Variation of drag coefficient with wind wave development

Turbulent air flows over developing wind waves in the air-sea boundary layer are numerically simulated without considering wave breaking. Influences of wind waves on air flows are considered using a model of significant wave and surface roughness, with a formula proposed for calculating the surface roughness, k - epsilon model is adopted to simulate turbulent flows. The results of the drag coefficient and turbulence characteristics agree well with the observations.

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. (C) 2002 Elsevier Science Ltd. All rights reserved.

风浪频谱的成长方式研究

目前，风浪频谱因其在理论研究和实际应用中的重要作用，得到了相当广泛的研究。但由于客观现象的复杂性，迄今尚没有自理论上获得风浪频谱的方法。所以现在普遍采取的一种方法是：先假定海浪可由某种现有的谱形来描述，然后用相关方法研究其中的参量，以满足理论研究和工程应用方面的需求。在以往研究中，主要依靠现场观测、数值模拟等手段得出的谱参量与风场要素的经验或半理论半经验关系，此类方法对观测数据的依赖较大，且缺乏普适性。为解决上述问题，本文基于侯一筠、文圣常等提出的三参量风浪频谱，在谱参量的统计研究中，建立受动力学原理支配的控制模型，给出受动力学方程控制的谱参量（谱宽度 、谱的零阶矩 、谱的峰频率 ）随风场要素（风区）的成长关系。将本文的结果与先前得到经验关系进行比较，并用实测数据进行检验，结果表明： 如（图3、图9和图10）所示，谱参量在风浪成长的初期，随风区迅速变化；随着风浪的不断成长，其随风区的变化趋势也逐渐放缓；直到风浪达到充分成长，谱参量亦不再变化。这一描述，符合风浪发展的客观规律。此外，通过所选的10组实测数据的验证，亦可证明本文提出的结果与实际海浪的符合程度比其它现有关系更好。可见，本文将动力学原理引入风浪频谱的研究，建立的谱参量随风区的变化关系与先前的经验公式相比更加合理，且普适性更强。 本文给出了波陡、波龄与谱宽度的简化形式，该形式与先前的结果相比，更加直观的描述了波陡、波龄与谱宽度的关系，并且可以更加简便的应用于相关理论推导。文中从波浪成长的物理本质出发，得出新的受风场要素控制的谱的零阶矩和谱的峰频率之间的关系，阐明了先前的各种经验关系是新关系在取不同风区值时的特例。因此，视零阶矩与峰频率的关系随无因次风区变化更为合理，这是对传统结果的一个有力改进。 此外，本文基于已得到的谱参量随风区的变化关系，对四种形式的三参量风浪频谱作了深入的研究，得到其随风区的成长关系。在此基础上，直观地描述了风浪频谱成长过程中的超射现象在初期的发生以及在后期的消失。经过实测数据的验证，证明了三参量谱谱形的合理性，同时也进一步证明了谱参量随风区变化关系的正确性。

Influence of Wind and Grain Size on Migration of Asymmetric Sand Waves

Large parts of shallow seas are covered by regular seabed patterns and sand wave is one kind of these patterns. The instability of the sedimentary structures may hazard pipelines and the foundations of offshore structures. In the last decade or so, it's a focus for engineers to investigate the movement mechanism of sand waves. Previous theoretical studies of the subject have developed a general model to predict the growth and migration of sand waves, which is based on the two-dimensional vertical shallow water equations and the bed-form deformation equations. Although the relation between wave-current flow and sand bed deformation has been established, the topographic influence has not been considered in the model. In this paper some special patterns, which are asymmetric and close to the reality, are represent as the perturbed seabed and the evolution of sand waves is calculated. The combination of a steady flow induced by wind and a sinusoidal tidal flow is considered as the basic flow. Finally the relations of some parameters (grain size, etc.) and sand waves' growth and migration are discussed, and the growth rate and migration speeds of asymmetric sand waves are carried out.

Effect of low-frequency Rossby wave on thermal structure of the upper southwestern tropical Indian Ocean

We investigate the influence of low-frequency Rossby waves on the thermal structure of the upper southwestern tropical Indian Ocean (SWTIO) using Argo profiles, satellite altimetric data, sea surface temperature, wind field data and the theory of linear vertical normal mode decomposition. Our results show that the SWTIO is generally dominated by the first baroclinic mode motion. As strong downwelling Rossby waves reach the SWTIO, the contribution of the second baroclinic mode motion in this region can be increased mainly because of the reduction in the vertical stratification of the upper layer above thermocline, and the enhancement in the vertical stratification of the lower layer under thermocline also contributes to it. The vertical displacement of each isothermal is enlarged and the thermal structure of the upper level is modulated, which is indicative of strong vertical mixing. However, the cold Rossby waves increase the vertical stratification of the upper level, restricting the variability related to the second baroclinic mode. On the other hand, during decaying phase of warm Rossby waves, Ekman upwelling and advection processes associated with the surface cyclonic wind circulation can restrain the downwelling processes, carrying the relatively colder water to the near-surface, which results in an out-of-phase phenomenon between sea surface temperature anomaly (SSTA) and sea surface height anomaly (SSHA) in the SWTIO.

Responses of summertime extreme wave heights to local climate variations in the East China Sea

We detected the responses of summertime extreme wave heights (H-top10, average of the highest 10% of significant wave heights in June, July and August) to local climate variations in the East China Sea by applying an empirical orthogonal function analysis to Htop10 derived from the WAVEWATCH- III wave model driven by 6 hourly sea surface wind fields from ERA-40 reanalysis over the period 1958-2002. Decreases in H-top10 in the northern East China Sea ( Yellow Sea) correspond to attenuation of the East Asian Summer Monsoon, while increases in the south are primarily due to enhancement of tropical cyclone activities in the western North Pacific.

A new model to estimate significant wave heights with ERS-1/2 scatterometer data

A new model is proposed to estimate the significant wave heights with ERS-1/2 scatterometer data. The results show that the relationship between wave parameters and radar backscattering cross section is similar to that between wind and the radar backscattering cross section. Therefore, the relationship between significant wave height and the radar backscattering cross section is established with a neural network algorithm, which is, if the average wave period is <= 7s, the root mean square of significant wave height retrieved from ERS-1/2 data is 0.51 m, or 0.72 m if it is >7s otherwise.

Wave parameters retrieved from QuikSCAT data

A new algorithm is proposed to estimate significant wave height from QuikSCAT scatterometer data. The results show that the relationship between wave parameters and the radar backscattering cross section is similar to that between wind and the radar backscattering cross section. Therefore, the relationship between significant wave height and the radar backscattering cross section is established with a neural network algorithm. If the average wave period is less than or equal to 7 s, the root mean square errors of the significant wave height retrieved from QuikSCAT data are 0.58 m for HH polarization (HH-pol) and 0.60 m for VV polarization (VV-pol). If the average wave period is greater than 7 s, the root mean square errors of the significant wave height retrieved from QuikSCAT data are 0.83 m (HH-pol) and 1.10 m (VV-pol), respectively.

A microwave emissivity model of sea surface under wave breaking

With the effective medium approximation theory of composites, a remedial model is proposed for estimating the microwave emissivity of sea surface under wave breaking driven by strong wind on the basis of an empirical model given by Pandey and Kakar. In our model, the effects of the shapes of seawater droplets and the thickness of whitecap layer (i.e. a composite layer of air and sea water droplets) over the sea surface on the microwave emissivity are investigated by calculating the effective dielectric constant of whitecaps layer. The wind speed is included in our model, and the responses of water droplets shapes, such as sphere and ellipsoid, to the emissivity are also discussed at different microwave frequencies. The model is in good agreement with the experimental data of microwave emissivity of sea surface at microwave frequencies of 6.6, 10.7 and 37GHz.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

A parametric method of retrieving ocean wave spectra from synthetic aperture radar images

A parametric method that extracts the ocean wave directional spectra from synthetic aperture radar (SAR) image is presented. The 180 degrees ambiguity of SAR image and the loss of information beyond the azimuthal cutoff can be overcome with this method. The ocean wave spectra can be obtained from SAR image directly by using iteration inversion mapping method with forward nonlinear mapping. Some numerical experiments have been made by using ERS-1 satellite SAR imagette data. The ocean wave direction retrieved from SAR imagette data is in agreement with the wind direction from the scatterometer data.

Application of effective medium approximation theory to ocean remote sensing under wave breaking

Based on the effective medium approximation theory of composites, the empirical model proposed by Pandey and Kakar is remedied to investigate the microwave emissivity of sea surface under wave breaking driven by strong wind. In the improved model, the effects of seawater bubbles, droplets and difference in temperature of air and sea interface (DTAS) on the emissivity of sea surface covered by whitecaps are discussed. The model results indicate that the effective emissivity of sea surface increases with DTAS increasing, and the impacts of bubble structures and thickness of whitecaps layer on the emissivity are included in the model by introducing the effective dielectric constant of whitecaps layer. Moreover, a good agreement is obtained by comparing the model results with the Rose's experimental data.

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. (c) 2006 Elsevier Ltd. All rights reserved.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.