均匀介质n维随机波动的空间结构

研究了均匀介质中ｎ维随机波动的空间结构．导出了外观振幅、波数和相位的联合分布,据此分布,所有与空间有关的波要素的统计分布皆可导出．定义了外观波数谱并得到了其平衡区指数的上界为一（ｎ＋２）．二维时,海浪外观波数谱平衡区指数的上界与Ｐｈｉｌｌｉｐｓ通过动力学分析导出的Ｆｏｕｒｉｅｒ波数谱平衡区指数完全一样。     

海浪外观谱及其平衡域

定义了海浪能量的广义或n阶外观分布,导出了n阶海浪外观谱的解析形式,讨论了n阶外观谱的平衡域.结果表明,n阶外观谱的平衡域指数为-(3+n);平衡域指数上界为-3.任何波动现象,只要Fourier迭加原理和射线理论对它们的描述足够准确,则本文的结论皆成立.     

外观海浪谱的比较和验证

不同于通常意义下的海浪谱(以下简称为“内频谱”),外观海浪谱描述的是海浪能量随外观频率的分布,它可以依据表征海浪外观统计特征的波高与调期联合分布从理论上确定.本文在Huang、孙孚等已有工作的基础上,对外观海浪谱进行了较为深入的研究.首先,纠正了Huang等论文中的某些错误,并将Huang、孙孚等据不同的联合分布导出的外观海浪谱进行比较;然后,分别计算这两种外观海浪谱的前三阶矩,并与内频谱的矩进行比较;最后,用实验和现场资料对从理论上导出的外观海浪谱进行验证.结果发现,当谱宽度v≤0.3时,外观海浪谱矩与内频谱矩差异很小,理论谱形与实测结果也非常接近.因而,在实际问题的应用中,若谱宽度不大,则就可以用本文讨论的外观海浪谱去替代目前从理论上尚不能得到的通常意义下的海浪谱.     

基于卫星海面高度资料的太平洋海区涡旋能谱分析

在空间均匀和各向同性的假定下,地转湍流理论认为涡旋动能随尺度分布遵循k–n定律(k为波数)。但实际海洋受边界、地形、层结等,具有明显的非均匀、各向异性特征。鉴于此,我们基于近30a卫星高度计资料,分别计算了热带、副热带、中高纬度等海洋涡旋强度不同区域的海面高度异常(SSHA)波数谱,进而利用线性回归拟合方法估算出中尺度波段上SSHA波数谱的斜率,并与地转湍流理论预测进行了对比。研究结果显示:SSHA波数谱从赤道到中高纬度逐渐变陡,其斜率由–4减到–5,基本符合赤道线性波动理论和准地转湍流理论的预测。SSHA波数谱斜率存在纬向与经向差异,例如在赤道地区,纬向谱比相应的经向谱陡;而在南极绕极流区域,经向谱斜率大于纬向谱斜率。SSHA波数谱斜率的各向异性表明海洋中尺度运动受β效应影响,具有明显的经向和纬向差异。以上结果表明,海洋中尺度运动介于准二维和三维之间,不能用一个全球普适的湍流理论模型来描述。     

海浪外观波数谱与谱宽度最优确定

本文将外频谱转化为外观波数谱并设计了计算处理格式,提出了一种谱宽度参量的优化方法,为进一步研究海浪特征资料提取谱值和应用奠定基础。数值试验验证了此方法的可行性,但在高海况下风浪过程复杂,优化出的谱宽度偏大,外观谱解析形式需进一步改进     

海浪外观波数谱与谱宽度最优确定

本文将外频谱转化为外观波数谱并设计了计算处理模式,提出了一种谱宽度参量的优化方法,为进一步研究海浪特征资料提取谱值和应用奠定基础。数值试验验证了此方法的可行性,但在高海况下风浪过程复杂,优化出的谱宽度偏大,外观谱解析形式需进一步改进。     

调制Stokes波列长期演化过程中的熵值分析

深水Stokes波列的不稳定调制演化与实际海面的瞬变性、波浪破碎、畸形波等海洋现象密切相关,且波列在长期演化的过程中,演化特性会随着时间尺度的增加而改变,前人的研究多是针对其空间分布特性,对于波列内部能量的分布和变化趋势尚不清楚,因此引入熵的概念用于描述调制Stokes波列长期演化过程中任意时刻波浪场中不同频率波浪能量分布的均匀性。通过高阶谱方法数值模型,模拟了不同初始波陡条件下调制Stokes波列波数谱熵值的长期演化,给出不同阶段初始波陡和熵的关系,并将稳定状态熵值及谱形与典型海浪谱进行对比分析,发现调制Stokes波列长期演化的波数谱熵值和谱形均趋向实测JONSWAP谱,表明其经过长期演化发展,谱变宽变连续,波场内的能量分布趋向均匀并保持动态的平衡,同时也更加趋近于真实海浪。     

论风生波的正向力、切向力的共振、偶合及涡动耗散综合模式

本文从实际涡动海水的运动方程出发,导出了描述风生波初生阶段成长过程的波面演化方程,讨论了波面正向力、切向力以及涡动粘滞性在这个过程中的作用。第一、二节所导出的波面演化方程表明,海波成长过程类似一振动系统,其外扰动力为加权|k|/ρ的波面正向力场与波面切向力散度场的和,切向力与正向力一样也通过共振和偶合两种方式向海波输入能量。在第三节中给出了关于二维波数谱的解。它表明,在     

非线性海浪波面斜率的概率分布和白浪覆盖率的计算

依二维非线性海浪模型,在三阶近似下,利用特征函数展开技术和直接求矩的方法,导出了波面斜率的概率分布。据此分布,利用极限表面斜率判据,给出了白浪覆盖率的一个解析模式。该模式依赖于3个参量,这3个参量可由线性意义下的海浪波数谱及三类波-波相互作用所确定。     

二维EMD 方法在微尺度波斜率波数谱提取中的应用

进行海面微尺度波频率分析时,为消除重力波影响,引入二维 EMD(经验模态分解)方法滤除造成频率混叠的长重力波,然后进行傅立叶变换,得到海面微尺度波谱,进一步处理得到斜率波数谱。斜率波数谱提取结果表明：采用二维EMD方法可以有效滤除图像中混叠的长波信息,在此基础上进行微尺度斜率波谱计算的结果与国外已有结果基本一致。文中还将二维 EMD 方法与小波方法的处理结果进行了比对,结果表明在滤除长波的影响时,二维EMD方法具有其较明显的优势。     

Outer frequency spectrum of sea waves and its equilibrium range

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Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins’s linear model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper.     

风浪破碎对平衡域内谱形的影响

在实验室测得的大量风浪资料的基础上,经过谱分析和破波概率的计算,发现风浪破碎概率P     

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.     

Probability distribution of random wave–current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction 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 forces caused by waves propagating over a steady uniform current 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. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave–wave and wave–current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan–Pierson–Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied.     

以海浪波要素表示的外频谱形式

孙孕等（１９９４）提出了外频谱的概念,并推导出外频谱的理论形式,但其控制参量是由内频谱导出的,不便于实际应用,通过对实测海浪数据的分析,得到了控制外频谱的３个和内频谱有关的参量与波浪要素之间的关系,进而将外频谱表示以有效波高和有效波周期作为控制参量的形式,应用实测资料将本文得到的外频谱形式与理论外频谱进行了比较,发现二者符合良好。     

A note on the statistics of threshold crossing for a nonlinear wave field

Based on the non-Gaussian joint elevation and slope density function developed by Huang et al. (1984), the expected number of threshold crossing at an arbitrary level for a nonlinear wave field is derived. The distribution of the expected threshold crossing per unit time as a function of the crossing level is skewed with respect to the mean water level. This skewness also causes the mean zero crossing per unit time to deviate from the expected frequency of the wave field.     

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied.