A mathematical representation of random gravity waves in the ocean

We give a mathematical representation of random ocean surface waves in the gravity-wave regime. The so-called random gravity waves are treated as an asymptotic phenomenon when the wind pressure acting on the surface and the dissipation become negligible. We adopt a phenomenological model for the wind pressure such that it excites a surface consisting of wind-driven sea and swell. Starting from the Navier-Stokes equations, we derive a general system of the first-order perturbation equations governing the surface waves, and solve them with this wind pressure as the excitation. The resulting solution is decomposed into a part which is asymptotically dominant and another which is asymptotically negligible. The former consists of two groups: one which is a sum of superpositions of uncorrelated plane waves having approximate dispersion relations and the other a sum of random plane waves with their wavenumbers and frequencies approximately satisfying the dispersion relation. They correspond to the dominant parts of the wind-driven sea and the swell, respectively. Finally, we derive a limiting form of the directional-frequency spectrum in the gravity-wave regime.     

Air-Sea Interactions under the Existence of Opposing Swell

Data of a comprehensive laboratory study on the coexistent system of wind waves and opposing swell (Mitsuyasu and Yoshida, 1989) have been reanalyzed to clarify the air-sea interaction phenomena under the coexistence of wind waves and swell. It is shown that the magnitude of the decay rate of swell due to an opposing wind is almost the same as that of the growth rate of swell caused by a following wind, as measured by Mitsuyasu and Honda (1982). The decay rate is much smaller than that obtained recently by Peirson et al. (2003), but the reason for the disagreement is not clear at present. The effect of an opposing swell on wind waves is very different from that of a following swell; wind waves are intensified by an opposing swell while they are attenuated by a following one. The phenomenon contradicts the model of Phillips and Banner (1974), but the reason for this is not clear at this time. The high-frequency spectrum of wind waves shows a small increase of the spectral density. Wind shear stress increases a little due to the effect of opposing swell. The intensification of wind waves by opposing swell and the small increase of the spectral density in a high-frequency region can be attributed to the increase of wind shear stress. Such organized phenomena lead to the conclusion that the hypothesis of local equilibrium for pure wind waves (Toba, 1972) can also be satisfied for wind waves that coexist with opposing swell. The recent finding of Hanson and Phillips (1999) can be explained by this mechanism.     

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.     

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。     

Studies of TLP dynamic response under wind, waves and current

Investigated is the coupled response of a tension leg platform (TLP) for random waves. Inferred are the mass matrix, coupling stiffness matrix, damping matrix in the vibration differential equation and external load of TLP in moving coordinating system. Infinitesimal method is applied to divide columns and pontoons into small parts. Time domain motion equation is solved by Runge-Kutta integration scheme. Jonswap spectrum is simulated in the random wave, current is simulated by linear interpolation, and NPD spectrum is applied as wind spectrum. The Monte Carlo method is used to simulate random waves and fluctuated wind. Coupling dynamic response, change of tendon tension and riser tension in different sea conditions are analyzed by power spectral density (PSD). The influence of approach angle on dynamic response of TLP and tendon tension is compared.     

Influence of the type of sea waves on the backscattered radar cross section at medium incidence angles

We consider the influence of the sea surface state on the backscattered radar cross section and the accuracy of the wind speed retrieval from the scatterometer data. We used a joint set of radars and buoys to determine the type of sea waves. Three types of sea waves were distinguished: developing wind waves, fully developed wind waves, and mixed sea. It is shown that the retrieval error of the near surface wind speed using a one-parameter algorithm is minimal in the case of fully developed wind waves. We compared these data with the results of radio-altimeter data analysis and showed that in both cases underestimation of the retrieval wind speed exists for developing wind waves and overestimation occurs for mixed sea. A variety of swell parameters (length of the dominating wave, swell height, swell age) significantly influence the backscattered radar cross section, leading to a growth in the mean square error of the retrieved wind speed during vertical sounding (radio-altimeter data), and only slightly influence the mean square error of the scatterometer data (medium incidence angles). It is necessary to include the information about the parameters of sea waves in the algorithms and take into account the regional wave properties to increase the accuracy of wind speed retrieval.     

Typical fields of wind waves and swells in the Northern Pacific

Using all of the atmospheric patterns classified by Polyakova A.M., we accomplished calculations of the surface wind fields over the North Pacific for wind waves observable 6, 12, 18, and 24 hours after a storm and the swell waves observable 24, 48, and 72 hours after a storm. The considerable extension of the ocean creates quasi-unlimited speeding up of the wind waves during continuous strong winds (over 20 meters per second). This determines the presence of wide areas of highly developed wind waves with a 5% probability that the wave heights will exceed the 10–12 meter estimates. The swell waves decay faster: their height reduces by half in 24 h, while, in 72 h, they achieve the background level of the ocean’s swell waves.     

海浪双峰方向分布的一种物理解释

用 １８个波高计组成的直径为 ４０ｃｍ的圆形阵列在大型风浪槽内系统地测量了风浪和涌浪方向谱。用两种分辨力较高的方向谱估计方法最大似然法（ＭＬＭ）和贝叶斯方法（ＢＤＭ）分析的结果表明：风浪高频域出现的依赖于估计方法的双峰方向分布是一种物理假象;在较成长的涌浪低频域,得到跟传播方向对称、两峰间隔大约６０°－９０°非常规则的双峰方向分布,它跟频率和涌浪的成长状态有关,而跟估计方法无关,这种现象可以用非线性波－波相互作用过弱,在不同方向之间不能有效传递能量来解释。     

划分风浪与涌浪的一个新判据——海浪成份及其在南海的应用

使用风浪谱的零阶矩（Ｍ０ｗ）和混合浪谱的零阶矩（Ｍ０）定义的混合浪能量成份因子，作为划分风浪与涌浪的一个新判据，给出了混合浪能量成份因子和混合浪波高成份因子的计算公式。根据混合浪波高成份因子的计算公式，使用ＧＥＯＳＡＴ卫星高度计５０个重复周期的资料，计算了南海海域波高成份因子及其月变化规律，资料的样本长度是１个月。计算结果表明：该海域的混合浪波高成份因子具有明显的时间变化规律。海浪在１１、１２、１、２月份和５、６、７、８月份，混合浪波高成份因子的概率密度分布形状高而窄，而在３、４月份和９、１０月份，混合浪波高成份因子的概率密度分布形状低而宽。在１１、１２、１和２月份，最可能出现的混合浪波高成份因子等于１．２，有７０％的波浪含有涌浪成份，在整个海域涌浪占主导地位。在５、６、７月份，最可能出现的混合浪波高成份因子位于０．３～０．４之间，有６０％的波浪只含有风浪成份，在整个海域风浪占主导地位。其它月份，最可能出现的混合浪波高成份因子介于冬夏两季之间，亦即风浪和涌浪出现的概率几乎是相同的     

Study of sea waves under the action of deep cyclones

Data from full-scale observations of the coastal zone during the passage of deep cyclones are analyzed. The time interval when three deep cyclones acted in the region of observations was chosen. The generation of long-wave processes during cyclones with different meteorological parameters and at different directions of approaching the shore was of interest. Data from the Management of Hydrometeorological Service were invoked for compiling maps of weather conditions, and meteorological data obtained from digital meteorological stations, as well as the spectral characteristics of oscillations of the hydrostatic pressure level at observational points, were analyzed. The frequencies of excitation of long-wave oscillations caused by cyclones were determined. Particular attention was paid to the range of periods of swell and wind waves. It was detected that swell waves are excited during the approach of cyclones at uncharacteristic frequencies with their subsequent displacement into their own frequency range.     

Directional energy distribution of wind waves

Two-dimensional ocean wave spectrum developing under the atmospheric surface pressure fluctuations is linearly correlated with that of wind pressure itself, so that angular distribution of energy of ocean surface waves can be determined by directional properties of surface pressure fluctuations with the same frequency to the surface wave.From empirically determined spectral formula of the atmospheric surface pressure fluctuations the coefficients of Fourier series expanded around mean direction of wind are analytically integrated, from which r.m.s. angular distribution, spectral peakedness and long-crestedness are calculated, compared with previously proposed empirical formulae and observations carried out by ultrasonic current meter.     

粗糙度与风浪特征量关系的研究

在实验室风浪槽中观测风浪和风速,研究粗糙度与波面特征量的关系,发现风浪谱宽度增加,粗糙度增大。在窄谱时,粗糙度随谱宽的增加变化不明显,当波陡降低,粗糙度降低;在宽谱时,当谱宽度增加,即使波陡降低,粗糙度仍可增大。这一结果表明,波陡不足以完全决定粗糙度。当风浪波龄增加,粗糙度呈下降趋势,但由于谱宽度对粗糙度的影响,当波龄增加,部分波浪可有较大的粗糙度。由于这一因素,在粗糙度与波龄关系的观测结果中,数据点的散落不完全由观测误差造成。     

Water-temperature effect on the spectral density of wind gravity waves and on sea-surface roughness

The results of hourly measurements of sea roughness and hydrometeorological parameters, which were automatically taken from special buoys over a long period of time, were used. These buoys were located in the open regions of both the Atlantic and Pacific oceans in different climatic zones; the mean water-surface temperature around the buoys varies from 1–3°C to 26–28°C. In addition to measurement results, the tables contain data on the spectral density of sea roughness for a wide range of frequencies. An analysis of these data, which was made for a short-wave region of the wind-wave spectrum, for the first time revealed a noticeable watertemperature dependence of the spectral density of wind waves within the frequency range 0.30–0.40 Hz, which corresponds to wave lengths of 9-4 m. The presence of such dependence is explained by a rapid temperature change in kinematic sea-water viscosity. Earlier, we indicated the temperature dependence of only very short spectral components that relate to a centimetric wavelength range. The statistical significance of the watertemperature effect on the spectral density of waves of the indicated frequency is supported by the results of a variance analysis. Temperature variations in the parameter of sea-surface roughness, which is determined, first of all, by the energy of the spectral shortwave region, are estimated. Altimetry is the basic method which is used in remotely determining the velocity of near-water wind. This method allows one to obtain records of deviations of the sea surface from the geoid surface and to calculate (on the basis of these records) the spectral density of wave components of almost any frequency. It is known that the wave-spectrum components in the region of low frequencies are almost always affected by ripple. Consequently, the energy of these components is determined not only by wind forcing, and only the components in the range of frequencies exceeding approximately 0.3 Hz are purely windy. Therefore, using the results of sea-surface altimetry in order to determine the velocity of near-water wind, one should use the spectral densities of wave components in this frequency region. The water-temperature dependence of the spectral density of short wind waves is manifested only in a certain frequency interval, which supports this recommendation.     

Simulation of Random Waves and Associated Laminar Bottom Shear Stresses

This work presents a new approach for simulating the random waves in viscous fluids and the associated bottom shear stresses. By generating the incident random waves in a numerical wave flume and solving the unsteady two-dimensional Navier-Stokes equations and the fully nonlinear free surface boundaiy conditions for the fluid flows in the flume, the viscous flows and laminar bottom shear stresses induced by random waves axe determined. The deterministic spectral amplitude method implemented by use of the fast Fourier transform algorithm was adopted to generate the incident random waves. The accuracy of the numerical scheme is confirmed by comparing the predicted wave spectrum with the target spectrum and by comparing the nanlerical transfer function between the shear stress and the surface elevation with the theoretical transfer function. The maximum bottom shear stress caused by random waves, computed by this wave model, is compared with that obtained by Myrhaug＇ s model （1995）. The transfer function method is also employed to determine the maximum shear stress, and is proved accurate.     

Statistical properties of microwave backscattering from laboratory wind-wave surfaces

The microwave backscattering from wind-wave surfaces is observed in a windwave tunnel under various conditions of the wind and wind waves, and its statistical features are investigated. The dependence of the backscattered power on the wind speed and the incident angle shows similar features to those predicted by models proposed previously. However, the dependence of the backscattered power on the incident angles also corresponds to the asymmetrical feature of the wind-wave surfaces with respect to the wind direction. The spectral analyses of time series of the backscattered intensity show that the propagating speed of fine structures of the wind-wave surface contributing to the backscattering at large incident angles does not coincide with the phase speed of the freely propagating Braggwaves. Atupwind incidence, the surface structures of wind waves contributing to the backscattering propagates with the dominant waves at their phase speed. This result is inconsistent with the two-scale model in which the Bragg waves are simply superimposed on longer waves, but is consistent with the results of optical observation by Ebuchiet al. (1987). At downwind incidence, the propagating speed is slower than the phase speed of the dominant waves.     

Seasonal barotropic sea surface height fluctuation in relation to regional ocean mass variation

A consistency between seasonal fluctuation of actual sea surface height (SSH) and those caused by mass and density variations in gyre-scale regions is examined. The SSH obtained from satellite altimetry (altimetric SSH) is adopted as the actual SSH. SSH caused by mass variation (mass-related SSH) is simulated using a barotropic global ocean model forced by water flux, wind stress and surface pressure. SSH caused by density variation (steric SSH) is calculated from water density profile, i.e. temperature and salinity profiles. The model SSH well represents mass-related SSH for gyre-scale regional means, and seasonal fluctuation of the altimetric SSH corrected for the model SSH is similar to that of steric SSH above a pressure level larger than 300 dbar. The results indicate that the mass-related SSH does not much respond to the baroclinic adjustment to the seasonally varying wind stress curl. The mass-related SSH forced by wind stress and surface pressure should be accounted for regional evaluation, though it is not necessary for global mean evaluation. Detection of steric SSH from altimetric SSH would be useful for assimilation approaches in which the altimetric SSH is treated as the variable reflecting subsurface temperature and salinity.     

浙江东矶列岛海域实测波要素及典型台风浪特征分析

利用东矶列岛海域一年实测波浪资料,统计分析波要素特征,以台风“利奇马”为例,分析台风浪演变过程。结果表明：研究海域年平均有效波高0.88 m,年平均周期4.3 s,年最大波高8.67 m出现在夏季台风“利奇马”影响时。研究海域以轻浪为主,其次是小浪和中浪;常浪向为ESE,次常浪向为E和SE;强浪向为SSE,次强浪向为SE。波浪平均持续时间和波高之间符合指数衰减关系。台风“利奇马”影响期间,最大谱峰56.20 m²/Hz,台风浪谱型以双峰谱为主,台风浪类型经历了涌浪—混合浪—风浪—混合浪—涌浪这一演变过程。     

Second-Order Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation,a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper.For special case of slope angle β=π/2,this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline.Interactions between two edge waves including progressive,standing and partially reflected standing waves are also discussed.The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given.The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated,and the corresponding theoretical autocorrelation and spectral density functions of the first and the second orders are derived.The boundary conditions for the determination of the parameters of short edge wave are suggested,that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory.Finally some computation results are demonstrated.     

Spectral characteristics of Rossby waves in the Northwestern Pacific based on satellite altimetry

Using satellite altimetry measurement data for 1993–2013, we study the spectral characteristics of Rossby waves in the Northwestern Pacific (25°–50° N, 140°–180° E). For each latitude degree, we draw integral plots of spectral power density calculated with a two-dimensional Fourier transform (2D-FFT). We compare the dispersion equations of Rossby waves calculated from the WKB-approximation and an approximation of a two-layer ocean model with the empirical velocities determined by the slope of isopleths by the Radon method; also, we compare the dispersion equations with the spectral distributions of level variations. It is shown that the main energy of Rossby waves in the Northwestern Pacific corresponds to the first baroclinic mode. At almost all latitudes, there is good agreement between the empirical phase velocities calculated by isopleths by the Radon method and the theoretical values; also, the spectral peaks correspond to graphs of the dispersion equations for the first baroclinic mode Rossby waves, except for the Kuroshio region, where some peaks correspond to the second mode.     

Second-Oorder Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a constant plane sloping bottom is presented in this paper. For special case of slope angle b=p/2, this solution can be reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves were also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves were also discussed. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoretical autocorrelation and spectral density functions of the first and second orders are derived. The boundary conditions for the determining determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.