Is the wind wave frequency spectrum outdated

This paper presents a detailed examination of the practice of using the frequency spectrum to characterize wind waves. In particular, the issue of stationarity and Gaussian random process in connection with wind wave studies is addressed. We describe a test for nonstationarity based on the wavelet spectrum. When this test is applied to wind wave time series, the results significantly diverge from those expected for a Gaussian random process, thus casting critical doubts on the conventional concept of the wind wave frequency spectrum.     

The equilibrium range of wind wave frequency spectrum

-Theoretical form of equilibrium range is given on the basis of the wind wave frequency spectra proposed by Wenel al. (1988a,b,c, 1989a,b). The effects of peakness factor and water depth are discussed. In the case of deep water the e-quilibrium range is reduced to the form first proposed by Toba (1973) and the coefficient of the formula is shown to be the function of nondimensional fetch or peak frequency. Results of the present paper have been verified through field data.     

Theoretical wind wave frequency spectra in deep water——Ⅰ. Form of spectrum

In this part ot the paper theoretical wind-wave spectra nave been derived oy (I) expressing the spectrum in series composed of exponential terms; (2) assuming that the spectrum satisfies a high order linear ordinary differential equation; (3) introducing proper parameters in the spectrum; and (4) making use of some known charateristics of wind-wave spectrum, for instance, the law governing the equilibrium range. The spectrum obtained contains the zero order moment of the spectrum m0, the peak frequency ω0 and the ratio R =ω/ω0 (ω being the mean zero-crossing frequency) as parameters. The shape of the nondimensional spectrum S(ω) = ω0S(ω)/m0(ω=ω/ω0) changes with R and theoretically reduces to a Dirac delta function δ(ω-1) when R = 1. A spectrum of simplified form is given for practical uses, in which R is replaced by a peakness factor P=S(1).     

Generation mechanisms for capillary-gravity wind wave spectrum

We investigate the role of different physical mechanisms in the generation of the capillary-gravity wind wave spectrum. This spectrum is calculated by integrating a nonstationary kinetic equation until the solution becomes stready. The mechanisms of spectrum generation under consideration include three-wave interactions, viscous dissipation, energy influx from wind, nonlinear dissipation, and the generation of a parasitic capillary ripple. The three-wave interactions are taken into account as an integral of collisions without additional simplifications. It is shown that the three-wave interactions lead to solution instability if the kinetic equation takes into account only linear sources. To stabilize the solution, the kinetic equation should incorporate a nonlinear dissipation term, which in the range of short gravity waves corresponds to energy losses during wave breaking and microscale wave breaking. In the range of capillary waves, the account of nonlinear dissipation is also needed to ensure a realistic level of the spectrum for large wind velocities. For the steady-state spectrum, the role of three-wave interactions remains essential merely in the range of the minimum of phase velocity, where a trough on the curvature spectrum is formed. At the remaining intervals of the spectrum, the main contribution into the spectral energy balance is provided by the mechanisms of wave injection, nonlinear dissipation, and the generation of parasitic capillaries.     

Theoretical wind wave frequency spectra in shallow water

The method developed by Wen et al. (1988 a) for deriving theoretical wind wave frequency spectrum in deep water is extended to the case of water of finite depth, in which a parameter η=H/d is introduced, where H and d represent the average wave height and water depth respectively. The derived spectra reduce to those in deep water when η=0. The case of η=1/2 corresponds to waves impending to break because of the effect of the bottom. Simplified forms of spectra are given. The theoretical results agree with the observed spectra well.     

Assessing wind wave spectrum representations in a shallow lake

This paper presents an objective assessment of three published wave spectrum formulas for the shallow sea. It compares wave spectra estimated by these formulas with those calculated from actual field measurements made in Lake Erie during 1981 in depths ranging from 1.4 to 14.0 m. The results show that the models each have various degrees of effectiveness and applicability. The choice of which model to use may depend upon the availability of input parameters, and is still basically subjective. The models specifically developed for the shallow depth are found to be less effective. The form of spectral representation may remain similar at all depths, with depth affecting only the wave parameters that characterize the spectrum form.     

Influence of the wave spectrum form on the bottom sediment dynamics

This paper is dedicated to the investigation of the influence of the irregular wave spectrum form on the regularities of the bottom suspension and formation of the bottom topographic microforms (ripples). It is shown that the vertical profile of the suspended matter concentration and the possible partial deformation of the bottom ripples are related to the peculiarities of the frequency distribution of the energy in the wave spectrum (at the constant energy of the process).     

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.     

On the stability of the moments of the maximum entropy wind wave spectrum

The stability of some current wind wave parameters as a function of high-frequency cut-off and degrees of freedom of the spectrum has been numerically investigated when computed in terms of the moments of the wave energy spectrum.From the Pierson-Moskovitz wave spectrum type, a sea surface profile is simulated and its wave energy spectrum is estimated by the Maximum Entropy Method (MEM). As the degrees of freedom of the MEM spectral estimation are varied, the results show a much better stability of the wave parameters as compared to the classical periodogram and correlogram spectral approaches. The stability of wave parameters as a function of high-frequency cut-off result the same as obtained by the classical techniques.     

风浪局域小波谱峰的涨落

将湍流研究中已得到有效应用的局域小波能谱概念引入到风浪研究.分析了实验室不同风速下风浪的局域小波能谱.结果表明,局域小波谱峰值存在着显着的涨落,涨落的方差随风速的增加而增大.这不仅体现了风浪的局域结构,还意味着通常风浪谱的应用中除了要考虑平均意义下的频谱峰值外,还必须考虑局域小波谱峰值的涨落方差.     

Fluctuations of peak energy and peak frequency of local wavelet energy spectrum for wind waves

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X-波段雷达近海海浪频谱反演的神经网络模型

X-波段雷达作为国内海浪观测的一种新工具,在海浪频谱获取和有效波高反演方面仍存在较多问题.本文利用非线性回归方法,将现场实测浮标数据频谱和雷达一维图像谱分别与标准频谱模型进行拟合,发现浮标频谱和一维图像谱具有标准频谱的特征,能够较准确地获取相应的谱参数.提出了建立由雷达一维图像谱参数反演海浪频谱参数的神经网络模型,同时在模型中加入影像序列信噪比,进而反演有效波高,并将反演结果与现场实测数据和传统算法(建立影像序列信噪比与有效波高之间的线性回归方程)进行了对比,结果表明,获取谱参数的误差和反演有效波高的平均误差在20％以内,而传统算法计算有效波高平均误差在20％以上.     

Intermittency of wind wave group breaking

Knowledge on intermittency of wave breaking is so far limited to a few summary statistics, while the probability distribution of time interval between breaking events can provide a full view of intermittency. Based on a series of experiments on wind wave breaking, such probability distributions are investigated. Breaking waves within a wave group were taken as a single breaking event according to recent studies. Interval between successive wave groups with breaker is the focus of this paper. For intervals in our experiments with different fetch and wind conditions, their distributions are all skewed and weighted on small intervals. Results of Kolmogorov-Smirnov tests on time series of these intervals indicate that they all follow gamma distribution, and some are even exponential type. Average breaking-group-interval decreases with friction velocity and significant steepness until the wind is strong enough;most of them are more than 10 times the dominant wave period. Group breaking probability proposed by Babanin recently and the average number of breaking waves in wave groups are also discussed, and they are seemingly more reasonable and sensitive than traditional breaking probability defined in terms of single wave.     

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.     

泉州岸带土层剪切波速和地面脉动的频谱特性

本文根据泉州6种土层剪切波速和地面脉动观测资料,探讨有关参数与场地土层、场地土特性、场地类别等方面的关系。结果表明,本区6种不同土质剪切波速值随深度变化;各波速测孔附近地面脉动的峰值周期主要集中在0.18～0.56s间,其频谱特性可归为3类,各类与地层结构具有一定的对应关系。文中还讨论了利用地面脉动频谱特性研究土层平均剪切波速的可能性。     

星载合成孔径雷达海浪图像谱仿真研究

利用Hasselm ann 的完全非线性积分方法对文氏海浪谱的星载合成孔径雷达(SAR)图像谱进行了仿真研究。结果表明: (1) 在星载SAR海浪成像过程中, 速度聚束调制远比水动力调制、倾斜调制和距离向聚束调制重要;(2) 图像谱有180°的方向模糊和方位向的高波数截断,距离向传播海浪的图像谱存在双峰现象; (3) 不同极化方式和雷达视向的选取对图像谱无明显影响, 因而对于海浪的星载SAR遥感而言, 可以采用单一极化和单一视向。对于不同成长状态的风浪而言, 以上结果保持不变。     

南麂站定常波风浪波高与风速的经验关系

本文以南麂海洋站１９８３～１９９０年风、浪的实测资料为依据，建立了南麂海城春、夏、秋、冬季定常波风浪波高与风速的经验关系式。检验结果表明，曲线回归显著，计算值与实测值吻合良好。文中还对偏ＮＮＥ向和偏ＳＳＷ向计算波高随风速增大的快慢，同一方向在同一风速作用下计算波高的季节变化及其机理作了初浅的讨论。     

Experimental evidence of the transition between power law models in the high frequency range of the gravity wave spectrum

The existence of a transition in the slope of the wind-generated gravity wave spectrum from a f⁻⁴ to a f⁻⁵ power law, at a given frequency in the high frequency range, is examined. Evidence of its existence and of the non-uniqueness of the wave spectrum slope in the equilibrium range is presented. Furthermore, it is demonstrated that the statistical variability of the spectral estimates makes it difficult to obtain reliable results from limited sets of finite length wave records.     

波浪反射系数谱的特征分析

应用斜向不规则波反射系数的改进两点法(MTPM),用模型试验研究了混凝土护面堤和块石护面堤波浪反射系数的频率谱和方向谱,结果表明,分析的反射系数随入射波频率的增加、结构坡度的减小和入射角的加大而减小.给出了波浪反射系数频率谱及其随Iribarren数变化的规律,提出了反射系数三维谱的经验公式,由此可定量地描述斜向不规则波的反射系数随无量纲特征参数Iribarren数和入射波角度的变化规律.     

The high frequency spectrum of wind-generated waves

The high frequency part (10 Hz50 Hz) of the one-dimensional wave spectrum was measured in a wind-wave channel under accurately controlled conditions. The results are compared with the spectral forms for the capillary range that have been proposed recently byPierson andStacy (1973) andToba (1973). In a general sense, fairly good agreement is found between the present results and those ofPierson andStacy (1973) and ofToba (1973). The spectrum in the capillary range is clearly wind speed dependent, and the spectral density in that range increases with increasing wind speed.However, closer examination shows systematic deviations of the present results from those previously proposed, particularly for high speed winds.