On the measurement of directional wave spectra at the southern Brazilian coast

The detailed reconstruction of the directional spectrum of wind waves from measurements of the wave field is an essential requirement for several applications, including the numerical modeling of wave evolution. Three reconstruction techniques that provide estimates of the directional distribution function D(f,θ), given the one-dimensional frequency spectrum, are compared using data from a coastal locality at the southern Brazilian coast. The techniques are the maximum entropy method (MEM), the Fourier Expansion Method using a cos² type function (FEM_cos) and the Fourier Expansion Method using a sech type function (FEM_sech). The main patterns of the wave climate at the study site are qualitatively assessed. Three main sea states, including swell, transition between local sea and swell, and directionally bimodal wind sea, are identified. Time series from three events associated with the main sea states provide test cases for inter comparison of the three reconstruction techniques. Maximum entropy estimates of D(f,θ) provide results that are more consistent than those obtained from the two FEM techniques in all cases considered.     

Modelling of multipeaked directional wave spectra

An approach for modelling of multipeaked directional wave spectra is proposed. For model identification, a numerical optimization technique that uses the random linear search algorithm is applied. This technique allows the fitting of spectral models to measured or hindcast data. The HIPOCAS hindcast data for North Atlantic are used for an application study.     

Experiments on the reflection coefficients of a detached breakwater in a directional wave field

Results of estimating the directional wave fields in front of a detached breakwater are presented here in this paper. Two of non-phase-locked methods, i.e., the Maximum Likelihood Method (MLM) and the Extended Maximum Entropy Principle Method (EMEP), were adopted for the purpose. In general, the latter outperforms the former. It is shown that the reflection coefficients decrease with increasing distances away from the detached breakwater, and within four wavelengths from the detached breakwater, the rate of the decrease is faster for wave fields having larger directional spreads. When the measuring distance is more than four wavelengths away from the detached breakwaters, the reflection coefficients tend to reach to a constant value. It is shown that, with the use of the non-phase-locked EMEP method, the effective region can be extended, as compared with the results of Huntley and Davidson [J. Waterw. Port Coast. Ocean Eng. 124 (1998) 312].     

Estimation of wave directional spreading in shallow water

This paper describes wave directional spreading in shallow water. Waves were measured for a period of 2 months using the Datawell directional waverider buoy at 15 m water depth on the east coast of India in the Bay of Bengal. The study also showed that in shallow water wave directional spreading was narrowest at peak frequency and widened towards lower and higher frequencies. The wind direction was found to deviate from the wave direction during most of the time. The unidirectional spectrum was found to be satisfactorily represented by Scott spectra.     

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

Analysis of directional wave fields using X-band navigation radar

The aim of this work is to present an approach to describe complex sea states including the ones consisting of superpositions of swell and wind sea components, using a nautical radar in X-band as a remote sensing technique. In the present article, the inversion method to obtain the spectral representation of the wave fields is described. The method is applied to analyse data obtained from simulation techniques, as well as from measurements obtained during oceanographic campaigns in the Bay of Biscay and North Sea.     

Maximum entropy estimation of directional wave spectra from an array of wave probes

A procedure for estimating directional wave spectra from an array of wave probes based on the Maximum Entropy Method (MEM) is developed in the present paper. The MEM approach yields an angular spreading function at each frequency band consistent with the input cross-spectral density matrix. The method is evaluated using numerical simulations of directional sea states. The MEM is also used to analyze data obtained from the three-dimensional wave basin of the Hydraulics Laboratory, National Research Council of Canada. Finally, the MEM is compared with the Maximum Likelihood Method (MLM) and is shown to be a powerful tool for directional wave analysis.     

海浪方向谱估计方法的比较

分别利用数值模拟和实测资料对目前被认为分辨力较高的最大似然法(MLM)、扩展本征矢方法(EEV)、扩展最大滴方法(EMEP)以及贝叶斯方法(BDM)等四种海浪方向谱估计方法的可靠性进行了分析,从不同频率、不同噪声水平和不同方向集中度三个角度检验其再现性、稳定性和实用性,结果表明MLM、EEV和BDM大致给出相同的方向分布,其中BDM的再现性最好,但实用性逊于MLM和EEV,EMEP由于稳定性差,不适用于实测资料的分析.     

Efficient computation of cross-spectral densities in the stochastic modelling of waves and wave loads

A new method is presented for efficient calculation of auto- and cross-spectral densities in the stochastic modelling of ocean waves and wave loads. As part of the short-term response analyses, the method may contribute to more efficient long-term response prediction. Specifically the cross-spectral densities of the first order wave excitation forces are considered, but the method is straightforwardly generalized to other cross-spectral densities, e.g. for wave elevation, wave kinematics or second order loads. The method can be used with any choice of directional spreading function, but special attention is given to the commonly used cos-2s type directional distribution. In addition to the development of the new method, the traditional method using the trapezoidal rule for numerical quadrature is improved by developing an adaptive way of choosing the number of integration points. The accuracy of the adaptive method and the new method is investigated, revealing rapid convergence for both methods. However, the new method appears more robust as it avoids so-called spurious hat errors. When applied to two different pontoon type floating bridges the adaptive method and the new method both achieve a great improvement in computational effort compared to the traditional trapezoidal rule method. When the dimensions of the floating bridge increase, i.e. the number of pontoons and their relative distances increase, the new method is superior with respect to computation time.     

Application of the four models of directional spectra in the Bohai Sea

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Satellite-based RAR performance simulation for measuring directional ocean wave spectrum based on SAR inversion spectrum

Some missions have been carried out to measure wave directional spectrum by synthetic aperture radar (SAR) and airborne real aperture radar (RAR) at a low incidence. Both them have their own advantages and limitations. Scientists hope that SAR and satellite-based RAR can complement each other for the research on wave properties in the future. For this study, the authors aim to simulate the satellite-based RAR system to validate performance for measuring the directional wave spectrum. The principal measurements are introduced and the simulation methods based on the one developed by Hauser are adopted and slightly modified. To enhance the authenticity of input spectrum and the wave spectrum measuring consistency for SAR and satellite-based RAR, the wave height spectrum inversed from Envisat ASAR data by cross spectrum technology is used as the input spectrum of the simulation system. In the process of simulation, the sea surface, backscattering signal, modulation spectrum and the estimated wave height spectrum are simulated in each look direction. Directional wave spectrum are measured based on the simulated observations from 0° to 360°. From the estimated wave spectrum, it has an 180° ambiguity like SAR, but it has no special high wave number cut off in all the direction. Finally, the estimated spectrum is compared with the input one in terms of the dominant wave wavelength, direction and SWH and the results are promising. The simulation shows that satellite-based RAR should be capable of measuring the directional wave properties. Moreover, it indicates satellite-based RAR basically can measure waves that SAR can measure.     

三种设计波高计算方法比较

目前国际上设计波高的常用计算方法有三种:年最大波高法(Annual Maximum method)、波高阈值法(Peak-Over-Threshold method)和年N大波法(Annual-NLargest method)。利用澳大利亚悉尼观测站连续16年的实测资料和Gumbel概率分布函数对这三种方法进行分析和比较,选出一种比较好的计算方法。结果表明,由年最大波高法计算得到的设计波高值偏大,线性回归系数较小,均方误也较大;波高阈值法计算所得结果与阈值本身取值关系并不大,线性回归相关性也较好;年N大波法计算得到的设计波高与每年大波数量取值无关(N≥5时),均方误较小,线性回归相关性较好。因此,在这三种方法中,年N大波法更适合用来计算设计波高,建议每年大波数取5~6个。     

On the effects of wave drift on the dispersion of floating pollutants

The movement of floating pollutants such as oil slicks on the surface of the sea is due to a number different factors, among which wave drift is certainly significant.In principle, it has been known since Stokes' time that a floating particle is subject to the movement caused by the orbital motion of water particles and that an average drift velocity results because the trajectories are not closed. In the past, however, this effect was often either disregarded or simply included with the surface wind induced current. In recent times the difference between the two effects has been conceptually clarified, so that the average wave drift in random one-dimensional seas has been the object of research and the results are now included in most handbooks and models for oil slick forecasting.Due to the chaotic nature of the wave field, however, the drift also causes floating substances to disperse, and this phenomenon is a much more neglected area of research. Recent work by Bovolin et al. [IAHR Congress, 1997] and Sobey and Barker [J. Coast. Res. 13 (1997)] has brought the subject to attention, and computational tools can now be made to quantify the effect and to verify when and how it should be taken into consideration in oil slick accident practise.The work presented in this paper is based on random simulation of the wave induced Eulerian velocity field in a directional sea, by making use of standard offshore wave directional models and on the ensemble averaging of floating particles trajectories in order to compute the spatial dispersion.     

Probabilistic determination of critical wave height for a multi-degree of freedom capsize model

In this paper a statistical methodology is extended to the nonlinear multi-degree of freedom vessel capsize problem in random seas. It is demonstrated that the study of transient motions, through analysis of the erosion of the vessel's safe basin mapped in the space of initial conditions [Soliman, M.S. Thompson, J., 1991. Transient and steady state analysis of capsize phenomena. Applied Ocean Research 13, 2], leads to significantly less conservative and potentially more accurate predictions of ultimate dynamic stability. The work presented herein pairs this approach with a statistical framework to yield feasible stability criteria.     

碟形浮标观测方向波谱误差分析及修正

改进了方向波谱的分析方法及噪声谱经验公式，使本法随测波环境及仪器特性自动修正经验参值，更易于实际应用。基于Maximum heave/pitch quad-spectrum method，由时域及频率域上的浮标动力反应数值计算，推求反应增益因子及相位延迟项，并进一步将其导入方向波谱计算，使其能修正资料浮标对波浪之轴不对称动态反应所造成的相位延迟不一致及主波向误差。经数值仿真验证，该方法的确能消减因资料浮标对波浪之轴不对称动态反应所造成的相位延迟及对主波向估算所造成之影响。应用花莲现场观测资料验证改良之主波向估算方法，得出是否考虑波浪运动与浮标运动间之振幅响应因子及相位延迟因子，所得之主波向的差异介于0－12℃之间。     

三维随机海浪的数值模拟

本文首先分析了三维随机海浪的方向谱函数和三维随机海浪的数学模型,然后在ＭＡＴＬＡＢ环境下设计了数值模拟程序,并模拟出三维随机海浪的方向谱和三维随机海浪的三维空间模型。     

波浪增减水的实用数学模型及其数值模拟

提出了一种模拟近岸区波浪增减水的实用数学模型.首先采用考虑波能损失的抛物型缓坡方程数值模拟波浪破碎引起的波浪复振幅变化,接着根据计算得到的波浪复振幅,采用一种新的辐射应力公式计算辐射应力分量,然后采用深度平均方程计算波浪破碎产生的增减水.采用该模型对规则波和不规则波破碎引起的增减水进行了数值模拟,数值模拟结果与实验结果吻合良好,表明该模型可有效模拟近岸区由于波浪破碎引起的增减水.     

Numerical simulation of random wave slamming on structures in the splash zone

The numerical investigation of random wave slamming on superstructures of marine structures in the splash zone is presented in this paper. The impact pressures on the underside of the structure are computed based on the improved volume of fluid method (VOF). The governing equations are Reynolds time-averaged equations and the two equation k– model. The third order upwind difference scheme is applied to the convection term to reduce the effect of numerical viscosity. The numerical wave flume with random wave-maker suitable for VOF is established. Appropriate moving contact-line boundary conditions are introduced to the model wave in contact with and separated from the underside of structure. Parametric studies have been carried out for different incident waves, structure dimensions and structure clearance. The numerical results are verified by the experimental results.     

On the recovery of surface wave by pressure transfer function

Except the commonly selected pressure transfer function derived from the linear wave theory, a previous study on the pressure transfer function for recovering surface wave from underwater pressure transducer suggested that the pressure transfer function is a function of frequency parameter only. With careful analysis, this study showed that the pressure transfer function should include a transducer submergence parameter as that given by the linear theory. It was found that the previously suggested empirical formula should be restricted to measurements with the pressure transducer close to the surface; otherwise overestimation of wave height would result. Field measurements were carried out with an acoustic wave gauge and a synchronized pressure transducer located at various depths with submergence parameter close to 1 (near the sea floor). It was shown that the previous one-parameter empirical formula might overestimate the significant wave height by more than 30%. This study found that with deep-water wave bursts excluded, the transfer function based on the linear wave theory provided a fairly good estimation on the significant wave heights, with an average deviation of 3.6%.