Some statistical aspects of wave-induced drift in sea states

The paper provides a simple analytical tool which can be used to give estimates of the mean value and the standard deviation of the Stokes drift for sea states. This is achieved by providing bivariate distributions of significant wave height with surface Stokes drift as well as with volume Stokes transport. These Stokes drift parameters are defined in terms of significant wave height and characteristic wave periods. Also bivariate distributions of spectral peak period and these two Stokes drift parameters are provided. The paper presents statistical aspects of the Stokes drift parameters, such as the conditional expected values and the conditional variances for given significant wave height, as well as examples of results corresponding to typical field conditions. The present analytical results can be used to make assessment of Stokes drift based on e.g. global wave statistics.     

随机波浪下斯托克司漂移速度是否引起水面漂移物离散的研究

漂浮于自由水面的污染物的的迁移、扩散会受到天然随机海浪的影响。之前的研究（以Herterich和Hasselmann（1982）为代表）普遍认为,随机波浪作用下的斯托克司漂移速度会引起水面污染物的离散,这个离散甚至有可能跟风和海流引起的离散同一量级。本研究就随机波浪作用下的斯托克司漂移速度是否会引起水面漂移物的离散进行理论和试验探讨。从理论推导可知,随机波浪下的质量输移速度是个定常分量,因此它不会随时间变化而引起水面漂移物的离散。随后我们在实验室水槽中进行了漂移物在随机波浪（P-M谱）作用下的漂移过程的测量。试验结果也印证了随机波浪作用下的斯托克司漂移速度不会引起水面漂移物离散的结论。     

An analytical approximation for the horizontal drift force acting on a deep draught spar in regular waves

An analytical solution is presented for the horizontal drift force acting on a uniform circular cylinder that is undergoing surge and pitch motion in regular waves. The solution is exact to second order, for a perturbation expansion in terms of wave steepness, but is limited in a strict sense to the hypothetical case when the draught is equal to the water depth. The formulation is used to provide an analytical approximation for investigating the influence of key parameters on the horizontal drift force acting on a deep draught spar.     

Stokes drift estimation for deep water waves based on short-term variation of wave conditions

The paper provides a simple analytical method which can be used to give estimates of the Stokes drift based on short-term variation of wave conditions. This is achieved by providing bivariate distributions of wave height and surface Stokes drift as well as wave height and volume Stokes transport for individual random waves within a sea state. The paper presents and discusses statistical aspects of these Stokes drift parameters, as well as examples of results corresponding to typical field conditions.     

海滩侵蚀的数值分析模型

介绍了有关海滩侵蚀造成海岸演变问题的数学分析模型。根据海岸线演化和海滩断面的沉积物迁移理论建立一种顺岸方向和垂直岸线方向海岸形状变化的耦合模型。将海滩沉积物被海浪迁移的机理看作由于海水在海滩介质孔隙内渗流侵蚀和海浪对海滩介质冲刷所致的海滩介质的孔隙损伤变化。这种结合数值和解析分析的综合方法可用于模拟海岸演变问题中海岸线 (沿岸方向 )和海滩断面 (垂直海岸线方向 )的变迁情况     

Wave drift enhancement effects in multi column structures

A theoretical assessment is made of mean wave drift forces on groups of vertical circular cylinders, such as the columns of a floating offshore platform. A complete analytical solution is obtained for two cylinders extending from seabed to free surface, and a long wave approximation is found to provide reliable predictions of the drift force in line with the waves at low frequencies. For moderate separation between the two cylinders, this force is found to tend at low frequencies to a value four times the force on an isolated cylinder.A numerical method is employed to study two surface piercing cylinders truncated below the free surface, and an arrangement of four vertical cylinders characteristic of a floating offshore platform. The mean vertical drift force is found to be reasonably well approximated, over the frequency range of practical interest, by the force on an individual cylinder considered in isolation multiplied by the number of cylinders in the group. Interaction effects, however, have a profound influence on the total horizontal drift force. At low frequencies this force is found to tend to the force on an isolated cylinder multiplied by the squate of the number of cylinders in the group.     

Minimization of drift force on a floating cylinder by optimizing the flexural rigidity of a concentric annular plate

The deployment of suitable configurations of mutually interacting floating bodies for efficiently controlling their hydrodynamic interactions towards the reduction of the wave drift forces and, thus, of the mooring lines’ loads, has, nowadays, gained a great scientific interest. In this paper, the hydrodynamic behaviour of a floating cylinder and a concentric annular flexible plate is analysed in the frequency domain aiming at the minimization of the drift forces acting on the cylinder by optimizing the flexural rigidity of the plate. The diffraction/radiation problem is solved using a higher-order boundary element method. The analysis is implemented assuming that both floating bodies oscillate freely in heave, while for the plate, flexible modes are, additionally, considered for describing its structural deformations. The required modes shapes are determined in vacuum (“dry” mode superposition approach) through analytical expressions. The flexural rigidity of the plate, D, is optimized at a specific wave number using a real-coded genetic algorithm. Initially, results are compared with numerical results of other investigators for the case of two rigid concentric floating cylinders. Next, extended results are presented, focusing on the effect of D, including its optimum value, on various physical quantities describing the behaviour of both the cylinder and the plate. Contrary to the isolated cylinder, the presence of the plate introduces sharp peaks in the variation pattern of the drift force of the cylinder, bounded at specific wave numbers, where resonance of the seiche mode of water motion in the annular cavity or of specific flexible modes of the plate occurs. However, by reducing D to its optimum value, the cylinder’s drift force obtains practically zero values at the target wave number, due to an efficient improvement of the wave field in the annular cavity around the cylinder. Moreover, a great reduction of the drift force compared to the isolated cylinder is achieved in the subsequent high frequency range.     

Mean drift forces on an articulated column oscillating in a wave tank

An analytical solution is presented for calculating the regular wave induced respones of an articulated column in a wave tank. Extension of the procedure leads to calculation of second order mean drift forces and moments. Hydrodynamic interaction between a cylindrical column and the parallel walls of the tank is shown theoretically to be highly significant and experimental data are presented to corroborate this finding.     

Transient wind drift currents in a tidal inlet: Theoretical analysis of Ekman drift current and field experiments in Suonada,the Seto Inland Sea

Time-dependent wind drift currents in a basin with finite depth have been solved analytically in order to understand their fundamental behavior in coastal waters. The drift currents due to the land/sea breeze, as a typical example of time-dependent winds, have been examined with attention to the manner of their oscillation in their vertical profiles. The theoretical analysis indicates that the drift current due to the land/sea breeze might be amplified effectively around the southern part of Japan, where the oscillating period of the wind is near to the inertial period. The analysis of the physical process of the drift current reveals the following two important aspects: the Ekman boundary layer in a rotating frame is physically consistent with the Stokes boundary layer due to oscillating currents in an inertial frame, and so the inertial motion due to the wind is dispersed to the deeper level by the vertical viscosity in a rotating frame. The harmonic analysis was performed for the residual data after removal of the four main tidal constituents, M2, S2, K1 and O1, from the raw data observed in Suonada sound, the Seto Inland Sea. The feature of the analytically solved drift currents corresponded well to the observed picture. The vertical viscosity in this field has been estimated at 10⁻³ m²/s by adjusting the harmonically analytical result of the observed data to the vertical profile of the analytically solved drift current.     

Steady drift force on vertical cylinder - viscous vs. potential

The contribution of the steady drift force on a floating structure may arise from waves, wind and current. The component of the wave drift force may be due to the second-order diffraction theory or potential effect and may be due to the velocity squared force or viscous effect. The presence of current in waves increases the effect of the viscous force. The expressions for these terms for a vertical cylinder are derived and their relative importance is investigated. Plots are presented showing the regions where the viscous or potential drift force predominates. Experiments were conducted with both small and large diameter cylinders. The mean drift forces obtained in these tests are compared with the theory.     

Wave-induced drift of an elliptical surface film

This study investigates experimentally the drift velocity of an elliptical surface film advected by deep-water waves. Thin polyethylene sheets were used to simulate the inextensible surface film. The drift velocities were obtained by recording and analyzing a sequence of images captured using a video camera. The results show that the drift velocity increases with the longitudinal length of the polyethylene sheet until approximately 0.8 times the wavelength. Beyond that, further increment would not result in substantial increase in the drift velocity. The effect due to the normalized transverse width is found to be significant within a particular range. At large wave steepness, the drift velocity appears to be limited by the Stokes drift. A set of best-fit empirical equations based on the sigmoidal function is introduced for oil spill trajectory prediction.     

平直斜坡上破波带内质量输移流对污染物输移影响的数值研究

破波带内外都有质量输移流存在,其对破波带内污染物输移有怎样的影响,需要进一步深入研究。本文基于实验以及考虑质量输移流的对流扩散数学模型研究了平直斜坡上破波带内质量输移流对污染物输移影响。数学模型包括波浪模型、近岸流模型以及对流扩散模型。首先建立了破波带内污染物输移数学模型,其中波浪场基于波能守恒方程来计算,波导流场基于Longuet-Higgins提出的辐射应力模拟,污染物对流扩散方程中考虑了质量输移流的影响,并利用算例验证该数学模型。其次简要介绍了平直斜坡上破波带内污染物输移实验,并分析了污染物输移特性。连续投放污染物会形成污染带,本文分析了两种波况下不同时刻污染带与岸线夹角的变化,以及污染物在垂直岸线和沿岸线方向的输移速度,结果表明对两种波况来说在初始10-40s污染团向岸线方向输移速度分别约为0.05m/s、0.017m/s,之后速度分别减小为0.001m/s、0.011m/s。数值模拟结果与实验结果比较表明：考虑质量输移流的模拟结果与实验更为吻合。因而,通过实验以及数模研究表明破波带内质量输移流对破波带内污染物在垂直岸线方向的输移有重要影响,而对沿岸方向的输移则影响较小。     

Ekman drift and vortical structures

In this article, the authors study the influence of a constant wind on the displacement of a vortex. The well known Ekman current develops in the surface layer and is responsible for a transport perpendicular to the wind: the Ekman drift.An additional process is, however, evidenced, whose importance is as strong as the Ekman drift. There indeed exists a curl of the wind-driven acceleration along isopycnic surfaces when they are spatially variable (they enter and leave the depth where the wind stress acts), which generates potential vorticity anomalies. This diabatic effect is shown to generate potential vorticity anomalies which acts on the propagation of vortical waves and non linear vortices.It is shown that this effect drastically reduces the effect of the Ekman drift for linear waves and surface intensified vortices, while extending its effect to subsurface vortices. It also generates along wind propagation, whose sign depends on the vortex characteristics.     

Effect of Stokes drift on upper ocean mixing

Stokes drift is the main source of vertical vorticity in the ocean mixed layer. In the ways of Coriolis - Stokes forcing and Langmuir circulations, Stokes drift can substantially affect the whole mixed layer. A modified Mellor-Yamada 2. 5 level turbulence closure model is used to parameterize its effect on upper ocean mixing conventionally. Results show that comparing surface heating with wave breaking, Stokes drift plays the most important role in the entire ocean mixed layer, especially in the subsurface layer. As expected, Stokes drift elevates both the dissipation rate and the turbulence energy in the upper ocean mixing. Also, ilffluence of the surface heating, wave breaking and wind speed on Stokes drift is investigated respectively. Research shows that it is significant and important to assessing the Stokes drift into ocean mixed layer studying. The laboratory observations are supporting numerical experiments quantitatively.     

Iceberg drift affected by wave action

A mathematical model to predict iceberg drift pattern has been developed, which includes the wave drift force, in addition to the other conventional force components such as forces due to wind, current, Coriolis effect, and geostrophic effect. Trajectories of two icebergs were computed first with the wave effect then without the wave effect. All were compared with the observed results from the field. The model with the wave effect shows a significant improvement in the correlation.     

热力学效应及斯托克斯漂流对混合层影响的研究

本文通过理想化的外部强迫以及海洋站点实测数据驱动普林斯顿海洋模式来研究海洋热力学效应和斯托克斯漂流对上混合层数值模拟的影响。在Mellor-Yamada湍流闭合方案中,经常出现夏季海表面温度偏暖和混合层深度偏浅的模拟误差。实验表明,斯托克斯漂流在冬季和夏季均能增强湍流动能,加深混合层深度。这种效应可以改善夏季的模拟结果,但与观测数据相比,将增大冬季混合层深度的模拟误差。斯托克斯漂流可以通过增强湍动能来加深混合层深度。结果表明,将斯托克斯漂流与冷皮层和暖层对上部混合层的热效应相结合,可以正确地模拟混合层深度。在夏季,海洋冷皮层和暖层通过“阻挡结构”和双温跃层结构模拟出更真实的上混合层变化。在冬季,海洋热力学效应通过增强上层海洋层结平衡了斯托克斯漂流的影响,并且由斯托克斯漂流引起的过度混合被校正。     

On the determination of parameters of mesoscale eddies from remote sensing data

In the real case, the steady estimates of mesoscale eddy parameters can be obtained by integrating three types of remote data: measurement of kinematics of IR tracers, integral characteristics of scales, and local estimates of the SST partial derivatives. An appropriate analytical model of the eddy is selected based on the data of numerical modelling. A method for the estimation of the drift current velocity is suggested on the basis of the discrimination of the ageostrophic components of the tracer's translation.Translated by Mikhail M. Trufanov.     

基于FY-3/MERSI数据的北冰洋流冰自动提取与跟踪方法

北冰洋航路是未来全球航运的重点开拓领域,海冰运动对北冰洋航路开发有重要影响。本文利用风云三号卫星中分辨率光谱成像仪(FY-3/MERSI)数据的特点和优势,研究北冰洋流冰自动提取和运动跟踪的方法。首先在分析流冰灰度分布特征的基础上,提出分区域阈值分割与梯度差分相结合的方法实现块状流冰提取,然后根据块状流冰的多种几何特征匹配同名流冰并计算其运动速度。应用这种方法跟踪2011年6月弗雷姆海峡流冰运动,跟踪结果与美国国家冰雪数据中心提供的极地网格化日均海冰运动矢量整体趋势一致,验证了方法的有效性。这种方法获取各块流冰实际运动速度,可以有效弥补网格化海冰运动平均速度场分布和细节的不足,为北冰洋航路开发提供更详细的流冰运动信息。     

波浪辐射应力对海流模式影响的数值分析

将波浪辐射应力,特别是地转意义下的波浪辐射应力引入海流数值模式POM(princeton ocean model),在渤海海域进行了初步的数值研究。在目前的数值分析中仅考虑了波浪辐射应力的横向分量(也是最重要的分量)。在POM模式中引入非地转和地转意义下的波浪辐射应力两种方案,并与原模式直接运行(即不考虑波浪辐射应力)的结果进行比较。比较显示,波浪辐射应力,特别是地转意义下的波浪辐射应力对海流模式结果的影响不容忽略。在海浪场存在的条件下,由风应力和地转意义下浪致作用力共同作用产生的海流强度应比理论上Ekman漂流的强度大,尤其是在浪致作用力显著的表层,表层流将明显增强,且不会完全符合Ekman漂流理论的转向规律。     

Wind-wave generation of ocean current: on model identification

It is shown how stochastic models based on inertial fluctuations, forced by Stokes drift and wind stress, give apparently accurate predictions of sea surface current. A parameter estimation procedure that gives subjectively reasonable results may therefore also be found. However, objective model identification turns out to be difficult and an estimation model capable of following large-scale model errors is necessary for reasonably accurate parameter estimates. Such a model is proposed and simulation results are presented and discussed. In this mode the inertial oscillation damping, is easily overestimated and the Stokes drift effect is seen to be smaller than the wind stress effect. The latter appears to be uncertain