A Whitecap Coverage Model Based on the Surface Slope For Criterion of Wave Breaking

Using the limit surface slope as a criterion of wave breaking,a simple model for estimatingthe spatial fraction of breaking surface of sea at an instant,which is regarded as the whitecap coverge inthis paper,is analytically derived from the probability density of surface slope based on Gaussianstatistics.The resulting fraction is found depending on the fourth moment of wave spectum,m_4,as well asthe critical threshold of surface slope.By expressing the fourth moment in terms of the Neumannspectrum,a formula linking the fraction and wind speed for fully developed sea states is obtianed.Anotherformula relating the fraction to both wind speed and fetch(or duration)is achieved by expressing m_4 interms of the Krylov spectrum and applying the empirical relationships used in the SMB ocean wave pre-dicting technique.A comparison between these results and the field data of whitecap coverage collected byMonahan and O＇Muircheartuigh shows an encouraging agreement.     

基于卫星数据改进计算白冠覆盖率的模型

本文基于白冠覆盖率的历史研究,总结了计算白冠覆盖率的参数化方案和海浪破碎统计模型,并分析比较其优缺点。通过结合基于卫星数据的参数化公式,利用最优拟合的方法,得到不同限制条件下模型中的系数C_en和n。通过分析考虑海浪破碎条件,确定了适用于一般海浪状况的系数值。通过比较白冠覆盖率的卫星数据和原始模型的模拟结果,可知改进后模型的结果更合理,同时与历史研究结论相符。文中还分析了从1998年到2008年十年平均的全球白冠覆盖率的季节性分布特征。在中高纬度海域,全年白冠覆盖率的值最大,而在低纬度和赤道海域,白冠覆盖率小于0.5%,全球白冠覆盖率的平均值大约为1% ~3%。北半球中高纬度海域的白冠覆盖率的季节性变化显著大于南半球。     

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。     

An analytically derived whitecap coverage model

Ａｎａｎａｌｙｔｉｃａｌｌｙｄｅｒｉｖｅｄｗｈｉｔｅｃａｐｃｏｖｅｒａｇｅｍｏｄｅｌ￥ＸｕＤｅｌｕｎａｎｄＬｉｕＷｅｎｔｏｎｇ（ＬａｂｏｒａｔｏｒｙｏｆＰｈｙｓｉｃａｌＯｃｅａｎｏｇｒａｐｈｙ，ＯｃｅａｎＵｎｉｖｅｒｓｉｔｙｏｆＱｉｎｇｄａｏ，Ｑｉｎ...     

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.     

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.     

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.     

基于白冠覆盖率的飞沫生成函数参数化

海浪破碎使得海面产生飞沫水滴，由于飞沫水滴的存在改变着大气和海洋之间的能量传输。飞沫生产函数一般认为是水滴初始半径和风速的函数，但海浪时刻存在于海-气界面，仅仅考虑海面风的作用，而忽略海浪的影响是不够完善的。白冠覆盖率是海浪破碎的重要特征参数，有研究者发现白冠覆盖率与海面风速和海浪均存在相关性。本文尝试从白冠覆盖率出发，构建飞沫水滴的生成函数参数化方案，将描述不同飞沫水滴半径的飞沫生成函数基于白冠覆盖率参数有机整合，然后结合白冠覆盖率和海浪状态的关系，利用实验室观测数据，分析不同海浪状态条件下海浪对飞沫生成函数的影响。研究结果表明，新的考虑波浪效应的飞沫生成函数可以合理地描述不同海浪状态条件下飞沫水滴的生成过程。     

海浪破碎对北太平洋海表面温度模拟的影响

基于海浪模式WAVEWATCH Ⅲ模拟北太平洋海浪要素,结合NDBC浮标资料进行验证,发现模拟出的有效波高与浮标测量值具有很好的一致性。基于改进型白冠覆盖率耗散模型,利用海浪模式模拟出的有效波高、有效波周期和摩擦速度等海浪要素计算出单位面积水柱内因海浪破碎产生的湍动能通量。通过改变环流模式sbPOM湍动能方程的上边界条件,引入海浪破碎产生的湍动能通量,并探究海浪破碎对北太平洋海表面温度模拟的影响。研究表明,由于海浪破碎的引入,环流模式sbPOM对北太平洋海表面温度模拟的准确程度得到提升,这为大气模式提供一个准确的北太平洋下边界条件具有重要意义。     

一种适用于小入射角条件下的白冠海面后向散射模型

本文提出了一种白冠海面的小入射角星载雷达后向散射模型,模型包括海面非波浪破碎部分和波浪破碎部分的后向散射。在风的作用下,海浪破碎形成白冠,对星载雷达的后向散射信号造成影响。文中利用TRMM PR和ECMWF的时空匹配数据集,拟合得出小入射角下星载雷达海面波浪破碎部分的后向散射模型,并分别与高斯分布/非高斯的海浪斜率分布海面的准镜面散射模型组成了白冠海面小入射角星载雷达后向散射模型。经实测数据对比,本文提出的由非高斯准镜面散射和考虑波浪破碎组合模型有效。     

微尺度滑动平均方法计算海浪谱奇阶矩的公式

Glazman提出了一种计算海浪谱高阶谱矩的微尺度平均方法,但是,他利用随机过程理论导出的计算偶阶矩的公式和参照偶阶矩结论定义的奇阶矩计算公式之间存在着内在的不一致性.本文在Glazman工作的基础上根据随机过程理论推导了“微尺度平均方法”计算奇阶谱矩的公式,纠正了他的错误.上述结论随即应用于讨论破碎对波面水质点水平速度分布的影响.通过破碎的加速度判据考虑了破碎对速度分布的限制,给出了未破碎波面上水质点水平速度的的统计分布的初步结果.该分布取决于谱宽度参数及白浪覆盖率的大小,当白浪覆盖率较大时明显偏离正态分布.     

海浪波面极大值分布的非线性影响

依非线性海浪模型,在二阶近似下,利用特征函数展开技术和直接求矩的方法,导出了定点波面位移及其对时间的一阶和二阶导数的联合分布。由此联合分布,导出了二阶非线性近似下的波面极大值分布。它由线性意义下的海浪频谱及所考虑的二阶级。波相互作用所确定。当忽略非线性影响时,文中给出的波面极大值分布退化为Cartwright和Longuet-Higgins所导出的分布。     

海浪微波散射理论模式

在假设海面白帽为球形气泡层的基础上,利用白帽海面的矢量辐射传输方程各随机粗糙面散射模型建立了海面的微波散射模型。辐射传输方程利用迭代法求解,随机粗糙面散射模型采用双尺度散射模型,利用白帽覆盖率的经验公式计算海面的微波散射特性。数值计算结果表明,随着气泡厚度的增加球形气泡散射系数越来越接近球形粒子散射系数;白帽对散射同的贡献随风速增大而增大;侧风情况比逆风和顺风情况影响均大;水平极化比垂直极化影响大     

Acoustically relevant bubble assemblages and their dependence onmeteorological parameters

A detailed physical model of the life history of a typical bubble plume, from its formation by a breaking wave to its dissipation into the background bubble population, is given, and the relationship between the early, acoustically relevant stages in bubble-plume development and the associated, remotely detectable whitecap is described. The manner in which the fraction of the sea surface covered by stage A spilling crests and by stage B mature whitecaps depends upon wind speed and upon wind stress or friction velocity is investigated. Formal expressions are given whereby near-surface bubble concentrations can be estimated from observations of fractional whitecap coverage or from measurements of the 10-m elevation wind speed     

一个新的破碎波统计模式

由运动方程和涡度方程所导得的两个首次积分估计给出了海波破碎的发生条件和破碎波的波面限制。由这两个条件所构造的新的破碎波统计模式，可导出海波的破碎面积率、破碎体积率和破碎能量损耗率的解析表达式，加之一个简单的白冠物理模型又导出了一个新的白冠覆盖率的解析表达式。     

Determination of the gas exchange rate in whitecaps using measurements of the bubble concentration

The effective gas exchange rate in whitecap formations, determined as the ratio of the total gas stream through the bubbles to the variation in the concentration of the gas dissolved in sea-water from that balanced with the atmosphere, is calculated for nitrogen and oxygen. The gas stream was determined from experimentally derived data on the distribution of air bubbles in the whitecap using remotein situ macrophotography. The dependence of the gas exchange rate on the relative saturation of the water with gas and the wind velocity is analysed. The gas exchange rate in whitecap formations for nitrogen is three times that for oxygen.Translated by Mikhail M. Trufanov.     

Coupled process-based cyclone surge simulation for the Bay of Bengal

We have developed a wind-wave-surge coupled process-based numerical model for simulating storm surge, consisting of a meso-scale atmospheric model (MM5), a third-generation spectral wave model (WW3) and a coastal ocean model (POM). We introduced an additional sea surface shear stress by wave dissipation into the model to consider the process of energy transfer from winds to currents through whitecap breaking. We demonstrate the importance of this energy transfer path through a hindcast simulation of a cyclone surge in April, 1991 in the Bay of Bengal: it helps generate mean current and has wave effects on wind-induced current fields in extremely shallow water areas.     

一种白浪覆盖率与风要素关系模式

采用Ｇｌａｚｍ ａｎ 提出的“微尺度平均”的方法,在合理选择平均尺度的基础上计算了ＪＯＮＳＷＡＰ谱的四阶矩,并将此结果与Ｓｎｙｄｅｒ提出的白浪覆盖率模式结合,从而建立起依赖于风速和风区两者的半经验、半理论的白浪覆盖率与风要素关系模式。此模式给出的结果与Ｍｏｎａｈａｎ 等汇集的海洋白浪覆盖率测量数据总体符合良好。     

Probability distribution of random wave forces in weakly nonlinear random waves

Based on the second-order random wave theory, the joint statistical distribution of the horizontal velocity and acceleration is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random wave forces are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. It is found that the distribution of wave forces depends solely on the frequency spectrum of sea waves associated with the first order approximation and the second order wave–wave interaction.     

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.