Generation mechanisms for capillary-gravity wind wave spectrum

We investigate the role of different physical mechanisms in the generation of the capillary-gravity wind wave spectrum. This spectrum is calculated by integrating a nonstationary kinetic equation until the solution becomes stready. The mechanisms of spectrum generation under consideration include three-wave interactions, viscous dissipation, energy influx from wind, nonlinear dissipation, and the generation of a parasitic capillary ripple. The three-wave interactions are taken into account as an integral of collisions without additional simplifications. It is shown that the three-wave interactions lead to solution instability if the kinetic equation takes into account only linear sources. To stabilize the solution, the kinetic equation should incorporate a nonlinear dissipation term, which in the range of short gravity waves corresponds to energy losses during wave breaking and microscale wave breaking. In the range of capillary waves, the account of nonlinear dissipation is also needed to ensure a realistic level of the spectrum for large wind velocities. For the steady-state spectrum, the role of three-wave interactions remains essential merely in the range of the minimum of phase velocity, where a trough on the curvature spectrum is formed. At the remaining intervals of the spectrum, the main contribution into the spectral energy balance is provided by the mechanisms of wave injection, nonlinear dissipation, and the generation of parasitic capillaries.     

Physical model of the spectrum of capillary-gravity waves

A model for the spectrum of capillary waves has been constructed. These waves are generated at the crests of short gravity waves and decay due to viscosity. Capillary wave generation leads to short gravity wave dissipation. Using empirical data on the short gravity wave dissipation spectrum, a relation for the capillary wave spectrum is derived from the equation of energy balance of capillary waves. The capillary wave spectrum is matched with the known Donelan-Pierson spectrum for short gravity waves. The obtained relation for the spectrum of wind-generated ripple is compared with the data of laboratory experiments. Translated by Vladimir A. Puchkin.     

高频表面波对定常Ekman流解的影响

基于Jenkins(1989)建立的包含Stokes漂流、风输入和波耗散影响的修正Ekman模型,采用Paskyabi等(2012)使用的推广的Donelan等(1987)中的谱和波耗散函数,并利用Paskyabi等(2012)中修正方法给出的包含高频波的风输入函数,在粘性不依赖于水深及粘性随深度线性变化的条件下,研究了包含高频毛细重力波的随机表面波对Stokes漂流和Song(2009)导出的波浪修正定常Ekman流解的影响。结果表明高频表面波使Stokes漂流在海表面剪切加强,对定常Ekamn流解的影响通常不能忽略,但对Ekman流场的角度偏转影响很小。最后,将考虑高频表面波尾谱影响所估算的定常Ekman流解与已有观测结果以及经典Ekman解进行了比对分析。     

The relationship between the amplitudinal characteristics of the high-frequency spectral components of wind-generated waves and the wind velocity over the sea

The relationship between the RMS amplitudes of the wind wave spectral components and the wind speed has been studied at ten frequencies in the band of 0.65–23 Hz. To measure the parameters of the high-frequenci waves, a resistance elevation wave gauge was operated, which was deployed in the Black See on an oceanographic platform near Katsively. The correlation between the wave amplitudes and the wind velocity at high frequencies of 5–23 Hz, corresponding to gravitation-capillary ripples, was found to reach a value of 0.8. At lower frequencies of 0.65–4.3 Hz, corresponding to short gravity waves, it dropped to 0.5–0.7. The response of spectral components to the wind speed variations in the gravity-capillary range is higher than in the range of short gravity waves. The results obtained differ from Phillips' idea about a saturated range for the frequency form of the spectrum of high-frequency gravity waves, since a linear dependence of the spectral amplitudes on the wind speed is established at a wind of force 1–8.Translated by Mikhail M. Trufanov.     

Rainfall effect on wind waves and the turbulence beneath air-sea interface

Rainfall effects on wind waves and turbulence are investigated through the laboratory experiments in a large wind-wave tank. It is found that the wind waves are damped as a whole at low wind speeds, but are enhanced at high wind speeds. This dual effect of rain on the wind waves increases with the increase of rain rate, while the influence of rainfall-area length is not observable. At the low wind speed, the corresponding turbulence in terms of the turbulent kinetic energy （TKE） dissipation rate is significantly enhanced by rain- fall as the waves are damped severely. At the high wind speed, the augment of the TKE dissipation rate is suppressed while the wind waves are enhanced simultaneously. In the field, however, rainfall usually hin- ders the development of waves. In order to explain this contradiction of rainfall effect on waves, a possibility about energy transfer from turbulence to waves in case of the spectral peak of waves overlapping the inertial subrange of turbulence is assumed. It can be applied to interpret the damping phenomenon of gas trans- fer velocity in the laboratory experiments, and the variation of the TKE dissipation rates near sea surface compared with the law of wall.     

On the intensification of decimeter-range wind waves in film slicks

The physical influence of the intensification of decimeter waves on a water surface covered by a surfactant film is proposed. The damping of a long wave caused by the loss of its energy on the modulation of short (centimeter) wind waves is analyzed. The damping coefficient of waves of decimeter-meter lengths is calculated, and this coefficient is shown to decrease in the presence of a surfactant film. The strong suppression of the spectrum of centimeter wind waves in a film slick is the physical factor responsible for such a decrease. Due to a decrease in the damping coefficient of decimeter-meter waves, their intensity in the slick increases. Within the framework of a model of the spectrally local energy balance of wind waves, the results of calculations satisfactorily agree with the experiment.     

Modulation of short wind waves by a long surface wave: a mechanism for feedback with an air flow

The paper concentrates on the evolution of a spectrum of short wind waves (SW) along the profile of a long surface wave (LW). Short wave spectral variations are considered in the relaxation approximation. The SW spectrum is modulated by the orbital velocities of long waves and by the variations of wind stress along the LW profile. The latter effect occurs due to wind flux perturbations induced by both the long wave proper and variations of the sea surface roughness induced by the SW modulations. To describe this effect, a feedback mechanism is introduces—the growth of energy of short waves results in the larger roughness of the sea surface, thereby contributing to the local wind stress, which facilitates, in turn, the growth of short waves. With moderate and strong winds being involved, this effect (aerodynamic feedback) is shown to be dominant in the short wave spectrum modulation. The mechanism becomes more efficient with intensification of the wind and decreasing of the long waves' frequency. Results of model calculations are in agreement with the known experimental data. Translated by Vladimir A. Puchkin.     

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。     

论风浪的局域结构──Ⅰ.风浪的局域结构与局域小波能谱

基于小波变换,引入了能刻画风浪局域结构的局域小波能谱。论述了风浪的整体结构与局域结构。指出了在不同时间尺度上,风浪具有不同的局域化特征。提出了风场演化过程中整体的共振在线性相互作用是否存在的质疑。     

Validation of the three-wave quasi-kinetic approximation for the spectral evolution in shallow water

This paper aims at validating the three-wave quasi-kinetic approximation for the spectral evolution of weakly nonlinear gravity waves in shallow water. The problem is investigated using a one-dimensional numerical wave propagation model, formulated in the spectral representation. This model includes both a nonlinear triad interactions term and a wave breaking dissipation term. Some numerical tests were carried out in order to show the importance of using the triad nonlinear term in wave propagation spectral models, particularly to describe both behavior of the spectral integral parameters and of the spectral shape evolution in shallow water depth. Furthermore; a comparison against different set of experimental observations was carried out. Comparing the numerical results with the experimental observations made it possible to show the modeling efficiency of the three-wave quasi-kinetic approximation.     

基于微结构图像的风生微尺度波频率谱初探

利用海面微结构光学测量装置实验获取到的微尺度波图像来给出风生微尺度波的波数谱,在此基础上利用频散关系建立微尺度波波数谱和频率谱之间的关系,最终得到微尺度波频率谱.对微尺度波的频率谱随频率变化的响应进行了研究,发现频率谱与频率的a次方成正比关系,a的值随风速的增加而增加,同一风速下a几乎为定值.     

The Role of Evolution Mechanisms in the Formation of a Wind-Wave Equilibrium Spectrum

The formation of a stationary (equilibrium) range in a wind-wave spectrum is investigated by numerical simulation. The equation of evolution of the wind-wave spectrum is solved using the exact calculation of the Hasselmann kinetic integral and involving various modifications of known parameterizations of the mechanisms of wave pumping by wind (In) and of wave dissipation (Dis). It is shown that it is these two mechanisms that are responsible for the shape of the stationary range of the wind-wave spectrum, whereas the nonlinear mechanism plays a stabilizing but subsidiary role. With an appropriate choice of mathematical representations for In and Dis, any known empirical shape of the stationary range of the spectrum can be obtained. During the calculations it is found that, for real wind waves, the known representations of In and Dis do not ensure the existence of the inertial interval required for Kolmogorov-type spectra formation due to the nonlinear interactions between waves.     

A coupled discrete wave model MRI-II

An ocean wind-wave prediction model MRI-II is developed on the basis of the energy balance equation which contains five energy transfer processes, namely, the input by the wind, the nonlinear transfer among the components of windsea by resonant wave-wave interactions, wave breaking, frictional dissipation and the effect of opposing winds. The nonlinear energy transfer is expressed implicitly together with the wind effect by Toba's one-parameter representation of windsea, but neither swell-swell nor swell-windsea resonant interactions are considered. Hypothetical assumptions are introduced to describe wave breaking effects. The numerical constant required in the assumptions of wave breaking is determined through trial test runs for a hindcast performed on the North-western Pacific Ocean. The significant wave height, one-dimensional wave spectrum and two-dimensional wave spectrum hindcasted by this new model are in more reasonable agreement with observations than those obtained with our old model MRI.     

A Model for Nonlinear Irregular Waves in Coastal Area

Based on the refraction-diffraction theory of irregular waves in the waters of slowly-varying cur-rents and depths,and the generation dissipation theory of wind wave,a model for nonlinear irregular wavesin coastal area is developed.In light of the specific conditions of coastal wave character and engineering ap-plication,a practical mathematical model for the nonlinear irregular waves is presented.with directional spec-trum in coastal area.Coast effect,refraction,whitecapping.bottom friction.current,wind and nonlinearaction are considered in this model.The numerical methods and schemes for wave refraction ray,energy con-servation of propagation,energy balance of the generation and dissipation of wind waves have been studied.Finally,the model is used for the directional wave spectrum computation in the Daya Bay.Compared withthe measured data with 956 wave bouys in the Daya Bay,the model results are in good agreement with themeasured results.     

Five-wave kinetic equation for surface gravity waves

A kinetic equation for the spectrum of random surface gravity waves, describing the spectral energy transfer over the spectrum, due to the combined effects of four- and five-wave weakly non-linear interactions has been developed. Equation kernels are given in the explicit form for a fluid of finite depth. It is noted that five-wave interactions break the wave conservation law inherent to the four-wave kinetic equation.Translated by Vladimir A. Puchkin.     

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.     

Measurements of the atmospheric turbulence in the coastal zone of the sea during weak wind from a mountainous coast

Results of measurements of the atmospheric turbulence in the layer between 1.5 and 21 m above sea level and the drag coefficient of the sea surface as the wind blows from a 4-km-long mountainous slope with a mean inclination of 11° are presented. The measurements of wind-speed profiles and its fluctuations at several levels, waves, and the main meteorological parameters were carried out in autumn 2005 and 2008 from a stationary platform located in the Black Sea at a distance of approximately 1 km from the southern coast of Crimea. It is shown that during weak synoptic wind a low-level wind jet develops at night over the sea with a maximum velocity up to 5–6 m/s at a level of approximately 6 m over the sea induced by the katabatic wind over the coastal slope. According to the approximate estimates, the horizontal scale of the low-level jet can reach a few tens of kilometers. This flow is characterized by the dissipation rate of the turbulence energy independent of height and low-frequency velocity fluctuations related to the gravity waves and advection of turbulence from the coast. It is shown that the lower part of the boundary layer (up to a height of 3 m) is adjusted to the sea-surface roughness. The dependencies of the drag coefficient on the wind speed or wave age are steadier than in the data for the open sea. However, the age of the waves is not a universal parameter at long and short fetches.     

Numerical simulation and preliminary analysis of typhoon waves during three typhoons in the Yellow Sea and East China Sea

In this study,typhoon waves generated during three typhoons(Damrey(1210),Fung-wong(1416),and Chan-hom(1509))in the Yellow Sea and East China Sea were simulated in a simulating waves nearshore(SWAN)model,and the wind forcing was constructed by combining reanalyzed wind data with a Holland typhoon wind model.Various parameters,such as the Holland fitting parameter(B)and the maximum wind radius?,were investigated in sensitivity experiments in the Holland model that affect the wind field construction.Six different formulations were considered and the parameters determined by comparing the simulated wind results with in-situ wind measurements.The key factors affecting wave growth and dissipation processes from deep to shallow waters were studied,including wind input,whitecapping,and bottom friction.Comparison with in-situ wave measurements suggested that the KOMEN scheme(wind input exponential growth and whitecapping energy dissipation)and the JONSWAP scheme(dissipation of bottom friction)resulted in good reproduction of the significant wave height of typhoon waves.A preliminary analysis of the wave characteristics in terms of wind-sea and swell wave revealed that swell waves dominated with the distance of R to the eye of the typhoon,while wind-sea prevailed in the outer region up to six to eight times the R values despite a clear misalignment between wind and waves.The results support the hypothesis that nonlinear wave-wave interactions may play a key role in the formation of wave characteristics.     

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.     

Experiment Study of Dynamics Response for Wind Turbine System of Floating Foundation

The floating foundation is designed to support a 1.5 MW wind turbine in 30 m water depth. With consideration of the viscous damping of foundation and heave plates, the amplitude-frequency response characteristics of the foundation are studied. By taking into account the elastic effect of blades and tower, the classic quasi-steady blade-element/momentum (BEM) theory is used to calculate the aerodynamic elastic loads. A coupled dynamic model of the turbine-foundation- mooring lines is established to calculate the motion response of floating foundation under Kaimal wind spectrum and regular wave by using the FAST codes. The model experiment is carried out to test damping characteristics and natural motion behaviors of the wind turbine system. The dynamics response is tested by considering only waves and the joint action of wind and waves. It is shown that the wind turbine system can avoid resonances under the action of wind and waves. In addition, the heave motion of the floating foundation is induced by waves and the surge motion is induced by wind. The action of wind and waves is of significance for pitch.