wave power. Experimental results demonstrate that both the surge wave force and power capture of a flap-type WEC increase in shallow water.     

Numerical simulation of nonlinear wave radiation by a moving vertical cylinder

In this paper the fully nonlinear potential model based on a finite element method is used to investigate the nonlinear wave motion around a moving circular cylinder. The results for the cylinder in transient motion are compared with the experimental data and a much better agreement than the linear theory is found. Further simulation for a circular cylinder in sinusoidal motion is made. It is found that when the ratio of the cylinder diameter D to the wavelength L is relatively small at a fixed motion amplitude the nonlinear components of the runup on the cylinder surface at the second- and third-harmonic frequencies become more important and this is confirmed by the experimental data. Results for the hydrodynamic force are also provided for a cylinder oscillating in a channel. It is noticed that when the frequency of the cylinder motion in a channel is between the first and the second natural frequencies of the symmetric mode, the time history has components not only at the frequency of the cylinder motion but also at the first natural frequency. The latter remains significant over the period that the simulation is made. This has important implications to model testing. If measurement is to be made at such a frequency it may take long time for the motion to become periodic at the frequency of the cylinder motion.     

珊瑚岛礁孤立波爬坡的平面二维数值模拟研究

为了探究岛屿周围珊瑚礁在抵御海啸灾害中的作用,采用激波捕捉类Boussinesq模型FUNWAVE-TVD,对孤立波在理想化三维岛礁地形上的传播及爬坡开展了现场尺度的平面二维数值模拟,分析了入射波高、礁坪水深、礁坪宽度、礁前斜坡坡度、礁后斜坡坡度、珊瑚礁糙率对岛屿四周孤立波爬高分布的影响。结果表明,珊瑚礁的存在总体上可有效降低岛屿四周孤立波的最大爬坡高度;入射波高、礁坪水深、礁坪宽度、珊瑚礁糙率是影响珊瑚岛礁四周孤立波爬坡分布的主要因素,岛礁四周最大爬坡高度会随入射波高和礁坪水深的增大、礁坪宽度和珊瑚礁糙率的减小而不断增大;当礁坪水深增大到一定程度时,珊瑚礁主要会对岛屿背浪面的爬高失去影响,而当礁坪宽度和珊瑚礁糙率减小至一定程度时,会出现岛礁四周最大爬高高于无珊瑚礁时爬高的现象;礁后斜坡的变缓会使岛礁周围的最大爬高有所减小,而礁前斜坡坡度对珊瑚岛礁周围的最大爬高几乎没有影响。     

Third order wave force on axisymmetric bodies

The third order triple-frequency wave load on fixed axisymmetric bodies by monochromatic waves is considered within the frame of potential theory. Waves are assumed to be weak non-linearity and a perturbation method is used to expand velocity potentials and wave loadings into series according to a wave steepness of kA. Integral equation method is used to compute velocity potentials up to second order in wave steepness. The third order triple-frequency wave loads are computed by an indirect method and an efficient method is applied to form the third order forcing term on the free surface quickly. The method can be used to compute third order triple-frequency surge force, heave force and pitch moment on any revolution bodies with vertical axes. The comparison with Malenica and Molin's results is made on surge force on a uniform cylinder, and comparison with experimental results is made on third order surge force, heave force and pitch moment on a truncated cylinder. More numerical computations are carried out for third order forces and moments on a uniform cylinder, truncated cylinders and a hemisphere.     

Statistical characteristics of long waves nearshore

The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width.     

福建沿海浪潮耦合漫堤风险评估:以台风天兔为例

漫堤是天文潮、风暴潮与海浪等物理要素作用于海堤后海水翻越海堤的物理过程。本文利用天文潮-风暴潮-台风浪耦合模式(ADCIRC+SWAN)、基于非结构三角形网格和高分辨率地理数据(海堤位置和高程、岸线和水深等)构建福建沿海精细化漫堤风险等级评估系统。该系统在近岸网格分辨率最高达50m,可精确刻画福建沿海复杂地形。利用模拟的水位与海浪参数,采用波浪爬高公式计算得到各海堤堤前波浪爬高。按照总水位与波浪爬高之和与海堤高程的对比,将漫堤风险分为五个等级。对2013年的超强台风天兔过程进行后报检验。结果显示,该系统计算的漫堤情况与灾后调查的漫堤实况基本一致,结果准确,说明本研究中采用的漫堤风险评估标准和方法是可行的。在此基础上,设计了4种不同的台风强度等级,对福建沿海206条海堤进行了漫堤风险等级评估,探究台风强度对漫堤风险的影响。结果表明:波浪爬高对漫堤风险的影响高于单纯的风暴潮增水;风暴潮增水随台风强度的增强增量较小,对于漫堤的风险影响较小;福建沿海波浪爬高普遍较高,随着台风强度的增强,波浪爬高会显著增加漫堤的风险等级,且应重视台风浪对海堤造成的冲击所导致的溃堤灾害。本研究可为沿海防灾减灾提供科学依据。     

Empirical parameterization of setup,swash, and runup

Using shoreline water-level time series collected during 10 dynamically diverse field experiments, an empirical parameterization for extreme runup, defined by the 2% exceedence value, has been developed for use on natural beaches over a wide range of conditions. Runup, the height of discrete water-level maxima, depends on two dynamically different processes; time-averaged wave setup and total swash excursion, each of which is parameterized separately. Setup at the shoreline was best parameterized using a dimensional form of the more common Iribarren-based setup expression that includes foreshore beach slope, offshore wave height, and deep-water wavelength. Significant swash can be decomposed into the incident and infragravity frequency bands. Incident swash is also best parameterized using a dimensional form of the Iribarren-based expression. Infragravity swash is best modeled dimensionally using offshore wave height and wavelength and shows no statistically significant linear dependence on either foreshore or surf-zone slope. On infragravity-dominated dissipative beaches, the magnitudes of both setup and swash, modeling both incident and infragravity frequency components together, are dependent only on offshore wave height and wavelength. Statistics of predicted runup averaged over all sites indicate a − 17 cm bias and an rms error of 38 cm: the mean observed runup elevation for all experiments was 144 cm. On intermediate and reflective beaches with complex foreshore topography, the use of an alongshore-averaged beach slope in practical applications of the runup parameterization may result in a relative runup error equal to 51% of the fractional variability between the measured and the averaged slope.     

Benchmark computations of wave run-up on single cylinder and four cylinders by naoe-FOAM-SJTU solver

The benchmark simulations of wave run-up on a fixed single truncated circular cylinder and four circular cylinders are presented in this paper. Our in-house CFD solver naoe-FOAM-SJTU is adopted which is an unsteady two-phase CFD code based on the open source package OpenFOAM. The Navier-Stokes equations are employed as the governing equations, and the volume of fluid (VOF) method is applied for capturing the free surface. Monochromatic incident waves with the specified wave period and wave height are simulated and wave run-up heights around the cylinder are computed and recorded with numerical virtual wave probes. The relationship between the wave run-up heights and the incident wave parameters are analyzed. The numerical results indicate that the presented naoe-FOAM-SJTU solver can provide accurate predictions for the wave run-up on one fixed cylinder and four cylinders, which has been proved by the comparison of simulated results with experimental data.     

Characteristic of tsunami force acting on shelter with mooring

Tsunami shelter has been designed and built as a refuges in case tsunami occurs. In recent year, different kinds of tsunami shelter have been proposed and developed, which is either a building type or a floating one. The main purpose of this research is to propose a new type of tsunami shelter with elastic mooring in comparison with a fixed type of shelter and to investigate tsunami force acting on the shelter and motions due to tsunami wave. Three different kinds of tsunami shelter were compared, rectangular, trapezoid and streamline type, with two conditions such as fixed on the ground and floating with elastic mooring. To compute interaction between run-up tsunami wave and the tsunami shelters with mooring, the numerical model has been developed by using particle based method, Smooth Particle Hydrodynamic (SPH) coupling with Extended Discrete Element Method (EDEM) for elastic mooring. Based on the validation of tsunami force and shelter motions with experimental results, the numerical results indicated that the model can simulate interactions between tsunami wave and shelter in fixed and mooring case. The result also shows that the tsunami force on the fixed tsunami shelter can be higher than that on the tsunami shelter with elastic mooring and then the mooring system can reduce tsunami force, 35% for averaged value and 50% for maximum one and the surge and pitch motions can be also reduced. The tsunami shelter with elastic mooring system could be a useful option for evacuating from tsunami attacking.     

Modeling of storm-induced coastal flooding for emergency management

This paper describes a model package that simulates coastal flooding resulting from storm surge and waves generated by tropical cyclones. The package consists of four component models implemented at three levels of nested geographic regions, namely, ocean, coastal, and nearshore. The operation is automated through a preprocessor that prepares the computational grids and input atmospheric conditions and manages the data transfer between components. The third generation spectral wave model WAM and a nonlinear long-wave model calculate respectively the wave conditions and storm surge over the ocean region. The simulation results define the water levels and boundary conditions for the model SWAN to transform the storm waves in coastal regions. The storm surge and local tides define the water level in each nearshore region, where a Boussinesq model uses the wave spectra output from SWAN to simulate the surf-zone processes and runup along the coastline. The package is applied to hindcast the coastal flooding caused by Hurricanes Iwa and Iniki, which hit the Hawaiian Island of Kauai in 1982 and 1992, respectively. The model results indicate good agreement with the storm-water levels and overwash debris lines recorded during and after the events, demonstrating the capability of the model package as a forecast tool for emergency management.     

Nonlinear wave interaction with a vertical circular cylinder. Part II: Wave run-up

Theoretical results for second-order wave run-up around a large diameter vertical circular cylinder are compared to results of 22 laboratory experiments conducted in regular nonlinear waves. In general, the second-order theory explains a significant portion of the nonlinear wave run-up distribution measured at all angles around the cylinder. At the front of the cylinder, for example, measured maximum run-up exceeds linear theory by 44% on average but exceeds the nonlinear theory by only 11% on average. In some cases, both measured run-up and the second-order theory exceed the linear prediction by more than 50%. Similar results are found at the rear of the cylinder where the second-order theory predicts a large increase in wave amplitude for cases where the linear diffraction theory predicts little or no increase. Overall, the nonlinear diffraction theory is found to be valid for the same relative depth and wave steepness conditions applicable to Stokes second-order plane-wave theory. In the last section of the paper, design curves are presented for estimating the maximum second-order wave run-up for a wide range of conditions in terms of the relative depth, relative cylinder size, and wave steepness.     

Study on Influences of Fringing Reef on Harbor Oscillations Triggered by N-Waves

Influences of topographic variations of the offshore fringing reef on the harbor oscillations excited by incident Nwaves with different amplitudes and waveform types are studied for the first time. Both the propagation of the Nwaves over the reef and the subsequently-induced harbor oscillations are simulated by a Boussinesq-type numerical model, FUNWAVE-TVD. The present study concentrates on revealing the influences of the plane reef-face slope,the reef-face profile shape and the lagoon width on the maximum runup, the wave energy distribution and the total wave energy within the harbor. It shows that both the wave energy distribution uniformity and the total wave energy gradually increase with decreasing reef-face slope. The profile shape of the reef face suffering leading-elevation Nwaves(LEN waves) has a negligible impact on the wave energy distribution uniformity, while for leading-depression N-waves(LDN waves), the latter gradually decreases with the mean water depth over the reef face. The total wave energy always first increases and then decreases with the mean water depth over the reef face. In general, the total wave energy first sharply decreases and then slightly increases with the lagoon width, regardless of the reef-face width and the incident waveform type. The maximum runup subjected to the LEN waves decreases monotonously with the lagoon width. However, for the LDN waves, its changing trend with the lagoon width relies on the incident wave amplitude.     

Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders

The interaction of water waves with arrays of bottom-mounted, surface-piercing circular cylinders is investigated theoretically. The sidewall of each cylinder is porous and thin. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an eigenfunction expansion approach first proposed for impermeable cylinders by Spring and Monkmeyer (1974), and later simplified by Linton and Evans (1990). Analytical expressions are developed for the wave motion in the exterior and all interior fluid regions. Numerical results are presented which illustrate the effects of various wave and structural parameters on the hydrodynamic loads and the diffracted wave field. It is found that the porosity of the structures may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave runup.     

The diffraction of linear waves by a uniform vertical cylinder with cosine-type radial perturbations

The interaction of linear waves with a uniform, bottom-mounted, surface-piercing cylinder whose diameter exhibits a cosine-type variation is investigated. Two solution methods are presented. One method is based on a perturbation theory, using a perturbation parameter defined in terms of the surface geometry of the cylinder. The analysis includes terms up to the first-order in this parameter, where the zeroth-order solution corresponds to a circular cylinder. The velocity potentials at the zeroth and first orders are expressed as eigenfunction expansions involving unknown coefficients that are subsequently determined through the cylinder boundary conditions. The second method is based on Green's theorem and gives rise to an integral equation for the fluid velocity potential on the cylinder surface. A comparison between the results of these two methods has proved that they are in good agreement for small values of the perturbation parameter. Numerical results are presented that illustrate the influence of the magnitude and frequency of these perturbations on the resulting hydrodynamic force and the wave runup on the cylinder.     

Analysis of dynamic effects relevant for the wear damage in hydraulic machines for wave energy conversion

The present paper deals with a mathematical model of a heaving-buoy Wave Energy Converter (WEC) equipped with high-pressure hydraulic power take-off machinery for energy conversion. This model is based on linear hydrodynamic theory, and a hybrid frequency-time domain model is used to study the dynamics of the heaving-body exposed to an irregular incident wave. For the power take-off system, end-stop devices are provided to protect the hydraulic machinery when the buoy is exposed to severe sea states. The model also takes into account the lubricated friction force and pressure drops of orifice flow through the valves in the hydraulic system. All the forces mentioned in the hydraulic power take-off machinery have non-linear features. A complete non-linear state space model for the WEC system is presented in this study.The WEC system was numerically simulated for different cylinder lengths under a fixed volume. The effect of fluid compressibility in the cylinder has been investigated in the mathematical model. High frequency oscillations (HFOs) caused by the compressibility of the fluid are displayed in the time series and in corresponding power spectra, and variation is shown for different cylinder sizes. Piston ring and cylinder bore wear damage is estimated by using Archard’s equation on the basis of the simulation results. A comparison of these results with a performance of an identical WEC system which neglects fluid compressibility has been done in this work. It shows that although the spectral power is small, HFO can make a large contribution to both the ring and cylinder bore wear. For the purpose of wear prediction, oscillations at or below the wave frequency and HFO may be equally important.     

Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

Three-dimensional experiments on landslide generated waves at a sloping coast

This paper describes new three dimensional experiments on water waves generated by landslides. The landslide is reproduced by a rigid elliptical body, sliding along an inclined plane (slope of 1/3, 1 vertical, 3 horizontal). The generated water waves are free to propagate both offshore and alongshore, since the plan dimensions of the used wave tank are of at least one order of magnitude larger than the width of the landslide, which can be considered to be a scale of the wave length. The experimental study has been carried out reproducing both subaerial and partially submerged landslides. The wave generation process is studied by means of video records of the near field flow and measurement of the landslide movement; the properties of the waves propagating along the coast are described on the basis of runup gauges. The waves observed during the experiments always present first a crest and then a trough; as the first wave propagates away from the generation area the crest tends to become smaller than the trough and the maximum runup along the coast is given by the second or by the third wave. An important feature is that the observed runup along the coast firstly grows with the distance from the generation area, it reaches a maximum value at about two times the width of the landslide, and then decreases. An estimate of the celerity at which the waves propagate along the coast is given on the basis of gauge measurements; it results that the crests propagate faster than the troughs, and the wave period increases.     

Solitary wave interaction with a concentric porous cylinder system

Theoretical investigations on solitary waves interacting with a surface-piercing concentric porous cylinder system are presented in this paper. The outer cylinder is porous and considered thin in thickness, while the inner cylinder is solid. Both cylinders are rigidly fixed on the bottom. Following Isaacson's [Isaacson, Micheal de St. Q., 1983. Solitary wave diffraction around large cylinder. Journal of the Waterway, Port, Coastal and Ocean Engineering 109(1), 121–127.] approach, we obtained the solutions for free-surface elevation and the corresponding velocity potential in terms of Fourier integrals. Numerical results are presented to show the effects of incident wave condition, porosity of the outer cylinder and radius ratio on wave forces and wave elevations around the inner and outer cylinders.