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     

Statistics of nonlinear wave crests and groups

Groups of large nonlinear waves with sharper higher crests can pose hazards to ships, induce harbor resonance and cause wave-overtopping of fixed and floating structures. Past interest in wave groups has mostly been focused on the statistics and modeling of linear wave groups. Studies on nonlinear wave groups are surprisingly few, and address deep water waves only. Here, statistics of nonlinear wave crests and wave-crest groups in deep and transitional water depths are considered, using an appropriate second-order representation for crest heights and the continuous wave-envelope approach. In particular, theoretical expressions describing the statistics of nonlinear wave crests and their groups are posed in the form of a simple second-order transformation of well-known results on linear waves. Predictions from the transformation so posed compare well with nonlinear wave data gathered in the North Sea, and demonstrate that nonlinearities do affect the statistics of large wave crests and their groups significantly.     

Long waves dissipation and harmonic generation by coastal vegetation

In this paper, we study the harmonic generation and energy dissipation as water waves propagating through coastal vegetation. Applying the homogenization theory, linear wave models have been developed for a heterogeneous coastal forest in previous works (e.g. [17], [10], [11]). In this study, the weakly nonlinear effects are investigated. The coastal forest is modeled by an array of rigid and vertically surface-piercing cylinders. Assuming monochromatic waves with weak nonlinearity incident upon the forest, higher harmonic waves are expected to be generated and radiated into open water. Using the multi-scale perturbation theory, micro-scale flows in the vicinity of cylinders and macro-scale wave dynamics are separated. Expressing the unknown variables (e.g. velocity, free surface elevation) as a superposition of different harmonic components, the governing equations for each mode are derived while different harmonics are interacting with each other because of nonlinearity in the cell problem. Different from the linear models, the leading-order cell problem for micro-scale flow motion, driven by the macro-scale pressure gradient, is now a nonlinear boundary-value-problem, while the wavelength-scale problem for wave dynamics remains linear. A modified pressure correction method is employed to solve the nonlinear cell problem. An iterative scheme is introduced to connect the micro-scale and macro-scale problems. To demonstrate the theoretical results, we consider incident waves scattered by a homogeneous forest belt in a constant shallow depth. Higher harmonic waves are generated within the cylinder array and radiated out to the open water region. The comparisons of numerical results obtained by linear and nonlinear models are presented and the behavior of different harmonic components is discussed. The effects of different physical parameters on wave solutions are discussed as well.     

A three-point method for estimating wave reflection of obliquely incident waves over a sloping bottom

A three-point method for estimating wave reflection is proposed to account for monochromatic oblique incident waves propagating over a sloping beach. The amplitudes of reflected wave and incident wave are separated using wave amplitudes measured at three fixed wave gauges with a distance. The applicability of the theory is verified by comparing the simulated results with the available theoretical, numerical and experimental results for the estimation of wave reflection. The sensitivity is also tested to provide a more accurate prediction of the reflection coefficient.     

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoc unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application.     

Analysis and simulation of wave records through fast Hartley transform

The Hartley transform, a real-valued alternative to the complex Fourier transform, is presented as an efficient tool for the analysis and synthesis of ocean surface wave records. Basic theoretical properties of this real-valued transform are briefly reviewed. Similarities and differences between Fourier and Hartley integral transforms, as well as computational benefits and disadvantages between numerical algorithms used to evaluate their discrete versions, are presented. The fast Hartley transform algorithm is used to simulate stationary Gaussian time series of the sea surface elevation and to estimate the spectral density function, the Hilbert transform and the envelope function of wave records.     

Theoretical Approximation of Focusing-Wave Induced Load upon A Large-Scale Vertical Cylinder

Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.     

Effect of Nonlinearity on Groupiness of Random Wave Fields

Theoretical studies so far on random wave groups have all been in linear ways.Methods to sim-ulate random wave groups,an important subject in ocean engineering,also employ relationship resulting froma Gaussian process.Many filed measurements have shown that the real sea surfase displacement deviatessomewhat from Gaussian distribution.Tayfun et al.have further depicted in theory that the envelope spectralpeak frequency is constantly zero for a Gaussian process which means that the groupiness factors will be con-stants,too.In this paper,the effect of nonlinearity on groupiness of a random wave field is examined via thetheoretical results derived by Tayfun et al.from an expression of amplitude-modulated Stokes waves.Whenthe surface displacement is treated as a non-Gaussian process,it is found that the group height factors GF_1and GF_2 proposed by Zhao et al.and Yu et al.,respectively,depend on a nonlinearity factor as well as aspectrum-bandwidth factor,deferring from the case of a Gaussion process.Compariso     

聚焦波作用下半浸没圆柱所受波浪载荷理论研究

由于畸形波的物理机制较复杂,有关畸形波-结构物相互作用的理论研究进展缓慢。然而对于较简单的畸形波模型与规则结构体,可以给出畸形波-结构物相互作用的理论解。本文基于畸形波的一种基本模型聚焦模型,采用解析方法研究其对半浸没圆柱体产生的波浪载荷。为保留畸形波的大部分特征,聚焦模型采用高斯包络描述。通过流场分隔给出绕射势,进而给出圆柱所受水平波浪力与波浪弯矩。采用适当方法简化理论公式,并与数值结果进行对比验证。此外,系统分析了聚焦程度、浸没深度与聚焦位置等参数对波浪载荷的影响。     

Wave group statistics from numerical simulations of a random sea

Two commonly used methods of simulating random time series, given a target power spectrum, are discussed. Wave group statistics, such as the mean length of runs of high waves, produced by the different simulation schemes are compared. The target spectra used are obtained from ocean measurements, and cover a wide range of ocean conditions. For a sufficiently large number of spectral components, no significant differences are found in the wave group statistics produced by the two simulation techniques.     

Analysis of wave groups by wave envelope-phase and the Hilbert Huang transform methods

The wave groups are studied by both conventional wave analysis methods and by the non-stationary Hilbert Huang Transform (HHT) method. Full-scale wave records containing abnormal waves are used. Instantaneous quantities, such as envelope, phase and frequency, are adopted to study the wave grouping. A refined definition of wave group is proposed considering that the wave process is simultaneously amplitude and frequency modulated. The validation of the proposed definition is conducted by analysis of numerical simulation data. Group parameters are proposed based on the time-frequency distribution of energy. An attempt is made to find the relationship between the characteristics of abnormal waves and the group characteristics.     

Effects of wave breaking on wave statistics for deep-water random wave train

The experimental studies of the breaking effects on wave statistics for deep-water random waves are presented. It is especially focused on the behavior of kurtosis of surface elevations due to wave breaking. Wave breaking suppresses the maximum limit of kurtosis of the surface elevation, although skewness depends on characteristic wave steepness. The mean instantaneous wave steepness of breaking waves defined using the zero-down-crossing method was much lower than expected from the Stokes waves.     

Wave-height distributions and nonlinear effects

Theoretical distributions proposed for describing the crest-to-trough heights of linear waves are reviewed briefly. To explore the effects of nonlinearities, these are generalized to second-order waves, utilizing quasi-deterministic results on the expected shape of large waves. The efficacy of Gram–Charlier models in describing the effects of third-order nonlinearities on the distributions of wave heights, crests and troughs are examined in detail. All models and a fifth-order Stokes–Rayleigh type model recently proposed are compared with linear and nonlinear waves simulated from the JONSWAP spectrum representative of long-crested extreme seas, and also with oceanic data gathered in the North Sea. Uncertainties arising from the variability of probability estimates derived from sample populations of limited size are considered. Ultimately, the comparisons show that nonlinearities do not have any discernable effect on the crest-to-trough heights of oceanic waves. Most of the linear models considered yield similar and reasonable predictions of the observed data trends. Gram–Charlier type distributions seem neither effective nor particularly useful in describing the statistics of large wave heights or crests under oceanic conditions. However, they do surprisingly well in predicting unusually large wave heights and crests observed in some 2D wave-flume experiments and 3D numerical simulations of long-crested narrow-band random waves.     

The prediction of the dynamic and structural motions of a floating-pier system in waves

In this study, a two-dimensional floating pier consists of single rectangular impermeable pontoon with side supporting pile-columns is studied. The purpose of this study is to present a theoretical solution for the linearized problem of incident waves exerting on a floating pier with pile-restrained. All boundary conditions are linearized in the problem, which is incorporated into a scattering problem and radiation problem with unit displacement. The method of separation of variables is used to solve for velocity potentials. For the radiation problem with unit heave and pitch amplitude, the boundary value problem with non-homogeneous boundary condition beneath the structure is solved by using a solution scheme. By calculating the wave force from velocity potential and solving the equation of motion of the floating structure simultaneously a close form theoretical solution for the problem is developed. The finite element method was also applied to calculate the dynamic responses on the supporting piles subjected to the pontoon motions and incident waves.     

Wave height distributions in bimodal sea states from offshore basins

The paper presents results for the distribution of wave heights from laboratory generated bimodal sea states. Data collected at the DHI offshore basin are analyzed and compared with results based on wave records from the MARINTEK offshore basin. The comparisons are done for three groups of mixed sea states: wind-sea dominated, swell-dominated and energy-equivalent, determined on the basis of the parameter sea-swell energy ratio (SSER), which have been generated according to the model of Guedes Soares (1984). In some sea states abnormal or freak waves have been observed.The quasi-determinism theory of Boccotti is used to expand some linear narrowband models to second order, thus providing validation of the adequacy of the equations to represent the linear components of the wave heights. Also, the data are compared with the predictions of a third order model using as a nonlinear correction the coefficient of kurtosis. Due to the coexistence of wind-sea and swell, the core of the autocovariance function in some cases demonstrates a global minimum which is the second local minimum in the sequence. This can affect the fitting ability of distributions whose parameters depend on the form of the autocorrelation function or its envelope.The results for MARINTEK and DHI data show similar patterns of fit between predicted and observed exceedance probabilities for the considered classes of bimodal spectra.     

THE DISTRIBUTION OF SIGNIFICANT CREST HEIGHTS OF SEA WAVES

Based on linear theory of sea waves, the height distribution of the intersections of wave surface with its envelope is derived. The distribution may be regarded as that of the significant crest heights under certain conditions. Some properties of this distribution are discussed in analogy to maxima theory. Data are found to be in good agreement with the theoretical curve.     

Bow impact loading on FPSOs 1—Experimental investigation

Steep wave impact pressures and the structural dynamic response of floating production storage and offloading platform (FPSO) bows are studied using 1:80 scale segmented, instrumented models. The construction of these segmented models is discussed. The ‘new-wave’ theory is adopted and extended to generate steep waves and a limiting form of steep wave that might be found in deep water is proposed. A comparison between linear theoretical, experimental and suggested wave models is made. Experimental results with systemically varying parameters are presented.     

Generation and propagation of transient nonlinear waves in a wave flume

A semi-analytical nonlinear wavemaker model is derived to predict the generation and propagation of transient nonlinear waves in a wave flume. The solution is very efficient and is achieved by applying eigenfunction expansions and FFT. The model is applied to study the effect of the wavemaker and its motion on the generation and propagation of nonlinear waves. The results indicate that the linear wavemaker theory may be applied to predict only the generation of waves of low steepness for which the nonlinear terms in the kinematic wavemaker boundary condition and free-surface boundary conditions are of secondary importance. For waves of moderate steepness and steep waves these nonlinear terms have substantial effects on wave profile and wave spectrum just after the wavemaker. A wave spectrum corresponding to a sinusoidally moving wavemaker possesses a multi-peak form with substantial nonlinear components, which disturbs or may even exclude physical modeling in wave flumes. The analysis shows that the widely recognized weakly nonlinear wavemaker theory may only be applied to describe the generation and propagation of waves of low steepness. This is subject to further restrictions in shallow and deep waters because the kinematic wavemaker boundary condition as well as the nonlinear interaction of wave components and the evolution of wave energy spectrum is not properly described by weakly nonlinear wavemaker theory. Laboratory experiments were conducted in a wave flume to verify the nonlinear wavemaker model. The comparisons show a reasonable agreement between predicted and measured free-surface elevation and the corresponding amplitudes of Fourier series. A reasonable agreement between theoretical results and experimental data is observed even for fairly steep waves.     

Linear irregular wave generation in a numerical wave tank

In the design of any floating or fixed marine structure, it is vital to test models in order to understand the fluid/structure interaction involved. A relatively inexpensive method, compared to physical model testing, of achieving this is to numerically model the structure and the wave conditions in a numerical wave tank. In this paper, a methodology for accurately replicating measured ocean waves in a numerical model at full scale is detailed. A Fourier analysis of the measured record allows the wave to be defined as a summation of linear waves and, therefore, Airy's linear wave theory may be used to input the wave elevation and associated water particle velocities. Furthermore, a structure is introduced into the model to display the ability of the model to accurately predict wave–structure interaction. A case study of three individual measured waves, which are recorded at the Atlantic marine energy test site, off the west coast of Ireland, is also presented. The accuracy of the model to replicate the measured waves and perform wave–structure interaction is found to be very high. Additionally, the absolute water particle velocity profile below the wave from the numerical model is compared to a filtered analytical approximation of the measured wave at a number of time-steps and is in very good agreement.     

Distribution of nonlinear wave crests

The distribution of nonlinear wave crests is examined on the basis of a theoretical probability density previously given elsewhere (J. Eng. Mech. 120 (1994) 1009). Certain errors contained in the original theoretical density are corrected, and the corresponding exceedance distribution is derived. The resulting theoretical forms of the probability density and exceedance distribution are then slightly simplified and compared with nonlinear wave data gathered under hurricane conditions. The results indicate that the proposed theoretical forms describe the observed distributions of large wave crests better than the Rayleigh law. However, the quantitative accuracy of the predictions is somewhat poor, as is typical of approximate theories based on Gram–Charlier-type expansions.