分析海浪方向谱的扩展本征矢方法

采用Ｌｏｎｇｕｅｔ－Ｈｉｇｇｉｎｓ形式的方向分布函数作为已知谱，用模拟数据检验了作者是所提出的估计方法ＥＥＶ合理性，并与扩展最大似然方法（ＥＭＬＭ）及Ｌｙｇｒｅ等（１９８６）的最在熵方法（ＭＥＭ）作了比较，在验证和比较中，使用纵摇－横摇浮标，星形阵形和ＣＥＲＣ阵列作为复合阵列，计算表明，ＥＥＶ优于ＥＭＬＭ和ＥＭＥ。最后将ＥＥＶ和ＥＭＬＭ两种方法应用于仪器阵列的外海观测数据，得到了比较合理的海浪方向     

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.     

分析海浪方向谱的EEV方法的一种迭代形式

将Pawka为改进最大似然方法（MLM）而提出的迭代方案应用于扩展本征关方法（EEV），作为EEV的一种迭代形式（IEEV）。用模拟数据检验了IEEV的合理性，并与EEV作了比较。计算结果表明，IEEV的估计性状较EEV有改善。最后将IEEV及EEV用于分析仪器阵列的外海观测数据。     

Stochastic simulations of ocean waves: An uncertainty quantification study

The primary objective of this study is to introduce a stochastic framework based on generalized polynomial chaos (gPC) for uncertainty quantification in numerical ocean wave simulations. The techniques we present can be easily extended to other numerical ocean simulation applications. We perform stochastic simulations using a relatively new numerical method to simulate the HISWA (Hindcasting Shallow Water Waves) laboratory experiment for directional near-shore wave propagation and induced currents in a shallow-water wave basin. We solve the phased-averaged equation with hybrid discretization based on discontinuous Galerkin projections, spectral elements, and Fourier expansions. We first validate the deterministic solver by comparing our simulation results against the HISWA experimental data as well as against the numerical model SWAN (Simulating Waves Nearshore). We then perform sensitivity analysis to assess the effects of the parametrized source terms, current field, and boundary conditions. We employ an efficient sparse-grid stochastic collocation method that can treat many uncertain parameters simultaneously. We find that the depth-induced wave-breaking coefficient is the most important parameter compared to other tunable parameters in the source terms. The current field is modeled as random process with large variation but it does not seem to have a significant effect. Uncertainty in the source terms does not influence significantly the region before the submerged breaker whereas uncertainty in the incoming boundary conditions does. Considering simultaneously the uncertainties from the source terms and boundary conditions, we obtain numerical error bars that contain almost all experimental data, hence identifying the proper range of parameters in the action balance equation.     

Comments on `Theory and application of calibration techniques foran NDBC directional wave measurements buoy' by K.E. Steele, et al.:nonlinear effects

For original paper see ibid., vol. OE-10, no.4, p.382-96 (1985). The authors of the above mentioned paper present an extensive set of linear calibration techniques that are applied to National Data Buoy Center wave-buoy sensor spectral output before calculating and disseminating directional wave spectra. The commentators identify and estimate the nonlinear effects that produce biases still present in the output, due both to wave nonlinearities themselves and to constraints on the buoy and mooring system to the driving forces. Simple models show that these nonlinearities can produce spectral energy biases of 5-15% at and above the spectral peak frequency, and even greater errors below it. NDBC presently records wave data from vertically stabilized and fixed accelerometers and slope sensors. Calculations show that these sensors all incur bias due to wave nonlinearities: this is greater for vertically stabilized accelerometers and least for slope sensors. Effects of the resulting inconsistencies between the different sensors are most pronounced below the spectral peak where the nonlinear terms dominate; these effects are illustrated with measured data     

Directional spread parameter at intermediate water depth

The characteristics of directional spread parameters at intermediate water depth are investigated based on a cosine power ‘2s' directional spreading model. This is based on wave measurements carried out using a Datawell directional waverider buoy in 23 m water depth. An empirical equation for the frequency dependent directional spreading parameter is presented. Directional spreading function estimated based on the Maximum Entropy Method is compared with those obtained using a cosine power ‘2s' parameter model. A set of empirical equations relating the directional spreading parameter corresponding to the peak of wave spectrum to other wave parameters like significant wave height and period are obtained. It shows that the wave directional spreading at peak wave frequency can be related to the non-linearity parameter, which allows estimation of directional spreading without reference to wind information.     

Extreme wave crest distribution by direct numerical simulations of long-crested nonlinear wave fields

The wave crest height qualification checks are required during the wave calibration before the model test in wave basin. However, the reliable criteria of nonlinear wave crest probability distribution in 3-h duration (full-scale) has not been well established yet. We investigate wave crest-height statistics of long-crested nonlinear wave fields using high-order spectral (HOS) method, which can take the effects of both second-order bound waves and third-order free waves into account. The energy dissipation effects due to wave breaking were included by employing an eddy viscosity model. Sensitivity analyses to the wave breaking onset criterion have been performed. Validation is provided by comparing the obtained numerical results with the available calibration test data. Based on extensive and direct numerical simulations, semi-empirical single realization distributions for wave calibration have been developed through 3-parameter Weibull fitting and systematic regression analyses. Particular attention has been paid to the tail of upper bound of wave crest distributions. The effects of wave steepness and water depth on the maximum wave crest height in 3-h duration have been examined. It is found that with the increase of wave steepness, the extreme wave crest height increases until it reaches a critical value. In addition, for the scale water depth k_ph < 1.36, the maximum crest height decreases as the water depth increases, while in the opposite case the maximum crest height increases as the water depth increases. Moreover, it is confirmed that that the fourth-order nonlinearity does not have significant effects on the distribution of the wave crest height.     

海浪双峰方向分布的一种物理解释

用 １８个波高计组成的直径为 ４０ｃｍ的圆形阵列在大型风浪槽内系统地测量了风浪和涌浪方向谱。用两种分辨力较高的方向谱估计方法最大似然法（ＭＬＭ）和贝叶斯方法（ＢＤＭ）分析的结果表明：风浪高频域出现的依赖于估计方法的双峰方向分布是一种物理假象;在较成长的涌浪低频域,得到跟传播方向对称、两峰间隔大约６０°－９０°非常规则的双峰方向分布,它跟频率和涌浪的成长状态有关,而跟估计方法无关,这种现象可以用非线性波－波相互作用过弱,在不同方向之间不能有效传递能量来解释。     

Surface wave predictions in weakly nonlinear directional seas

We have employed laboratory and numerical experiments in order to investigate propagation of waves in both long and short-crested wave fields in deep water. For long-crested waves with steepness, ϵ = k_ca_c = 0.1 (a fairly extreme case), reliable prediction can be performed with the modified nonlinear Schrödinger equation up to about 40 characteristic wavelengths. For short-crested waves the accuracy of prediction is strongly reduced with increasing directional spread.     

Tide and surge dynamics along the Iberian Atlantic coast

The eastern Atlantic barotropic dynamics (in a region spanning from 20° N to 48° N and 34° W to 0°) are studied through numerical modelling and in situ measurements. The main source of data is the tidal gauge network REDMAR, managed by Clima Marítimo (Puertos del Estado). The numerical model employed is the HAMSOM, developed both by the Institut für Meereskunde (Hamburg University) and Clima Marítimo.In this paper, tidal and storm surge dynamics are studied for the region, focusing particularly on the nonlinear transfer of energy between the different forcings.The results of tidal simulations show good agreement between semidiurnal harmonic components and the values obtained from the tidal gauges (both coastal and pelagic) and current metres. The nonlinear transfers of energy from semidiurnal to higher order harmonics, such as M4 and M6, were mapped. Those transfers were found to be important in only two areas: The French continental shelf in the Bay of Biscay and the widest part of the African shelf, south of Cabo Bojador. The modelled diurnal constituents show larger relative differences with measurements than semidiurnal harmonics, especially in data concerning the phase.A method to isolate the nonlinear transfers of energy between tidal and atmospheric forcing during a storm surge was developed. These transfers were found to be significant in the same areas where tidal nonlinear activity was present. The effect of short period wind generated waves on sea surface elevation was also investigated. The magnitude of the spatial derivatives of radiation stress was compared with wind-induced stress. As a result of this comparison, we found the inclusion of a forcing term that depends on radiation stress in ocean model simulations at this scale and resolution to be not essential. The effect of computing wind-induced stresses, with a formulation that explicitly depends on sea state, was also explored by means of a coupled run of the HAMSOM and the spectral wave model WAM for a storm surge event in the Spanish coast. This formulation was not found to be an improvement over a classical parameterisation which only depends on wind fields.     

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.     

Forces on a pitching plate: An experimental and numerical study

A flat plate in pitching motion is considered as a fundamental source of locomotion in the general context of marine propulsion. The experimental as well as numerical investigation is carried out at a relatively small Reynold number of 2000 based on the plate length c and the inflow velocity U_∞. The plate oscillates sinusoidally in pitch about its 1/3 − c axis and the peak to peak amplitude of motion is 20°. The reduced frequency of oscillation k = πfc/U_∞ is considered as a key parameter and it may vary between 1 and 5. The underlying fluid-structure problem is numerically solved using a compact finite-differences Navier–Stokes solution procedure and the numerical solution is compared with Particle Image Velocimetry (PIV) measurements of the flow field around the pitching foil experimental device mounted in a water-channel. A good agreement is found between the numerical and experimental results and the threshold oscillation frequency beyond which the wake exhibits a reverse von Kármán street pattern is determined. Above threshold, the mean velocity in the wake exhibits jet-like profiles with velocity excess, which is generally considered as the footprint of thrust production. The forces exerted on the plate are extracted from the numerical simulation results and it is shown, that reliable predictions for possible thrust production can be inferred from a conventional experimental control volume analysis, only when besides the wake's mean flow the contributions from the velocity fluctuation and the pressure term are taken into account.     

Statistical Analyses of Wave Height Distribution for Multidirectional Irregular Waves over A Sloping Bottom

The main objective of this paper is to examine the influences of both the principal wave direction and the directional spreading parameter of the wave energy on the wave height evolution of multidirectional irregular waves over an impermeable sloping bottom and to propose an improved wave height distribution model based on an existing classical formula. The numerical model FUNWAVE 2.0, based on a fully nonlinear Boussinesq equation, is employed to simulate the propagation of multidirectional irregular waves over the sloping bottom. Comparisons of wave heights derived from wave trains with various principal wave directions and different directional spreading parameters are conducted. Results show that both the principal wave direction and the wave directional spread have significant influences on the wave height evolution on a varying coastal topography. The shoaling effect for the wave height is obviously weakened with the increase of the principal wave direction and with the decrease of the directional spreading parameter. With the simulated data, the classical Klopman wave height distribution model is improved by considering the influences of both factors. It is found that the improved model performs better in describing the wave height distribution for the multidirectional irregular waves in shallow water.     

The form of the asymptotic depth-limited wind-wave spectrum: Part III — Directional spreading

The directional spreading of both the wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the wavenumber and frequency forms are narrowest at the spectral peak and broaden at wavenumbers (frequencies) both above and below the peak. The directional spreading of the wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of wavenumber spectra, rather than frequency spectra.     

A new scheme of nonlinear energy transfer among wind waves: RIAM method-algorithm and performance-

A numerical scheme for calculating the nonlinear energy transfer among wind waves (RIAM method) was developed on the basis of the rigorous method of Masuda. Then the performance of the RIAM method was examined by applying it to various forms of wind-wave spectra and different situations of wind-wave evolution, in comparison mainly with the WAM method. The computational time of the Masuda method was reduced by a factor of 300 by the RIAM method, which is still 2000 times slower than the WAM method simply because the RIAM method processes thousands of resonance configurations whereas the WAM method does only one. The RIAM method proves to give accurate results even for spectra of narrow band widths or bimodal spectra, whereas the WAM method often calculates an unrealistic magnitude and pattern of nonlinear energy transfer functions. In the duration-limited evolution of wind-wave spectra, the RIAM method yields a unimodal directional distribution on the low-frequency side of the spectral peak, whereas the WAM method produces a spurious bimodal one there. At higher frequencies, however, both methods give a bimodal directional distribution with two oblique maxima. The RIAM method enhances the growth of the total energy and peak period of wind waves in comparison with the WAM method. Nevertheless, Toba's constant of his 3/2-power law approaches almost the same standard value of 0.06 in both methods. For spectra of a narrow band width or for those perturbed by a small hump or depression, the RIAM method tends to recover the monotonic smoother form of spectrum whereas the WAM method often yields unrealistic humps or depressions.     

Modelling of the temporal and spatial evolutions of weakly nonlinear random directional waves with the modified nonlinear Schrödinger equations

The temporal and spatial evolutions of nonlinear wave group with an initial Gaussian envelope are theoretically studied under the governing of MNLS equations, demonstrating that the temporal and spatial versions of numerical model are not always consistent in the whole evolution process, particularly in the presence of strong nonlinearity. Moreover, a large set of numerical simulations, performed respectively by these two versions of numerical model, are systematically compared to mechanically generated waves with different initial directional spreading and Benjamin–Feir Index, mainly focusing on the evolution properties of surface elevations such as the coefficients of skewness and kurtosis, the probability density function, and the maximal surface elevation. On the whole, it can be argued that the statistical properties of both numerically simulated wave fields are basically consistent with the laboratory observations.     

Three-dimensional nonlinear random wave groups in intermediate water depth

High waves at ocean occur during a complex space–time evolution of wave groups. In this paper the nonlinear structure of three-dimensional sea wave groups at intermediate water depth is investigated. To this purpose, the Boccotti's Quasi-Determinism theory is firstly applied to describe the linear wave groups when a given exceptionally high crest occurs. Then, the second-order correction to the linear solution is derived for the general condition of three-dimensional wave groups, at a finite water depth. Several numerical applications, finally, have been carried out in order to show how both the spectral bandwidth and the directional spreading modify the nonlinear high waves at different water depth.     

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。     

Modelling the wave-current interactions in an offshore basin using the SWAN model

The theoretical background of the wave-current interactions, including the transformation of the wave spectrum and breaking waves due to currents, are first presented in this work. In the next part of the work, experimental data resulted from studies performed in an offshore wave basin of the Danish Hydraulic Institute concerning the wave-current interactions were presented in parallel with some wave model simulations performed in similar conditions. SWAN, which is presently the state-of-the-art spectral model for the wave transformations, was adopted for performing numerical simulations. In general, a good agreement was encountered between the experimental data and the simulation results.     

An unstructured spectral/hp element model for enhanced Boussinesq-type equations

A spectral/hp element method for solving enhanced Boussinesq-type equations in two horizontal dimensions is introduced. The numerical model is based on the discontinuous Galerkin method on unstructured meshes with expansions of arbitrary order. Numerical computations are used to illustrate that the computational efficiency of the model increases with increasing (i) expansion polynomial order, (ii) integration time and (iii) relative depth. Thus, the spectral/hp element technique appears to offers potentially significant savings in computational time for a fixed numerical error, compared to low-order numerical methods, for large-scale and long-time simulations of dispersive wave propagation. The practical applicability of the model is illustrated by several test cases.