深水风浪的风区指数律

对已有根据观测提出的幂函数形式风浪成长关系进行了分析。发现这些风浪成长关系在消去无因次风区后一致地与3／2指数律相协调，尽管它们原来存在较大的不协调性。发现Jeffreys，Sverdrup和Munk以及Platit的风能输入源函数在谱积分意义下具有相似性，而Tsikunov，Hasselmann和Phillips的破波耗散源函数在谱积分意义下也具有相似性，尽管这些源函数的原始形式和物理背景显著地不同。利用有效波能量平衡方程，将3／2指数律和发现的风能输入及破波耗散源函数相似性相结合，提出了深水风浪随风区成长的分式指数律，以得到的分式指数律拟合已有基于观测提出的风浪成长关系提出了半经验的风浪成长关系，与已有观测数据符合。     

Wind speed scaling and the drag coefficient

[1]Banner M L, Chen W, Walsh E J, et al.     

海面粗糙度方案的适用性研究

由量纲分析导出海面粗糙度与波龄及海面涌浪的状况有关,并对与波龄和波陡有关的两种海面粗糙度模型方案进行了敏感性测试,得出利用波龄模型方案计算粗糙度的误差比利用波陡模型方案小。基于国际上6个不同水深、风区和海况条件的海气交换试验资料,将其分为两组,一组是纯风海或以风海为主海况条件,另一组是以涌浪为主海况条件,测试波龄、波陡模型海面粗糙度方案在不同试验条件下的适用性。结果得出:在各种海况条件下,波龄模型粗糙度方案比波陡模型具有更好的普适性。在纯风海或以风海为主海况条件下,PS07,DGHQ03方案计算的粗糙度长度与实测资料计算结果最接近,GW06方案次之,O02方案计算结果明显偏高;涌浪为主海况条件下两种模型方案计算的粗糙度长度均偏低,O02方案计算的粗糙度长度误差相对较小,TY01方案误差最大。     

Growth of Wind Waves with Fetch in the Sea of Japan under Winter Monsoon Investigated Using Data from Satellite Altimeters and Scatterometer

By using wind vector fields observed by the NASA Scatterometer (NSCAT) and significant wave heights observed by the TOPEX/POSEIDON and European Remote Sensing Satellite-2 (ERS-2) altimeters, one-dimensional fetch growth of wind waves has been investigated under conditions of strong wind and high waves caused by the East Asian winter monsoon in the Sea of Japan. The evolution of fetch-limited wind waves can be observed by the altimeters along their ground tracks. The fetch is estimated by using vector wind fields observed by NSCAT. The derived growth characteristics of wind waves are compared with empirical relationships between the non-dimensional fetch and significant wave height proposed by previous studies. Good agreement is discernible with Toba's fetch graph formula normalized by the friction velocity, while Wilson's well-known formula normalized by the wind speed at a height of 10 m tends to underestimate the wave height under such severe conditions of high wind and very long fetch. This discrepancy is explained by the wind-speed dependence of the drag coefficient. A simple correction to Wilson's formula for the high wind conditions is proposed and compared with the observed data.     

锋面通过台湾海峡时引起的快速成长波高推算

每年冬季因中国北方冷空气前缘东移出海南下而形成的锋面是造成台湾海峡内恶劣海况的原因之一，锋面的到临常引发快速增高的波浪，这种海况是目前作业化数值预报模式在操作上不易反映的。经验证明根据元素波模式推衍所得的面积风域法推算波浪，适合于推导季风期间海况的一种方法。本文将锋面期间风域是移动的特性结合面积风域理论，作为推算锋面抵达时推算波高的方法。本文提出加权风场内插法计算各时刻各网格点的风速，使得面积风域理论简化为在网格点上的离散计算。文中根据锋面期间实际观测数据计算波能传播速率与风能传播系数等参数，经由案例分析的结果显示这个离散化面积风域法可以合理地推算锋面期间快速成长的波高。     

Analytically Derived Wind Wave Growth Relations

By the use of the 3/2 power law presented by Toba combined with the significant wave energy balance equation for wind wave, wind wave growth at a limited fetch is analytically investigated. The new wind wave growth relations (WWGRs) are analytically derived with shehering coefficient and wind drag coefficient as parameters. The geometrical average of observational values of shehering coefficient and the arithmetic average of observational values of wind drag coefficient are applied to detennine the new WWGRs. Comparisons with existing empirical WWGRs are made.     

Characteristics of developing waves as a function of atmospheric conditions,water properties,fetch and duration

For any specific wind speed, waves grow in period, height and length as a function of the wind duration and fetch until maximum values are reached, at which point the waves are considered to be fully developed. Although equations and nomograms exist to predict the parameters of developing waves for shorter fetch or duration conditions at different wind speeds, these either do not incorporate important variables such as the air and water temperature, or do not consider the combined effect of fetch and duration. Here, the wind conditions required for a fully developed sea are calculated from maximum wave heights as determined from the wind speed, together with a published growth law based on the friction velocity. This allows the parameters of developing waves to be estimated for any combination of wind velocity, fetch and duration, while also taking account of atmospheric conditions and water properties.     

The energy cycle of wind waves on the sea surface

The problems of wind-induced waves on the sea surface are considered. To this end, the empirical fetch laws that determine variations in the basic periods and heights of waves in relation to their fetch are used. The relation between the fetch and the physical time is found, as are the dependences of the basic characteristics of waves on the time of wind forcing. It is found that about 5% of wind energy dissipated in the near-water air layer contributes to the growth of wave heights, i.e. wave energy, although this quantity depends on the age of waves and the exponent in the fetch laws. With consideration for estimates of the probability distribution functions for the wind over the world ocean [11], it is found that the rate of wind-energy dissipation in the near-water air layer is on the order of 1 W/m². The calculations of wind waves [19] for the world ocean for 2007 have made it possible to assess the mean characteristics of the cycle of wave development and their seasonal variations. An analysis of these calculations [19] shows that about 20% of wind energy is transferred to the water surface. The remaining amount (80%) of wind energy is spent on the generation of turbulence in the near-water air layer. About 2%, i.e., one tenth of the energy transferred to water, is spent on turbulence generation due to the instability of the vertical velocity profile of the Stokes drift current and on energy dissipation in the surf zones. Of the remaining 18%, 5% is spent directly on wave growth and 13% is spent on the generation of turbulence during wave breaking and on a small-scale spectral region. These annually and globally mean estimates have a seasonal cycle with an amplitude on the order of 20% in absolute values but with a smaller amplitude in relative values. According to [19] and to the results of this study, the annually mean height of waves is estimated as 2.7 m and their age is estimated as 1.17.     

大型风浪水槽风浪统计特征的测量和分析

研究大型风浪水槽的风浪统计特征，采用多通道测波系统，同步采集沿水槽的１２个测点在不同风速下的风浪数据，从观测事实上分析风浪波面分布和有关要素特征，并建立水槽风浪统计要素与风速，风区长度之间的关系     

A GIS-based step-wise procedure for assessing physical exposure in fragmented archipelagos

Wind and waves are major forces affecting the geomorphology and biota in coastal areas. We present a generally applicable method for measuring and calculating fetch length, fetch direction and wave exposure. Fetch length and direction, measured by geographic information system-based methods, are used along with wind direction and wind speed data to estimate wave height and period by applying forecasting curves. The apparent power of waves approaching the shore, used as a proxy for wave exposure, is then calculated by a linear wave model. We demonstrate our method by calculating fetch lengths and wave exposure indices for five areas with varying exposure levels and types of meteorological conditions in the Finnish Archipelago Sea, situated in the northern Baltic Sea. This method is a rapid and accurate means of estimating exposure, and is especially applicable in areas with geomorphologically varying and complicated shorelines. We expect that our method will be useful in several fields, such as basic biogeographical and biodiversity research, as well as coastal land-use planning and management.     

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.     

Similarities of Some Wind Input and Dissipation Source Terms

Wind input parameterizations proposed by Jeffreys, Sverdrup and Munk, and Plant are analyzed. It is round by analogy that the similarity of integrals of the three wind input parameterizations exists. Wave breaking dissipation parmneterizations proposed by Tsikunov, Hasselmann, and Phillips are also analyzed. Likewise it is found by analogy that the similarity of integrals of the three dissipation parameterizations exists. The similarities of wind input and dissipation are applied to the investigation of the fetch-limited growth of wind waves, together with the 3/2 power law presented by Toba. Some semi-empirical formulas concerning the growth of wave height and period with fetch are presented. The results from the formulas are in good agreement with previous field observations.     

Local balance in the air-sea boundary processes

A new growth equation for wind waves of simple spectrum is presented upon three basic concepts. The period and the wave height of significant waves in dimensionless forms, which are considered to correspond to the peak frequency and the energy level, respectively, are used as representative quantities of wind waves. One of the three basic concepts is the concept of local balance, and the other two concern the acquisition of wave energy and the dissipation of wave energy, respectively. It is shown from some actual data that the equation, together with two universal constants concerning the acquisition and the dissipation of wave energy (B=6.2×10^?2 andK=2.16×10^?5, respectively), is applied universally to wide ranges of wind waves from those in a wind-wave tunnel to fully developed sea in the open ocean. “The three-second power law for wind waves of simple spectrum”, and a few relations as the lemmas, are derived, such that the mean surface transport due to the orbital motion of wind waves is always proportional to the friction velocity in wind, and that the steepness is inversely proportional to the root of the wave age. It is also derived that the portion of wind stress which directly enters the wind waves decreases exponentially with increasing wave age and is 7.5 % of the total wind stress for very young waves. Also, equations are presented as to the increase of momentum of drift current, and as to the supply of turbulent energy by wind waves into the upper ocean.     

涌浪对风浪能量影响的实验研究

在实验室风浪水槽中进行纯风浪和混合浪波面位移观测,研究波长较长的规则波对风浪能量的影响.本文用混合浪和纯风浪中的风浪显著波的零阶谱矩之比代表混合浪中的风浪与纯风浪能量之比,并以此表征涌浪对风浪能量的影响.研究了该能量比随涌浪波陡S、风区x、波龄倒数u/C、涌浪频率与纯风浪谱峰频率之比fs/fwp的变化规律.结果表明,涌浪对风浪能量的抑制作用随涌浪波陡的增加、波龄倒数的增大及涌浪频率与纯风浪谱峰频率之比的增大而增强.发现该能量比依赖于无因次量R=(1+80(πS)2)1.9(fs/fwp)0.9(u/C)0.27,并拟合得到2者的经验关系.此外,本文实验还发现,在某些情况下,涌浪的存在使风浪能量增加.     

Prediction of wave height and period for a constant wind velocity using the JONSWAP results

The results of the Joint North Sea Wave Project (JONSWAP), carried out in the North Sea in 1969, are used to derive formulae for significant wave height and wave period in terms of the wind speed (assumed constant) and fetch or duration. Values from the wave height formula are compared with those from the formulae of Bretschneider (1973) and Darbyshire (1963). It is proposed that the JONSWAP results be used for the prediction of fetch and duration limited waves formed under the action of the local wind field.     

稳定风浪场谱特征量间的关系

风浪宏观特征量是描述风浪场特征的重要物理量。作者基于风浪有停留在混乱运动状态的趋势的性质对风浪场特征量间的关系进行了研究。主频波频率附近的波动自风摄取能量,风浪吸收的能量通过非线性相互作用在谱中重新分配。谱中能量的重新分配产生多尺度波动,这导致风浪波面的混乱运动(风浪处于混乱运动状态)。在稳定状态,风浪运动最为混乱。当风浪状态偏离最混乱运动状态,谱中非线性相互作用引起的能量重新分配将使风浪回到该状态。基于线性海浪理论导出风浪场特征量间的关系。导出的关系与观测结果进行了对比,发现理论结果与观测结果很好地符合。风浪场宏观特征量间存在固有关系。尽管目前风浪场特征量关系的观测结果存在差异,但本文中证明,所导出的理论关系与实验结果很好地符合。     

Statistical characteristics of individual waves in laboratory wind waves

On the basis of data on the statistical characteristics of individual waves in laboratory wind waves reported in part I of this series, a self-consistent similarity regime is found to exist among properties of the individual waves, such as the nondimensional frequency, the wave number, the phase speed, and the steepness. Also, it is shown that forms of past empirical formulas for the development of the peak wave can be derived starting from the 3/2-power law, as an extension of the persent laboratory experimental data. In the derivation, only values of the coefficient of the 3/2-power law, and the fraction of momentum transferred from the wind retained by the wind waves, remain on an empirical basis.     

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.     

Adjustment of Wind Waves to Sudden Changes of Wind Speed

An experiment was conducted in a small wind-wave facility at the Ocean Engineering Laboratory, California, to address the following question: when the wind speed changes rapidly, how quickly and in what manner do the short wind waves respond? To answer this question we have produced a very rapid change in wind speed between U _low (4.6 m s^?1) and U _high (7.1 m s^?1). Water surface elevation and air turbulence were monitored up to a fetch of 5.5 m. The cycle of increasing and decreasing wind speed was repeated 20 times to assure statistical accuracy in the measurement by taking an ensemble mean. In this way, we were able to study in detail the processes by which the young laboratory wind waves adjust to wind speed perturbations. We found that the wind-wave response occurs over two time scales determined by local equilibrium adjustment and fetch adjustment, Δt ₁/T = O(10) and Δt ₂/T = O(100), respectively, in the current tank. The steady state is characterized by a constant non-dimensional wave height (H/gT ² or equivalently, the wave steepness for linear gravity waves) depending on wind speed. This equilibrium state was found in our non-steady experiments to apply at all fetches, even during the long transition to steady state, but only after a short initial relaxation Δt ₁/T of O(10) following a sudden change in wind speed. The complete transition to the new steady state takes much longer, Δt ₂/T of O(100) at the largest fetch, during which time energy propagates over the entire fetch along the rays (dx/dt = c _g) and grows under the influence of wind pumping. At the same time, frequency downshifts. Although the current study is limited in scale variations, we believe that the suggestion that the two adjustment time scales are related to local equilibrium adjustment and fetch adjustment is also applicable to the ocean.     

Probabilistic Models for the Probability of Wave Breaking and Whitecap Coverage Based on Kinematic Breaking Criterion

More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact moders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabihstic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks ff the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4.Then the JONSWAP spectrum is used to represent the fetch-limited sea waves in deep water, so as to relate the probahility of wave breaking and the whitecap coverage with wind parameters. To this end, the time-averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.