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.     

Validation of the Boccotti's generalized model for large nonlinear wave heights from laboratory mixed sea states

The presented work aims at validating the generalization of the asymptotic distribution model of Boccotti for large wave heights recently proposed by Tayfun [1] to laboratory generated mixed sea states with two-peak spectra. The input wave spectra are modelled as the sum of two JONSWAP spectra describing unidirectional wave systems with different or identical directions of propagation (crossing or following mixed seas). In order to account for the effect of the energetically dominant wave system on the largest observed waves, the Boccotti's parameters were calculated at the absolute minimum of the autocorrelation function which can differ from the first minimum for some cases of mixed seas, such as those dominated by the swell or seas with comparable contribution of the two spectral components. So far the proposed model has been validated elsewhere against samples of large wave heights exceeding the significant wave height in wind seas and in mechanically generated long-crested seas, both characterized by unimodal spectra and strong third-order nonlinearities. The present study demonstrates that it can predict equally well the tail of the distributions for mixed seas, irrespective of the type of the mixed sea, particularly when the third-order statistics is relatively large. Typically, the mixed seas from the considered offshore basin experiment display such conditions as the propagation distance from the wavemaker increases, though this effect is less pronounced for mixed following than for mixed crossing wave conditions. Moreover, the generalized model remains valid irrespective of the sign of the fourth-order sum Λ which is a key parameter of the distribution. Its good predictive ability is quantified here by the root-mean-square errors between observations and theory.     

Analysis of freak wave measurements in the Sea of Japan

This paper presents an analysis of a set of available freak wave measurements gathered from several periods of continuous wave recordings made in the Sea of Japan during 1986–1990 by the Ship Research Institute of Japan. The analysis provides an ideal opportunity to catch a glimpse of the statistics of freak waves in the ocean. The results show that a well-defined freak wave may occur in the developed wind–wave condition: S(f)∝f⁻⁴, with single-peak directional spectra. The crest and trough amplitude distributions of the observed sea waves including freak waves are different from the Rayleigh distribution, although the wave height distribution tends to agree with the Rayleigh distribution. Freak waves can be readily identified from the wavelet spectrum where a strong energy density occurs in the spectrum, and is instantly surged and seemingly carried over to the high-frequency components at the instant the freak wave occurs.     

Calculating nonlinear wave crest exceedance probabilities using a Transformed Rayleigh method

This paper concerns the calculation of the wave crest height exceedance probabilities in fully nonlinear mixed sea states. The exceedance probabilities have been calculated by incorporating a fully nonlinear wave model into a Transformed Rayleigh method. This is an efficient approach to the calculation of wave crest exceedance probabilities and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The nonlinear mixed sea states studied include a swell dominated sea state, two wind sea dominated sea states, and two states of mixed wind sea and swell with comparable energy. The wave steepness influence and the finite water depth effects are also considered in the study. The accuracy and efficiency of the Transformed Rayleigh method are validated by comparing the results predicted using the method with those predicted by using the Monte Carlo simulation method, the theoretical Rayleigh method and some empirical formulas.     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.     

宁波北仑海域风浪统计性质研究

根据宁波北仑海域的连续3a的实测风浪资料,讨论了在不同风速条件下波高分布和周期分布,以及两者的联合分布;通过与理论结果的比较,得出波高分布与Rayleigh分布基本符合,但有一些差异,周期分布与孙孚的理论周期分布较符合,而波高与周期的联合分布除了图形的形状以及大波对应的无因次周期的值与孙孚的理论值有差异外,两者吻合较好。     

Probability distributions of wave heights in bimodal seas in an offshore basin

This study aims at assessing the adequacy for describing bimodal sea states of different non-linear probability distributions that have been developed for single sea states. It is based on data collected at an offshore test basin. The measurements represent three bimodal sea states with individual unidirectional wave systems propagating at 60, 90 and 120 from each other. The wave spectra are separated into swell and wind sea components and the relative energy ratio between the areas under the associated spectral curves is estimated and is related with the statistics of the time series considered. Dependence is found between the normalized high order cumulants, which describe the non-Gaussian surface, and the predominant contribution of the wind sea energy. Furthermore, the probabilities of exceedance of the individual wave heights are estimated and compared with the Rayleigh model and with other models that take into account either the effect of spectral bandwidth or the effect of wave nonlinearities. The results are discussed with respect to three classes of sea states that reflect the relative contribution of swell and wind sea energy.     

Calibration and verification of a spectral wind–wave model for Lake Okeechobee

A spectral wind wave model SWAN (Simulation WAves Nearshore) that represents the generation, propagation and dissipation of waves was applied to Lake Okeechobee. This model includes the effects of refraction, shoaling, and blocking in wave propagation. It accounts for wave dissipation by whitecapping, bottom friction, and depth-induced wave breaking. The wave–wave interaction effect also is included in this model. Measurements of wind and wave heights were made at different stations and different time periods in Lake Okeechobee. Significant wave height values were computed from the recorded data. The correlation between wind stress and significant wave height also was analyzed. A 6-day simulation using 1989 data was conducted for model calibration. Another 6-day simulation using 1996 data was conducted for model verification. The simulated significant wave heights were found to agree reasonably well with measured significant wave heights for calibration and verification periods. Agreement between observed and simulated values was based on graphical comparisons, mean, absolute and root mean square errors, and correlation coefficient. Comparisons showed that the model reproduced both general observed trends and short term fluctuations.     

A novel technique in analyzing non-linear wave-wave interaction

During wave growth non-linear wave–wave interactions cause transfer of some wave energy from lower to higher wave periods as the spectrum grows. Wavelet bicoherence, which is a new technique in the analysis of wind–wave and wave–wave interactions, is used to analyze non-linear wave–wave interactions. A selected record of wind wave that contains the maximum wave height observed during 6 h of wave generation is divided into five segments and wavelet bicoherence is computed for the whole record, and for all divided segments. The study shows that the non-linear wave–wave interaction occurs at different bicoherence levels and these levels are different from one segment to another due to the non-stationarity feature of the examined data set.     

Coupling winds to ocean surface currents over the global ocean

A Wind stress–Current Coupled System (WCCS) consisting of the HYbrid Coordinate Ocean Model (HYCOM) and an improved wind stress algorithm based on Donelan et al. [Donelan, W.M., Drennan, Katsaros, K.B., 1997. The air–sea momentum flux in mixed wind sea and swell conditions. J. Phys. Oceanogr. 27, 2087–2099] is developed by using the Earth System Modeling Framework (ESMF). The WCCS is applied to the global ocean to study the interactions between the wind stress and the ocean surface currents. In this study, the ocean surface current velocity is taken into consideration in the wind stress calculation and air–sea heat flux calculation. The wind stress that contains the effect of ocean surface current velocity will be used to force the HYCOM. The results indicate that the ocean surface velocity exerts an important influence on the wind stress, which, in turn, significantly affects the global ocean surface currents, air–sea heat fluxes, and the thickness of ocean surface boundary layer. Comparison with the TOGA TAO buoy data, the sea surface temperature from the wind–current coupled simulation showed noticeable improvement over the stand-alone HYCOM simulation.     

基于选定风浪方向谱的海浪模拟方法(英文)

简要回顾当前第三代海浪模式中的困难。为避开这些困难,作者提出一种新的海浪模拟方法,其中特定定义的风浪组成波依常风下随时间成长的方向谱计算,而涌浪组成波藉考虑涡动黏性和底摩擦加以计算。并进行了常风场和变风场下系统的数值试验。在常风速情形中,模拟结果能精确地化为建立模拟所根据的谱和风浪成长关系。计算显示出台风中心附近浪场的极端复杂的谱结构。当风速骤然降低时,模拟的波高减小与观测符合。在风向逐渐或骤然改变情形下,计算的时间响应尺度与海上观测符合,而且演化中的二维谱结构得到良好刻画。对于涌浪在无风下的传播,模拟结果合理,包括波参量及谱结构的变化。后报得到的波高、周期和海上资料符合。与第三代模式相比,文中提出的方法较易改进,需用的计算机时间显著减少。最后讨论采用一个已知谱来建立谱形式的海浪预报模型的合理性以及有关的问题。     

A note on nearshore wave features: Implications for wave generation

This paper analyses 10 years of wave data from the Mediterranean Spanish (Catalan) coast considering the mean wave climate and storm events from the standpoint of wind-wave momentum transfer and wave prediction. The data, registered by a buoy at about 12 km from the coastline, revealed two main groups of wave storms, with NW and E directions. NW storms correspond to a fetch-limited situation since the intense wind blows from land. Low-pressure centres located over the Mediterranean Sea produce easterly storms. Near the coast the eastern winds from the sea are replaced by NW winds coming from meteorological patterns over northern Spain and south-western France. Wave storms are classified and studied to obtain their main features (including spectral width, wave length, wave age and bimodality) and discussed in terms of wind-wave momentum transfer for operational wave predictions. Observations show a complex coastal wave climate. Fetch-limited storms presented smaller spectral widths while varying wind situations presented larger widths due to the presence of bimodal spectra. These wave features are highly relevant for wind–ocean momentum transfer and, thus, for current and wave predictions. The spectral width proved to be a good indicator of sea complexity and is thus applicable for improved wind drag estimations. A new drag coefficient formulation is proposed, based on existing wind dependent drag expressions, but including also spectral wave properties (a spectral width parameter) that highlights the characteristics of wind-wave generation under pre-existing swell. Such a formulation, once properly validated with field observations, is expected to improve wind-wave predictions.     

Simulation of Typhoon-Driven Waves in the Yangtze Estuary with Multiple-Nested Wave Models

Typhoon-generated waves are simulated with two numerical wave models, the SWAN model for the coastal and Yangtze Estuary domain, nested within the WAVEWATCHIII （WW3） for the basin-scale East China Sea domain. Typhoon No. 8114 is chosen because it was very strong, and generated high waves in the Estuary. WW3 was implemented for the East China Sea coarse-resolution computational domain, to simulate the waves over a large spatial scale and provide boundary conditions for SWAN model simulations, implemented on a fine-resolution nested domain for the Yangtze Estuary area. The Takahashi wind model is applied to the simulation of the East China Sea scale （3-hourly） and Yangtze Estuary scale （1-hourly） winds. Simulations of significant wave heights in the East China Sea show that the highest waves are on the right side of the storm track, and maxima tend to occur at the eastern deep-water open boundary of the Yangtze Estuary. In the Yangtze Estuary, incoming swell is dominant over locally generated waves before the typhoon approaches the Estuary. As the typhoon approaches the Estuary, wind waves and swell coexist, and the wave direction is mainly influenced by the swell direction and the complex topography.     

Modified Joint Distribution of Wave Heights and Periods

The modified versions of the linear theoretical model of Longuet-Higgins (1983) are derived in this work and also compared with the laboratory experiments carried out in MARINTEK. The main feature of modifications is to replace the mean frequency in the formulation with the peak frequency of the wave spectrum. These two alternative forms of joint distributions are checked in three typical random sea states characterized by the initial wave steepness. In order to further explore the properties of these models, the associated marginal distributions of wave heights and wave periods are also researched with the observed statistics and some encouraging results are obtained.     

Obtaining the distribution of quiescent periods directly from the power spectral densities of Sea waves

There is a growing practical interest in the ability to increase the sea states at which marine operations can be safely undertaken by exploiting the quiescent periods that are well known to exist under a wide range of sea conditions. While the actual prediction of quiescent periods at sea for the control of operations is a deterministic process, the long term planning of future maritime tasks that rely on these quiescent periods is a statistical process involving the anticipated quiescence properties of the forecasted sea conditions in the geographical region of interest. It is in principle possible to obtain such data in tabular form either large scale simulation or from field data. However, such simulations are computationally intensive and libraries of appropriate field data are not common. Thus, it is clearly attractive to develop techniques that exploit standard wave spectral models for describing the quiescence statistics directly from such spectra. The present study focuses upon such techniques and is a first step towards the production of a computationally low-cost quiescence prediction tool and compares its efficacy against simulations. Two significant properties emerge for a large class of wave spectral models that encompasses the ubiquitous Neumann and Pierson Moskowitz or Bretschneider forms. Firstly, the auto-correlation function of the wave profile that are required to produce the quiescence property can be obtained analytically in terms of standard special functions. This considerably reduces the computational cost making desktop computer-based planning tools a reality. Secondly, for each class of these parametric spectra, the probability of a given number of consecutive wave heights (normalised to the significant wave heights) less than some critical value is in fact independent of absolute wave height. Thus, for a broad class of practically interesting wave spectra all that is required to obtain the statistical distribution of the quiescent periods is simple rescaling.     

Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan

Generation and propagation of several-day period fluctuations along the southeast coast of Honshu, Japan, were investigated by analyzing sea level data and by using a numerical model. The sea level data obtained at twelve stations from Choshi to Omaezaki in fall in 1991, showed energy peaks at the 3–6 day period at the eastern stations in this coast. Time lags of the 3–6 day period fluctuations between station and station indicate westward propagation along the coast. However, the energy level of the 3–6 day period fluctuations suddenly decreased south of the Izu Peninsula. Numerical experiments using a two-layer model were performed to clarify the generation and propagation mechanism of the several-day period fluctuations by periodical wind in fall. The amplitude distributions of observed sea level were qualitatively explained by a coastal-trapped wave (CTW) in the numerical experiment. From the discussions on propagation of a free wave, CTW with the characteristics of a shelf wave generated by the wind along the northeast of the Boso Peninsula was separated into two types of wave at the southeast of the peninsula. One is an internal Kelvin wave with large interface displacement and the other is the shelf wave propagating over the northern part of the Izu Ridge. The sudden decrease in the surface displacement with the 3–6 day period observed at the western stations is considered to be due to the local effect of the wind and phase relation between the internal Kelvin wave and shelf wave.     

涌浪作用下港内大型集装箱船运动特性数值研究

随着船舶大型化和港口建设深水化发展,外海不同周期波浪作用下大型系泊船泊稳问题与小型系泊船相比出现了新的特点。为此,利用数值模型方法研究了在不同入射角度和周期的涌浪作用下港内大型系泊船的水动力响应,针对系泊船的泊稳情况探讨了船舶的运动规律和运动特性。研究发现,在涌浪周期较大的情况下,限定波高的泊稳标准不足以用来确定系泊船的正常作业条件,港内泊船的水平运动（纵荡、横荡和艏摇）极易超出运动标准值并影响装卸作业效率,并且船舶的水平运动表现出主要由次重力波主导的低频运动特性,而垂直运动（垂荡、横摇和纵摇）表现出主要由短波主导的波频运动特性。     

The long-term trend of the sea surface wind speed and the wave height (wind wave, swell, mixed wave)in global ocean during the last 44 a

Utilizing the 45 a European Centre for Medium-Range Weather Forecasts(ECMWF)reanalysis wave data(ERA-40),the long-term trend of the sea surface wind speed and(wind wave,swell,mixed wave)wave height in the global ocean at grid point 1.5×1.5 during the last 44 a is analyzed.It is discovered that a majority of global ocean swell wave height exhibits a significant linear increasing trend(2–8 cm/decade),the distribution of annual linear trend of the significant wave height(SWH)has good consistency with that of the swell wave height.The sea surface wind speed shows an annually linear increasing trend mainly concentrated in the most waters of Southern Hemisphere westerlies,high latitude of the North Pacific,Indian Ocean north of 30 S,the waters near the western equatorial Pacific and low latitudes of the Atlantic waters,and the annually linear decreasing mainly in central and eastern equator of the Pacific,Juan.Fernandez Archipelago,the waters near South Georgia Island in the Atlantic waters.The linear variational distribution characteristic of the wind wave height is similar to that of the sea surface wind speed.Another find is that the swell is dominant in the mixed wave,the swell index in the central ocean is generally greater than that in the offshore,and the swell index in the eastern ocean coast is greater than that in the western ocean inshore,and in year-round hemisphere westerlies the swell index is relatively low.     

Wavelet bicoherence analysis of wind–wave interaction

A new technique in the analysis of wind–wave interaction, wavelet bicoherence, will be applied in this article. Wavelet bicohence has the ability to detect phase coupling and nonlinear interactions of the quadratic order with time resolution. It is used in this study to analyze wind–wave interaction during wave growth in a Mistral event. A selected record of simultaneously measured wind and wave data during Mistral is divided into five segments and the computations of the wavelet bicoherence are conducted for the whole record and for all divided segments. The results show that the phase coupling occurs between wind speed and wave height over a certain range of frequencies and that the range is different from one segment to another due to the non-stationary feature of the time series.     

The sheltering effect of the Balearic Islands in the hindcast wave field

The sheltering effect of the Balearic Islands in the hindcast wave field was studied for typical Mediterranean wave situations of Llevant, Tramuntana and Mestral and for mild conditions such as the Garbí and Ponent winds. For this purpose, a third generation wave model was applied to the Mediterranean Sea and different patterns of the sheltered areas were found for the various representative situations depending on the wind variability and on the magnitude of the wind speed. From the analysis it was concluded that the sheltered zones created during storms generally persist for short periods of time of the order of 6 h, possibly reaching a maximum of 12 h. In contrast with earlier results obtained for swell dominated ocean areas, it was observed that in this area, due to the short fetches the sea states are mainly local wind seas and thus the wave field behind the islands depends on the local wind.