Analytically derived wind-wave directional spectrum part 2. Characteristics,comparison and verification of spectrum

The dependence of the angular spreading on frequency and wind-wave growth status is discussed in great detail for the proposed spectrum. The calculated angular spreading agrees with the measurements of Donelanet al. but is slightly broader. Explanation is given to the appearance of the narrowest spreading at a frequency slightly smaller than that of the wind-wave frequency spectrum peak as found by these authors. There is also basic agreement between the calculated spreading and the formulas of Mitsuyasuet al. and Hasselmannet al. for the specific wind-wave status on which these empirical formulas are based, though the former is narrower. The wind-wave frequency spectrum obtained by integrating the proposed directional spectrum with respect to direction agrees with the JONSWAP spectrum and that derived by the authors previously. The proposed spectrum is preliminarily verified with field data obtained by optical method.Project supported by the National Natural Science Foundation of China.     

A proposed directional function and wind-wave directional spectrum

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The energy balance in the wind-wave spectrum

The spectral energy balance in the wind-wave spectrum is studied with taking into account the energy input from turbulent wind to waves, the energy rearrangement due to conservative nonlinear wave-wave interaction and the energy dissipation due to water turbulence. Using the Ichikawa's (1978) model on the turbulent wind field over wind-waves and assuming that the energy dissipation is times greater than that due to molecular viscosity of water, the energy input and dissipation are determined so as to satisfy the condition that the nonlinear-transfers of momentum and energy conserve the total momentum and energy of waves. The nonlinear energy-transfer is estimated from the energy balance at each frequency. It is found that the energy input and dissipation satisfying the condition on the conservative nonlinear-transfer are determined by the characteristic height of wind-wave field and the friction velocity of air, and that the spectral distribution of the nonlinear energy-transfer estimated in this paper is qualitatively similar to that estimated by the non-linear wave-wave interaction theory ofHasselmann (1962).     

Some characteristics of the development process of the wind-wave spectrum

The development process of wind-waves of which spectral peak distributes from 0.6 cps to 9.3 cps will be discussed on the basis of the wind tunnel experiments and of the field observations performed at Lake Biwa. The characteristics of power and slope spectra are here presented. The development process of these wind-waves is characterized by three stages;i.e. initial-wavelets, transition stage and sea-waves. In the wind tunnel experiments, the transition from the stage of the initial-wavelets to the transition stage occurs when the wave spectral peak arrives at the line 6.40×10^–4 k ^–2cm²·sec (wherek is wave number) or when the slope spectral density at the frequencyf _max becomes larger than 6.40×10^–4 sec. In the stage of sea-waves, the component wave of a wave-spectral peak is steepest in the component waves. And the wave spectral peak develops along the line 1.02×10² f ^–6 cm²·sec (wheref is the frequency corresponding to the wave numberk) untill it reaches the line 33.3f ^–4cm²·sec, and thereafter develops along the latter line, which indicates the constant density of slope spectrum. It is suggested that the nonlinearity of wind-waves must become stronger as wind-waves develop. The effective momentum flux _ws from the air flow to wind-waves in this stage is evaluated to be about 49% of the total stress ₀.     

Characteristics of a breaking wind-wave field in the light of the individual wind-wave concept

The relation between the intensity of breaking of individual wind-wave crests and parameters of wave size and wave form (e. g., height, period, steepness and skewness) is examined, and the process of change of these parameters is studied in a wind-wave tank (reference wind speed 15 m sec⁻¹, fetch 16 m). Distributions of the wave form parameters are different for breaking and nonbreaking waves. Fully breaking waves seem to hold the relationH ∞T ², whereH is the individual wave height andT is the period. The condition of breaking is not simply determined by the simple criterion of Stokes' limit. Wave height and steepness of a breaking wave are not always larger than those of a nonbreaking wave. This suggests the existence of an overshooting phenomenon in the breaking wave. The wave form parameters are found to change cyclically in a statistical sense during the wave propagation. The period of the cycle in the present case is estimated to be longer than four wave periods. An intermittency of wave breaking is associated with this cyclic process. Roughly speaking, two or three succeeding breaking-waves sporadically exist among a series of nonbreaking waves along the fetch.     

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.     

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。     

The mechanism of the development of wind-wave spectra

The mechanism of the development of wind-waves will be proposed on the basis of the observed wave spectra in the wind tunnels and at Lake Biwa (Imasato, 1976). It consists of two aspects: One is that the air flow over the wind-waves transfers momentum concentratively to the steepest component waves and the other is that the upper limit of the growth of a wave spectral density is given by the ultimate value in the slope spectral density. The first aspect means that the wave field has the momentum transfer filter on receiving the momentum from the air flow. Wind-waves in the stage of sea-waves receive the necessary amount of momentum by the form drag,e.g. according to the Miles' (1960) inviscid mechanism, through a very narrow frequency region around a dominant spectral peak. On the other hand, wind-waves in the stage of initial-wavelets receive it according to the Miles' (1962a) viscous model through a fairly broad frequency region around the peak. The upper limit ofS _max developing according to viscous mechanism is given byS _max =6.40×10^–4 k _max ^–2cm²s andS _max =2.03C(f _max )^–2cm²s(S _max is the power density of the wave spectral peak with the frequencyf _max ,k _max is the wave number corresponding to the frequencyf _max andC is the phase velocity).From the second aspect, the upper limit of the growth of wave spectral density is given by 33.3f ^–4cm²s in the frequency region of late stage of sea-waves. Therefore, the spectral peak, which has the largest value in the slope spectral density in the component waves of the wave spectrum, rises high over the line 4.15f ^–5cm²s. The energy is transported from the spectral peak to the high frequency part and to the forward face of a wave spectrum by nonlinear wave-wave interaction. This nonlinearity is confirmed by the bispectra calculated from the observed wind-wave data. In the stage of sea-waves, nonlinear rearrangement of the wave energy comes from a narrow momentum transfer filter, and, in the stage of initial-wavelets, it comes mainly from small corrugations and small steepness of the wave field.     

Elimination of directional wave spectrum contamination from noise in elevation measurements

The Surface Contour Radar (SCR) is a 36-GHz computer-controlled airborne radar which generates a false-color-coded elevation map of the sea surface below the aircraft in real time, and can routinely produce ocean directional wave spectra with post-flight data processing which have much higher angular resolution than pitch-and-roll buoys. The SCR range measurements are not error-free and the resulting errors in the elevations corrupt the directional wave spectrum. This paper presents a technique for eliminating that contamination.     

Kalman filtering of vessel motions for ocean wave directional spectrum estimation

This paper proposes a high-speed iterative procedure for estimating the ocean wave directional spectrum from vessel motion data. It uses as input data, the measurements from motion sensors that are commonly available on dynamically positioned vessels and which may easily be installed on any ship. Because the necessary sensors are relatively inexpensive or may already be installed, it becomes an ideal solution to provide initial estimates to offline estimation procedures and to give spectral updates under quickly changing weather conditions. The Kalman filtering algorithm, for iterative harmonic detection, and frequency domain vessel response data are used in the estimation procedure. The results and conclusions are still based on synthesized data, but very promising.     

贝叶斯统计方法在海浪方向谱研究中的应用

较详细介绍了贝叶斯统计方法在海浪方向谱估计中的应用,指出先验分布的不同对估计结果没有影响,由于均匀分布与最大熵原则相对应,使其具有某种特殊性.数值模拟表明贝叶斯方法对双峰方向分布估计的有效性,将其应用于黑海实测资料,证明双峰方向分布的出现依赖于估计方法分辨力的大小,而用最大似然法得到的双峰方向分布值得怀疑.最后给出出现双峰方向分布的一种可能物理解释.     

Measurements of directional spectrum of wind waves using an array of wave detectors Part II. Field observation

The directional spectrum of wind waves was observed using seven wave gauges at the marine observation tower. Directional spectrum was calculated by the method described inFujinawa (1974 a) which assures the high directional resolving power. Under the nearly uniform condition of the wind the process of wave development was studied by the use of the data of the directional spectrum. The analysis revealed that, 1) the mean wave direction does not necessarily coincide with the wind direction, 2) the directional spreading is much narrower than hitherto reported, 3) the growth rate is closely proportional to the square of cosine of the angle between the wave direction and the wind direction, 4) the resonancetype wave-wave interaction plays only minor role in the process of wave development for any wave component in the earlier stage of development and for the most rapidly developing component in the main stage of development.     

On the variability of the high-frequency part of the spectrum of wind-forced sea waves

Data on the temporal variability of sea wave spectral components in the frequency range 1–8 Hz, collected by a drifting vessel in the Pacific ocean (wind speed 1–10 m/s), are discussed in this paper. For the frequency range 3–6 Hz (wind speed 5–8 m/s), a weak variability of the ripples is observed, synchronous with long waves; in the remaining part of the spectral range studied the fluctuations are fortuitous. It is concluded that the wind plays a crucial role in forming the ripples' fluctuation characteristics in the high-frequency part of the spectrum.Translated by Vladimir A. Puchkin.     

Measurement of directional spectrum of wind waves using an array of wave detectors

A method is proposed to estimate the true directional spectrum of wind waves by making use of more than four wave detectors. The true spectrum of wind waves whose wave lengths lie between about 1.1 and 2.6 times the largest span between the wave gauges can be recovered with an error less than 0.5 %. An additional wave gauge with fixed maximum span extends its effectivity to shorter wave lengths, but does not effect the upper limit of wave length.The method is based on the fact that the spectrum estimated byBarber (1961) is connected with true directional spectrum by the Fredholm integral equation of the first kind if the wave component satisfies the dispersion relation. Solving the equation by using the Fourier series method, we can get true spectrum.     

锁相波浪场入、反射波方向谱及反射系数估算

通过数模波浪和物模实验，比较分析了估算多向不规则入射波与反射波相互叠加的锁相波浪场方向分布和反射系数方向分布的改进的贝叶斯估计法MBDM和扩展的最大似然法MMLM的性能。数模试验检验了不同波浪条件、不同波浪测量系统和结构物的不同反射特性等情况下的估算结果，同时还比较了两种分析方法的计算速度和稳定性，结果显示，对于波浪的方向分布估计，MBDM优于MMLM，对于反射系数的方向分布估计以及计算速度和稳定性，MMLM优于MBDM。     

基于多层感知器的风涌浪分离方法

风涌浪分离是研究风浪、涌浪各自特性的基础,但受限于海浪谱数据的匮乏,基于海浪谱的风涌浪分离方法难以普及应用,有效的解决办法是采用波浪观测中容易获取的基本波要素进行风涌浪分离。现有方法无法利用基本波要素全面计算出风浪、涌浪的比例及其特征参数,为此本文将机器学习引入到风涌浪分离中,以多层感知器模型为基础,提出了一种利用基本波要素、风要素准确计算出风涌浪参数的方法。该方法需要每个测站提供至少466笔、建议766笔及以上的实测波浪数据作为训练样本,适用于台湾海峡3个测站,在计算精度上显著优于基于海浪频谱的传统风涌浪分离方法,可为本海域缺乏海浪谱的测站提供替代性的风涌浪计算方案,有助于扩大实测风涌浪资料的来源,进而加强风涌浪分布特性以及预警预报研究。     

台湾海峡风涌浪分离方法研究

受狭管效应的影响,台湾海峡波浪较大且常与涌浪混合存在。涌浪对包括船舶在内的浮式结构物有着重要的影响,而风涌浪分离是研究涌浪特性的必要前提,也一直是研究的热点和困难问题。由于数据的欠缺和观测条件的限制,在风涌浪分离方法中被普遍认可的二维谱方法常常难以使用,如何选择更为精准的一维谱方法往往会成为实际研究和应用过程中必须面对的问题。利用台湾海峡内3个具有二维谱数据的测站,通过将二维谱分离结果作为参考,针对台湾海峡风浪和涌浪的特征,探讨了风涌浪分离一维谱方法在该海域的适用性问题,研究表明风速法相较其他方法精度更好,在这一基础上提出了一种将波谱积分法与风速法相结合的一维谱方法。     

Determining the influence of wind-wave breaking on the dissipation of the turbulent kinetic energy in the upper ocean and on the dependence of the turbulent kinetic energy on the stage of wind-wave development

New experimental data that make it possible to explain and predict the observed variability of turbulent-energy dissipation in the upper ocean are discussed. For this purpose, the dependence of the energy dissipation rate of breaking wind waves on their propagation velocity (see [1]) is used. The turbulent-energy dissipation values obtained earlier in [2, 3] by a direct method are compared to the results of radar measurements of individual breaking events presented in [1]. On the basis of this comparison, a strong dependence of the turbulent-energy dissipation value on the stage of wind-wave development, which is characterized by the ratio U _a /c _p (U _a is the wind speed and c _p is the phase speed of the peak of the wind-wave spectrum) is confirmed. This dependence was found earlier purely empirically. Moreover, it is shown that the theoretically obtained dependence (c _p /U _a )⁴, does not contradict the available empirical data. The results of this study opens possibilities for scientifically substantiated calculations of greenhouse-gas exchange (specifically, CO₂ exchange between the ocean and the atmosphere).     

Assessment of wind-forcing impact on a global wind-wave model using the TOPEX altimeter

The study presents assessment of an operational wave model (Wavewatch III), focusing upon the model sensitivity to wind-forcing products. Four wind fields are used to drive the model, including the NCEP/NCAR reanalysis and three other products that assimilate various satellite wind measurements having high spatial resolution, including the QuikSCAT scatterometer. Three wave field statistics: significant wave height, mean zero-crossing wave period, and mean square slope are compared with collocated TOPEX altimeter derivatives to gauge the relative skill of differing wind-forced model runs, as well as to demonstrate an extended use of the altimeter beyond simply supplying wave height for wave model validation and assimilation. Results suggest that model output is critically sensitive to choice of the wind field product. Higher spatial resolution in the wind fields does lead to improved agreement for the higher-order wave statistics.     

Discussion on the critical wind speed for wind-wave generation on the basis of shear-flow instability theory

Observed critical wind speeds for the generation of wind waves are compared with those derived from a shear-flow instability theory. The theory predicts that the critical wind speed depends on the fetch and, for the case of infinite fetch, it is 93 cm s^–1 at 30 cm above the mean water surface, which agrees well with observations at sufficiently large fetch. For water containing soap, the much larger critical wind speeds which are observed cannot be explained by the reduction of surface tension alone. A qualitative discussion suggests that the elasticity of surface films of soap can effectively increase the critical wind speed.