Improvement and application of a saturation based wave dissipation function in SWAN model

Wave dissipation characteristics in SWAN (Simulating Waves Nearshore) model are investigated through numerical experiments. It is found that neither the fully developed integral parameters of wind waves (significant wave height and peak frequency) nor the high frequency spectral tail can be well reproduced by the default wave dissipation source terms. A new spectral dissipation source term is proposed, which comprises saturation based dissipation above two times of peak frequency and improved whitecapping dissipation at lower frequency spectrum. The reciprocal wave age (u /c p ) is involved into the whitecapping model to adjust dissipation rate at different wind speed. The Phillips higher frequency saturation parameter in the saturation-based dissipation is no longer taken as a constant, but varies with wave age. Numerical validations demonstrate that both the wind wave generation process and higher frequency spectrum of wind waves can be well simulated by the new wave dissipation term.     

Dependence of sea surface drag coefficient on wind-wave parameters

The relationships between sea surface roughness z 0 and wind-wave parameters are analyzed,and spurious self-correlations are found in all of the parameterization schemes.Sea surface drag coefficient C D is fitted by four wind-wave parameters that are wave age,wave steepness,windsea Reynolds number R B and R H ,and the analyzed data are divided into laboratory,field and combined data sets respectively.Comparison and analysis of dependence of C D on wind-wave parameters show that R B can fit the C D most appropriately.Wave age and wave steepness are not suitable to fit C D with a narrow range data set.When the value of wave age has a board range,R H is not suitable to fit C D either.Three relationships between C D and R B are integrated into the bulk algorithm COARE to calculate the observational friction velocity,and the results show that the relationship between C D and R B which is fitted with field data set can describe the momentum transfer in the open ocean,under low-moderate wind speed condition,most appropriately.     

Sea-surface roughness length fluctuating in concert with wind and waves

When the nondimensional aerodynamic roughness parameter for the sea surface (gz ₀/u _* ²,g being the acceleration of gravity,u _* the air friction velocity) is plotted as a function of the wave age, the data points in the diagram are distributed mostly in a triangle area between the Charnock formula and the Toba-Koga formula; the nondimensional roughness perameter is not expressed as a unique function of the wave age, but rather there seem to be multiple regimes. In order to investigate the cause of the data point scattering, a reanalysis was made of the 4.5-hour time series of the wind profile and wind-wave statistics which were obtained at an oceanographic tower station under the conditions of a winter monsoon wind having slightly fluctuating speed and steadily growing wind waves.It is concluded that the averaged variation ofz ₀ is given by the Toba-Koga formula with a constant of value 0.015. However, as a result of the wind fluctuation on the time scales ranging from several minutes to an hour, data points show a conspicuous fluctuation on the nondimensional roughness parameter-wave age diagram in the direction transverse to the averaged variation. The variation inz ₀ directly reflects the degree of over- or under-saturation in the high-frequency range of the wind-wave spectra. Physical interpretation of these variations is also presented.     

The roughness height and drag law over the water surface based on the hypothesis of local equilibrium

A series of measurements of winds and wind-waves were carried out in wind-wave flumes. A data analysis based on the hypothesis of local equilibrium yielded a new empirical formula on the controversial quantity of roughness heightz ₀ over the water surface: , where the nondimensional roughness height is defined bygz ₀/u _* ² and the wave-wind parameterũ byω _p u _*/g, g being the gravitational acceleration,u _* the friction velocity of air,ω _p the peak frequency of wind-wave spectra. The obtained formula is compared with Charnock's (1955) and Toba's (1979) proposals; is constant in the former and inversely proportional toũ in the latter. As in Toba's, this formula immediately leads to a practically important conclusion that the drag coefficientC _d depends not merely on the usual variableU ₁₀ (wind velocity at 10m height over the water surface), but also on the surface state represented by wind-waves. An explicit expression is provided for the drag coefficient incorporating the wave-wind parameter; it covers the range ofC _d calculated from most of the previous drag formulas, by varying the wave-wind parameter.     

A new expression for the production rate of sea water droplets on the sea surface

A new set of empirical formulas for the production rate and the number concentration of sea-water droplets on the sea surface are proposed, synthesizing past observation data of sea-salt particles in the sea and water droplets in wind-wave tanks. A new levelz _c is introduced as the effective wind-sea surface where seawater droplets are produced. The new formulas are expressed in linear functions in logarithmic scales ofu*²/v _p , a parameter to describe overall conditions of airsea boundary processes, whereu _* is the friction velocity of air,v the kinematic viscosity of air and _p the peak angular frequency of wind-wave part of wave spectra. A model of coexistence of spray droplets and suspended particles near the sea surface is proposed. As for the independent parameter, a comparison between the uses ofu*²/v _p and ofu _* ³ which was the traditional way of parameterization excluding wave measure, shows that the advantage of usingu*²/v _p is statistically significant with a confidence limit 89% in F-test.     

On nondimensional correlation between roughness length and wind-friction velocity

Physical bases for nondimensional parameters,z ₀/(u ² _*/g) andz ₀/(u _*/), characterizing wind-wave interaction are discussed; data selected to support the latter are critically reviewed. Both parameters are herewith unified, with the former describing the primary growth of roughness length with wind and the latter the secondary effects due to waves.     

海洋环境因素对白冠覆盖率的影响及其数值估算

波浪破碎是一个强非线性过程,破碎时产生的大量气泡在海面上表现为白冠,白冠覆盖率是刻画波浪破碎一个重要参数。研究表明,白冠覆盖率与海上风速、海浪状态和大气稳定度等多种海洋环境因素有关。综合前人的观测数据,本文给出了更为可靠的依赖风速的白冠覆盖率公式,发现海水温度越高,白冠覆盖率越大。提出了以波浪破碎耗散函数为参数的白冠覆盖率公式,同时发现波龄小于某个临界值时,白冠覆盖率随波龄增大,波龄大于临界值时,白冠覆盖率保持不变,该临界值随风速增大而减小。     

On the local equilibrium of winds and wind-waves in relation to surface drag

Local equilibrium of winds and wind-waves is discussed as a basis for research of the drag coefficient of the water surface as well as for the spectral growth of wind-waves. This hypothesis assumes, in a narrow sense, that statistical properties are determined from four physical quantities, which represent winds and wind-waves: the friction velocityu _*, the gravitational accelerationg, the powerE of the surface displacement, and the peak frequency _p of a wind-wave spectrum. Then one has only one nondimensionalcontrol parameter, which may be either the wave age or wave nonlinearity (slope) of dominant waves. In a wide-sense, one can take into account viscosity and surface tension in terms of one more additional parameter by virtue of the virtual invariance of those material constants; that parameter describes the scale ratio between dominant waves and the short waves for which viscosity or surface tension is important. A unified expression for the roughness height according to this hypothesis turns out to include Charnock's and Toba's formulas as special cases. On the basis of a preliminary analysis of the experimental data, a new empirical formula is proposed.     

海洋白浪寿命的定义及测量结果

通过对国内外白浪研究和应用的分析,首次提出了有效白浪寿命的定义,给出了计算白浪寿命的公式及测量方法和结果,并报告了以此方法在渤海实测的结果,得到了白浪寿命ＴＬ与海面风速Ｕ１０的关系为ＴＬ＝０．２６Ｕ１０以及白浪寿命概率分布近于瑞利分布等。     

Field data support of three-seconds power law andgu *σ−4-spectral form for growing wind waves

Observational data on air-sea boundary processes at the Shirahama Oceanographic Tower Station, Kyoto University, obtained in November, 1969, was analyzed and presented as an example representing the structure of growing wind-wave field. The condition was an ideal onshore wind, and the data contained continuous records of the wind speed at four heights, the wind direction, the air and water temperatures, the tides, and the growing wind waves, for more than six hours. The main results are as follows. Firstly, in both of the wind speed and the sea surface wind stress, rather conspicuous variations of about six-minute period were appreciable. Secondly, the three-seconds power law and its lemma expressed byH ^*=BT ^*3/2 and=2BT ^*–1/2, respectively, are very well supported by the data, whereH ^*(gH/u _* ²) andT ^*(gT/u _*) are the dimensionless significant wave height and period, respectively, the wave steepness,u _* the friction velocity of air,g the acceleration of gravity, andB=0.062 is a universal constant. Thirdly, the spectral form for the high-frequency side of the spectral maximum is well expressed by the form of()= _sgu_*^–4, where is the angular frequency and() the spectral density. The value of _s is determined as 0.062±0.010 from the observational data. There is a conspicuous discrepancy between the spectral shape of wind waves obtained in wind-wave tunnels and those in the sea, the former containing well-defined higher harmonics of the spectral peak, and consequently there is an apparent difference in the values of _s also. However, it is shown that the discrepancy of _s may be eliminated by evaluating properly the energy level of the spectral form containing higher harmonics.     

An extended verification technique for solving problems of numerical modeling of wind waves

Based on different modifications of the source function in the WAM(C4) wind-wave model, a large series of verification calculations aimed at increasing the quality of the numerical model (with respect to the parameters of accuracy and performance) is performed. We propose a methodology allowing us to solve the following fundamental and practical problems of numerical modeling: (1) determining the minimum interval of verification of numerical wind-wave models, (2) finding a criterion for choosing the best model out of all models subjected to verification, and (3) formulating the accuracy requirement for specifying the input field necessary for the given accuracy of wind-wave field calculations. Particularly, we have found that (a) the minimum term of verification calculations for numerical wind-wave models is three months; (b) according to our criterion, the proposed modification of the WAM model impartially is “essentially preferable” to the original model; and (c) the relative errors (yielded by the proposed version of the WAM model) in the calculated wave heights ρH _s and average periods ρT _m for different levels of the relative error of the input wind-wave field ρW make it possible to solve the third problem mentioned above.     

Storm surge simulation using wind-wave-surge coupling model

Simulation of a storm surge caused by Typhoon 9918 in the Yatsushiro Sea, Kyushu, Japan was hindcasted by the synchronous coupled wind-wave-surge model composed of a Meso-scale meteorological model (MM5) for the wind and sea surface pressure, a spectral third-generation wind-wave model (Wavewatch III) for waves, and the coastal ocean model (Princeton Ocean Model). Inclusion of the whitecap wave breaking stresses (whitecap dissipation stress) in the coastal ocean model made it possible to reproduce the extreme surge height in the extremely shallow bay.     

Wind-wave spectra based on the hypothesis of local equilibrium

Wind-wave spectra measured in a wind-flume are analyzed according to the hypothesis of local equilibrium. The gross relation between the wave height and the frequency is reexamined to yield the basic validity of the 3/2-power law of Toba orE～? in the range of 0.4≦?≦1, where? is the wave-wind parameter defined by?=ω _p u _*/g; ω _p denotes the peak frequency of the wind-wave spectra,u _* the friction velocity andg the gravitational acceleration. Noticeable deviation is found, however, for?<0.4 or?>1. In particular, the data for large? suggest the existence of an upper limit of the wave nonlinearityE at about 5×10^?2, whereE=Eω _p ⁴ /g² withE the total power of the wind wave spectrum. Then, the spectral form is investigated in detail. As? decreases, the normalized spectrum becomes more gradual as a whole, but its forward (low frequency) part tends to show a steeper profile. In the high frequency region ( \(\tilde \omega \) >2.6), the spectrum is found to have a functional form likeu _* ² ω ^?3, which differs from the usualω-dependence asω ^?5 orω ^?4. It suggests weak dependence of the high-frequency spectra on the gravitational accelerationg and on the peak frequencyω _p ; spectral density at high frequencies may be saturated, so that its magnitude may be dominated by the frequencyω, the friction velocityu _*, the surface tension and the viscosity.     

波流作用下海底边界层沉积物再悬浮与影响因素研究

海底沉积物再悬浮及其分布取决于海洋水动力、沉积物类型与床面形态之间复杂的相互作用,准确地理解和确定沉积物再悬浮过程对于沉积物输运的研究具有重要的意义。本文在祥云湾海洋牧场典型海域开展现场原位观测,获取研究区波浪、海流及悬浮沉积物浓度数据;分析了波、流作用下海底边界层悬浮沉积物垂向分布特征,并探究了海洋水动力和床面形态对悬浮沉积物垂向分布的影响。结果表明,研究区波流之间的相互作用不显著,沉积物再悬浮受控于风暴浪作用,风暴浪作用下底床切应力可以达到沉积物临界切应力的10～15倍,沉积物的再悬浮滞后于风暴浪作用2～3 h。在波浪荷载微小的情况下,悬浮沉积物垂向分布呈现"I"型,波浪荷载下,悬浮沉积物垂向分布呈现幂指函数分布,表现为"L"型;床面形态随波、流作用而演化,影响沉积物的再悬浮过程,u_(?w)/u_(?c)=1.00可作为波浪和海流起主导控制作用的床面形态的判别依据,纯波浪荷载作用下的u_(?w)/u_(?c)显著高于波浪主控作用下,但二者之间的界线随着波浪荷载的增加而升高。     

Analytically derived wind-wave directional spectrum part 1. Derivation of the spectrum

In contrast with the usual method to obtain the wind-wave directional spectrum by multiplying the frequency spectrum with an empirical directional function, the authors attempt to derive analytically the directional spectrum by adopting proper spectral form and using effective parameters, namely, the zero order momentm ₀ of the wind-wave frequency spectrumS(), its peak frequency ₀ and the so-called peakness factorP=₀ S(₀)/m ₀, where is angular frequency. The directional spectrum is given in a form of frequency spectrum for each direction. The spectral directionality depends on, in addition to frequency, the wind-wave growth status, for the peakness factorP as introduced by the authors previously is a measure of the wave development stage. The salient features of the directional spectrum, comparison with existing formulas and the verification of the spectrum by observational data are to be given in the Part 2 of the paper.Project supported by the National Natural Science Foundation of China.     

Local balance in the air-sea boundary processes

A combination of the three-second power law, presented in part I for wind waves of simple spectrum, and the similarity of the spectral form of wind waves, leads to a new concept on the energy spectrum of wind waves. It is well substantiated by data from a wind-wave tunnel experiment.In the gravity wave range, the gross form of the high frequency side of the spectrum is proportional tog u _* ^–4, whereg represents the acceleration of gravity,u _* the friction velocity, the angular frequency, and the factor of proportionality is 2.0×l0^–2. The wind waves grow in such a way that the spectrum slides up, keeping its similar form, along the line of the gross form, on the logarithmic diagram of the spectral density,, versus. Also, the terminal value of, at the peak frequency of the fully developed sea, is along a line of the gradient ofg ^{2 –5}.The fine structure of the spectrum from the wind-wave tunnel experiment shows a characteristic form oscillating around the ^–4-line. The excess of the energy density concentrates around the peak frequency and the second- and the third-order harmonics, and the deficit occurs in the middle of these frequencies. This form of the fine structure is always similar in the gravity wave range, in purely controlled conditions such as in a wind-wave tunnel. Moving averages of these spectra tend very close to the form proportional to ^–5.As the wave number becomes large, the effect of surface tension is incorporated, and the ^–4-line in the gravity wave range gradually continues to a ^–8/3-line in the capillary wave range, in accordance with the wind-wave tunnel data. Likewise, the ^–5-line gradually continues to a ^–7/3-line.Also, through a discussion on these results, is suggested the existence of a kind of general similarity in the structure of wind wave field.     

Effects of wave age and air stability on whitecap coverage

The paper considers the effects of wave age and air stability on the whitecap coverage at sea. This is made by using the logarithmic mean wind velocity profile including a stability function as well as adopting a recent wave age dependent sea surface roughness formula. The results are valid for wind waves in local equilibrium with the steady wind. Examples of results demonstrate clear effects of wave age and air stability on the whitecap coverage. Comparisons are also made with field measurements by Sugihara et al. [Sugihara, Y., et al., 2007. Variation of whitecap coverage with wave-field conditions. J. Mar. Syst. 66, 47–60], representing unstable air stability conditions. Although the data basis is limited, the wave age independent Charnock sea roughness based predictions capture the main features of the observed whitecap coverage, suggesting a stronger dependence on air stability than on wave age in the data.     

白浪覆盖率模式中参量的研究

在波面位移为正态过程的假定下,推导出一种以平均周期和风速为参量的白浪覆盖率公式W=1-Φ[5.11094[-T/U10]0.7576].依据摩擦风速和U10的表达式,进一步推导出白浪覆盖率依赖于摩擦风速的形式W=1-Φ[0.5227[-T/U]0.7576]].考虑到在实际应用中,经常需要用波龄描述波浪的状态,将白浪覆盖率表示成一种形式简单的波龄的函数W=1-Φ(3.6496ξ0.7576),与Monahan等的海上测量数据符合良好.     

大通湖中华绒螯蟹(Eriocheir sinensis)自然生产潜力估算模型探讨

人放天养的中华绒螯蟹(Eriocheir sinensis)质量好、个体大、耐运输、肉质鲜美,是优质高档蟹的代表,但产量严重不足。建立一套湖泊中华绒螯蟹自然生产潜力估算的模型来估算湖泊中华绒螯蟹自然生产潜力,确定放养量,以达到湖泊中华绒螯蟹稳产已迫在眉睫。本文根据近20年来作者对湖泊中华绒螯蟹放养的经验,结合灰估理论,提出蟹自然生产潜力:W=[B1K1C1/R1+B2K2C2/R2]·(B1+B2)2/B12+B2和蟹种放养量:W0=P0[B1K1C1/R1+B2K2C2/R2]·U/P估算模型,并与生产实践进行求证。其结果与生产实践存在较好的一致性。其估算结果可作为指导湖泊中华绒螯蟹生产的依据。