Nonlinear Wave Force on Pier Group in Shallow Water

Based on the 1st order cnoidal wave theory, the wave diffraction around the pier group inshallow water is studied in this paper. The formulas for calculating the nonlinear wave forces are also presented here. In order to verify the theoretical results, model tests are conducted in the wave flume in The State Key Laboratory of Coastal and Offshore Engineering located in Dalian University of Technology. The range of the wave parameters in the experiments is characteristic wave period T g/d~(1/2) = 8.08- 22.86, characteristic wave height H/ d= 0.1 ~ 0.45. The results obtained from the experiments agree with the theoretical results quite well. It is shown that, in shallow water the nonlinear wave forces acting on a pier group are greater than those calculated by linear wave theory, the value of increment in wave force increases with the increases of the nonlinearity of the wave. In the wave range studied in this paper, the nonlinear wave force can reach over 4 times the force calculatecd by linear wave theory. Thus, it is suggested that, when Tg / d~(1/2)> 8, the wave force on the piers in the pier group in shallow water should be calculated by using the cnoidal wave theory.     

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.     

辐射应力理论在近岸区的应用及其研究进展

概述了波浪辐射应力理论,介绍了波浪辐射应力理论在海洋流体动力学尤其是近岸区的应用,重点分析了该理论在研究近岸波生流、波流相互作用等问题中的应用,总结了波浪辐射应力的研究进展,对辐射应力研究提出了建议。     

A study on kinematics characteristics of freak wave

Based on the 3rd-order Stokes wave theory, the speed of freak waves is formulated in terms of the period and the wave height. Finite modified wave steepness gives rise to a significant enhancement of the nonlinear contributions to the freak wave speed in comparison with the 3rd-order Stokes wave theory. For a fix modified wave steepness, the estimated amplification of the nonlinear contributions due to the deviation from the 3rd-order Stokes wave theory is 0.22～0.99. In addition, the velocity and acceleration fields are also documented in detail. In the present simulation, the horizontal velocities are smaller than the wave speed, and the freak wave exhibits a maximal horizontal velocity up to 37% of the wave speed and a maximal vertical acceleration up to about 20% of the gravitational acceleration.     

浅水区波浪非线性效应对砂质海床动力响应的影响

以广义Biot动力固结理论为基础,运用一阶椭圆余弦波和二阶Stokes波等非线性波浪理论考虑浅水区波浪荷载的非线性效应,在时域上采用有限元方法对非线性波浪力作用下饱和砂质海床的动力响应进行了数值求解,并与线性波浪作用下海床动力响应特性进行了对比分析。结果表明,随着波长与水深之比L／d及无量纲参数T(g/d)^1/2的增大,非线性波浪对海床动力响应的影响增大。与线性波浪理论相比,孔隙水压力与有效应力幅值的增大效应非常显著。因此在近海海洋建筑物设计与工程场地评价中,波浪力的非线性特性必须引起注意。     

Comparison of Linear Level I Green-Naghdi Theory with Linear Wave Theory for Prediction of Hydroelastic Responses of VLFS

Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided betler predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. it is found that the linear level     

Wave force on vertically submerged circular thin plate in shallow water

The paper presented is a solution of shallow water wave force, using small amplitude linear wave theory on two-dimensional vertically submerged circular thin plates under three different configurations: (1) a surface-piercing circular thin plate, (2) a submerged circular thin plate, and (3) a bottom-standing circular thin plate. Finally Morison's equation is used for the determination of wave force which is based on the linear wave theory. The plate is submerged in water near the shore on uniformly sloping bottom. The solution method is confined in a finite domain, which contains both the region of different depth of water and the plate. Laplace's equation and boundary value problems are solved in a finite domain, by the method of separation of variables and the small amplitude linear wave theory. The variation of horizontal force by single particle, total horizontal force and moment with respect to the wave amplitude are obtained at different depth of water and at different wave period. It is observed that the force and moment are converging with the increase of wave period and the gradients of force and moment with respect to the wave amplitude are extremely high for lower wave period.     

V形防波堤与圆弧型防波堤之浅水波绕射作用的比较

应用椭圆余弦波的绕射理论，推导了V形防波堤的浅水波浪绕射解析解，从而对现有的Airy微幅波理论进行了有效拓展。据此理论对V形防波堤的浅水波绕射作用进行了解析计算，并与几何形状相近的圆弧型防波堤结果加以了对比。结果表明：椭圆余弦波理论计算的V形防波堤最大波浪力和最大绕射波面明显大于微幅波理论的对应值。本方法适用于张角180°的有限长直立薄壁防波堤的浅水波绕射作用计算，从而将无限长直立薄壁堤的反射波理论加以有效拓展。张角同为120°的V形堤与圆弧堤的堤后防浪效果相近，而180°圆弧堤的堤后防浪效果优于张角90°的V形堤。     

空波包理论在海浪群性研究中的应用

用 Monte Carlo方法数值模拟海浪 ,研究其波包曲线跨某参考水平的波包中空波包所占的平均比例 ,并与 Ditlevsen和 L indgren关于空波包的理论相比较。结果表明 ,在二阶近似下该理论近似适用于海浪。在此基础上对 Longuet- Higgins的群性波包理论进行修正。修正后的理论与数值结果的比较表明本文所做的修正是十分有效的。修正后的群性波包理论克服了原理论的某些固有缺陷     

Numerical Simulation of Waves Generated by Seafloor Movements

Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the souree region, the seafloor lifts to a designated height by a generation function. The numerical tests show that the linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations η0^max are carried out by beth the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on η^max are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences be- tween the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the η0^max near-linearly varies with the wave amplitudes of the surface waves, and the η0^max has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, and these differences are significantly affected by the wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.     

Second-order wave maker theory using force-feedback control. Part II: An experimental verification of regular wave generation

This paper provides an experimental verification of the new wave maker theory outlined by Spinneken and Swan [2009. Second-order wave maker theory using forcefeedback control. Part I. A new theory for regular wave generation. Ocean Engineering, in press, doi:10.1016/j.oceaneng.2009.01.019]. This theory concerns the generation of regular waves by a flap-type wave maker using force-feedback control, providing the first quantitative evidence of the inherent advantages of this latter approach. When the wave maker is controlled by a first-order force command signal, comparisons between the theory and experimental observations confirm two key points: (i) The first-order behaviour is crucial for the absorption characteristics of the machine. (ii) The second-order behaviour leads to a spurious, or unwanted, freely propagating second harmonic that is substantially smaller in amplitude when compared to an identical wave paddle operating with first-order position control. Both aspects of this work, effective absorption and reduced second-order spurious wave generation, are investigated over a broad range of wave frequencies and shown to be widely applicable. Furthermore, the theory also provides a force command signal correct to second order. This is introduced in a separate set of experiments and shown to provide further improvement in the quality of the wave generation.     

我国海浪理论及预报研究的回顾与展望

作者从海浪谱、海浪统计分布、海浪预报方法及动力机制、破碎波和近岸的海浪 5个方面回顾与总结了我国在海浪理论及预报研究方面所取得的成果 ,最后对我国在新世纪的海浪研究做一展望。     

The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.     

Second-order wavemaker theory for irregular waves

Through the last decade the theory for second-order irregular wave generation was developed within the framework of Stokes wave theory. This pioneering work, however, is not fully consistent. Furthermore, due to the extensive algebra involved, the derived transfer functions appear in an unnecessarily complicated form. The present paper develops the full second-order wavemaker theory (including superharmonics as well as subharmonics) valid for rotational as well as translatory wave board motion. The primary goal is to obtain the second-order motion of the wave paddle required in order to get a spatially homogeneous wave field correct to second order, i.e. in order to suppress spurious free-wave generation. In addition to the transfer functions developed in the line of references on which the present work is based, some new terms evolve. These are related to the first-order evanescent modes and accordingly they are significant when the wave board motion makes a poor fit to the velocity profile of the desired progressive wave component. This is, for example, the case for the high-frequency part of a primary wave spectrum when using a piston-type wavemaker. The transfer functions are given in a relatively simple form by which the computational effort is reduced substantially. This enhances the practical computation of second-order wavemaker control signals for irregular waves, and no narrow band assumption is needed. The software is conveniently included in a PC-based wave generation system—the DHI Wave Synthesizer. The validity of the theory is demonstrated for a piston type wavemaker in a number of laboratory wave experiments for regular waves, wave groups and irregular waves.     

水下平板与波浪相互作用完全非线性数值模拟(英文)

利用完全非线性数值波浪水槽技术研究水下平板与波浪的相互作用。假定水下平板厚度极薄、刚性,位于有限水深并且非常接近自由水面。应用四阶龙格库塔方法追踪每一时刻的波面形状,采用阻尼层来吸收反射波以保证算法的稳定性,同时引入平滑和重组的方法抑制自由表面控制点的较高梯度。通过对波浪与浮动圆柱相互作用的数值模拟证实了数值波浪水槽方法的有效性,计算结果与线性理论吻合良好。在波浪数值水槽方法中引入造波板模拟波浪产生并与水下平板发生相互作用,应用傅立叶解析方法对波面变形、波浪力作了分析。结果表明在板非常接近自由水面的情况下会表现出现很强的非线性,揭示了线性理论的局限性。     

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.     

Reproduction of higher harmonics in irregular waves

The basic features of higher harmonic waves were originally presented by Stokes in 1847 who showed that a 2nd-order regular wave would attain a higher, sharper crest and a flatter trough than the basic linear one. In this paper, these characteristics are investigated for an irregular wave train. This was done to make it possible to reproduce in a laboratory flume a wave train which has the correct profile and rms according to 2nd-order theory. The 2nd-order wave heights and the overall horizontal asymmetries of the wave train were calculated for a 1st-order PM and a Jonswap spectrum. The theoretical predictions show that the traditional wave generation in a laboratory flume which is based on linear theory produces free 2nd-order waves in addition to the bound 2nd-order waves described by Stokes. These free, parasitic waves incorrectly distort the shape of the waves and produce a varying rms as a function of distance from the wave paddle. In the 2nd-order theory presented in this paper, these free (parasitic) waves are calculated for the entire spectrum. Knowing these, they can be eliminated by compensating for them by using a 2nd-order control signal on the wave paddle. This is verified by a series of model tests which show that realistic wave profiles can be generated only by means of 2nd-order control signals. The theory and corresponding paddle control are presented for any type of translating, rotating or combined wave generator.     

Detection of nonlinear waves and their contribution to ocean wave spectra Part I: Theoretical consideration

This is a Part I of a paper of nonlinearities of wind waves in the deep open ocean. First, considerations are given in order to verify the theoretical expression for bound waves from observed data. We compare the contribution of bound waves and double Bragg scattering to the second-order scattering, and we show that the contribution of bound waves is larger, and that bound waves can be detected by measuring the Doppler spectra of HF (high-frequency) radio wave scattering from the sea surface. Moreover, if the theory of the HF radio wave scattering from the sea surface is verified, so is the second-order perturbation theory for bound waves. Then, the contributions of bound waves to ocean wave spectra are investigated on the basis of the nonlinear theory. The bound waves are shown to modify frequency spectra and wave directional distributions at higher frequencies, and it is shown that although the modifications of frequency spectra are smaller for a two-dimensional field case than for a one-dimensional field case, they are not negligible at higher frequencies. On the other hand, the modifications of wave directional distributions are shown to be significant at higher frequencies. These discussions become significant only when bound wave predictions are verified in the open ocean. Consequently, it is shown that nonlinearities of water waves are important in considering both radio wave scattering from the sea surface and the detailed structures of ocean wave spectra at high frequencies.     

海底边坡稳定性分析中波浪力的求解

针对浅水区波浪的非线性特性,提出了在海底边坡稳定性分析中应用椭圆余弦波理论来研究波浪力的问题,利用非线性弥散关系建立了新的适用于整个水深范围的椭圆余弦波的近似求解方法.结合工程实例,确立了海底边坡波浪力的计算步骤,并编制了计算程序.