The damping of a group of sea waves

The signals from a wave probe, a buoy-mounted sensor at the water surface, and a three-component sonic anemometer were recorded during the passage of a discrete group of waves which were travelling against a light wind. Cross spectra between the wave signals and the pressure and sonic anemometer signals were obtained and are interpreted.Bedford Institute contribution No. 226.This work forms part of a Ph.D. dissertation at the Institute of Oceanography, University of British Columbia.     

Airborne radar measurements of ocean wave spectra and wind speed during the grand banks ERS‐1 SAR wave experiment

Abstract

Measurements of ocean directional wave spectra, significant wave height, and wind speed over the Grand Banks of Newfoundland were made using the combined capabilities of the radar ocean wave spectrometer (ROWS) and scanning radar altimeter (SRA). The instruments were flown aboard the NASA P‐3A aircraft in support of the Grand Banks ERS‐1 Synthetic Aperture Radar (SAR) Wave Experiment. The NASA sensors use proven techniques, which differ greatly from SAR, for estimating the directional long‐wave spectrum; thus they provide a unique set of measurements for use in evaluating SAR performance. ROWS and SRA data are combined with spectra from the SAR aboard the Canadian Centre for Remote Sensing (CCRS) CV‐580 aircraft, the first‐generation Canadian Spectral Ocean Wave Model (CSOWM) hindcast, and other available in situ measurements to assess the ERS‐1 SAR's ability to correctly resolve wave field components along a 200‐ to 300‐km flight line for four separate satellite passes. Given the complex seas present on the Grand Banks, the complementary nature of viewing the sea spectrum from the perspectives of multiple sensors and a wave prediction model is apparent. The data intercomparisons show the ERS‐1 SAR to be meeting the expected goals for measuring swell, but the data also show evidence of this remote sensor's inability to detect the shorter waves travelling in the azimuth or along‐track direction. Example SAR spectra simulations are made using a non‐linear forward transform with ROWS measurements as input. Additionally, surface wind and wave height estimates made using the ROWS altimeter channel are presented. These data demonstrate the utility of operating the system in its new combined altimeter and spectrometer configuration.     

Variation of the spectrum of wind ripple on coastal waters under the action of internal waves

The mechanism of flattening of surface wind waves in the centimetre wavelength range under the action of internal waves and in the presence of surfactants is considered. It is shown that internal waves give rise to perturbations of surfactant concentration proportional to the orbital velocities of wave particles. Accordingly, the damping coefficient of centimetre wavelength ripples is also modulated. Evolution of the wind wave spectrum is described by the energy balance equation. In the right-hand side of the equation the Phillips excitation mechanism, the Miles mechanism with a nonlinear spectrum limitation, and the dissipation caused by a surface-active film are taken into account. Assuming that the energy source and sink balance of the wind wave spectrum over the centimetre wavelength range is local, relative spectra (contrasts) for the case of gentle breeze are calculated. It is shown that the spectral components of ripples in the slicks can be order less than the uperturbed spectrum values.     

切变流中的CISK机制与惯性重力波

利用板对称，有切变的大气动力学方程组，由行波法导出非线性微分方程，通过非线性稳定性理论讨论方程的稳定性，求解了ＫＤＶ方程，并讨论了线性ＣＩＳＫ，非线性ＣＩＳＫ，惯性稳定度参数和大气风速垂切变对惯性重力孤波强度和宽度的影响，目的早通过了解影响惯性重力孤波发展的因子，更深入地理解低纬中尺度天气系统形成和发展的过程。     

DIAGNOSIS OF LOW FREQUENCY COMPONENT OF ENSO VARIABILITY-PART Ⅰ:GLOBAL-SCALE DYNAMIC CHARACTERISTICS OF THE COMPONENT

Composite investigation is performed of global dynamic characteristics of 3-4-year period low-frequency oscillation in ENSO variability of air-sea coupling in the context of monthly mean wind and SSTA.Evidence suggests that the horizontal(vertical) anomaly circulation at tropical latitudes (equatorial)exhibits their evolution to be,in substance,a kind of low-frequency wave slowly travelling eastward,featured by wave number 2 moving along the equator and zonal wind swiftly decaying off the equator in relation to divergence/convergence:the time that the low-frequency wave takes to move around the equator in its halfway is precisely the period of the ENSO low-frequency component (LFC) (approximately 4 years);the ocean also displays corresponding response to the component.     

THE CISK MECHANISM AND THE INERTIAL GRAVITATIONAL WAVES IN SHEAR FLOW

By using the symmetric equations of atmospheric dynamics in y-z plane with vertical and horizontal shear of wind, the nonlinear ordinary differential equation is derived with the method of travelling wave.Its stability is discussed by using the theory of nonlinear stability and the KDV equation is solved. The effects of linear CISK, nonlinear CISK, inertial stability and vertical shear of wind on the amplitude and the width of isolated inertial gravitational wave are discussed. In order to understand deeply the formation and development of meso-scale synoptic systems, such as the squall line, MCC, the cold surge of Asia high and typhoon, the factors of development of the isolated inertial gravity wave are analysed.     

Experimental study of nonlinear wave—wave interaction and white-cap dissipation of wind-generated waves

An experimental scheme was designed to obtain laboratory-scale verification of Hasselmann's nonlinear wave—wave interaction and white-cap dissipation theories. Water wave height and fluctuating air pressure were measured simultaneously in a fixed reference frame as a function of fetch in the Stanford Wind, Water-Wave Research Facility under the conditions of a steady wind and a stationary wave spectrum. All the data were obtained 5 mm above the highest point of the wind waves for five stations (3 m apart on average) and at three wind speeds (7.1, 8.0 and 8.9 m/sec). The wave height and fluctuating pressure were measured by a capacitance wave-height gauge and a crystal pressure transducer, respectively.Based on the experimental results, Hasselmann's nonlinear wave—wave interaction theory appears to be valid. Barnett's approximate parametric equation for calculating the energy transfer of nonlinear wave—wave interaction and Hasselmann's white-capping dissipation model were also verified and appeared to be applicable in the relatively low and intermediate frequency region of a wave spectrum for a normalized fetch range of 100–500. Based on the results of an overall energy balance in a gravity wind-wave spectrum, the nonlinear wave—wave interaction mechanism is shown to play a dominant role in the energy transfer processes after the wave spectrum is generated.     

斜压切变基流中横波型扰动的特征波动──Ⅰ:谱点分析

文中对谱点的分布作了定性分析和数值计算。结果发现：当基流存在切变时,无论是重力惯性波还是涡旋波都存在连续谱。在通常的环境下,对天气尺度的扰动,3支波动的连续谱不重叠,3支波动明显可分;当扰动尺度小于临界波长l0时,可出现涡旋波和一支重力惯性波的两波连续谱区的重叠,当扰动尺度小于l0／2时,可出现涡旋波和一对重力惯性波的三波连续谱区的重叠,此时两种波动不可分。当出现重叠谱时,若出现不稳定扰动,其频率的实部落在重叠谱区。     

An extended Miles' theory for wave generation by wind

Miles' inviscid theory of surface wave generation by wind is (a) modified by replacing the logarithmic shear velocity profile with one which applies right down to the wave surface and which exhibits an explicit dependence on the roughness of the surface, and (b) extended to include the effects of the interaction of wave with air flow turbulence by considering the wave-modified mean flow as the mean of the actual turbulent air flow over water waves and using this in a mixing-length model.The surface pressure is shown to depend significantly on the flow conditions being aerodynamically smooth or rough. Its component in phase with the surface elevation is practically unaffected by the wave-turbulence interaction. However, such interaction tends to increase the rate of energy input ß from wind to waves travelling in the same direction, e.g., the increase is 2gk ² for aerodynamically rough flow, where gk is the Von Karman constant. It also provides damping of waves in an adverse wind which can be about 10% of the growth rate in a favourable wind.     

Study on Atmospheric Travelling Wave Solutions and Review of Its Present Developments

The scientific achievements of travelling waves in a barotropic atmosphere are introduced, including i) the existence conditions of periodic solutions (wavetrain solutions) and solitary wave solutions (pulse solutions), together with the solution finding methods and a series of related problems, ii) seeking solutions of monotonous wave (wave front) and of nonmonotonous travelling wave (oscillatory wave) by using phase plane shooting technique and hi) progress in the study of travelling wave solution at home and abroad. The investigation of travelling wave solutions in recent years has been found in mathematics, physics, chemistry, biology and other sciences. Over the past decade the problem has been the subject of much interest and become an important area of research. So it is no doubt of great significance to investigate the travelling wave solutions and thereby explain phenomena of weather.     

热带气候风场的傅立叶分析方案及试验

给出了热带气候风场V-的一个傅立叶分析方案。对热带（30°S～30°N）区域1月850hPa气候风场V-的试分析结果表明：V-具有低维、低阶特征,｜m｜=0,4的9个低波数分量共拟合了V-模方的92.4%。0波分量V-0最重要,拟合了V-模方的56.4%,它主要给出了纬向平均信风带结构特征。定常波（V-＊）拟合了V-模方的43.6%,也具有低维、低阶特征,｜m｜=1,4的8个低波数分量拟合了V-＊模方的82.6%,由它们构成的定常波合成风场V-4＊与V-＊的相似系数高达0.909,它给出了V-＊的主要环流系统。因此,傅立叶分析方法是分析热带气候风场的一种有效方法。     

Spectral differences between a single gravity shear wave and a continuous superposition of modes

A continuous superposition of gravity waves, propagating upward in a shearing background wind, is analyzed. Starting from the gravity wave equations, it is proven, analytically and numerically, that a uniform spectrum has a resultant Doppler-shifted power spectrum with a −3 power law at large vertical wavenumber contrasting with the −1 power law that characterizes the power spectrum of the monochromatic wave perturbation profile. The preliminary results presented here show that, assuming conservative propagation (no dissipative processes), the Doppler shifting effect can account for observations.     

Effects of Sea-Surface Waves and Ocean Spray on Air-Sea Momentum Fluxes

The effects of sea-surface waves and ocean spray on the marine atmospheric boundary layer(MABL) at different wind speeds and wave ages were investigated. An MABL model was developed that introduces a wave-induced component and spray force to the total surface stress. The theoretical model solution was determined assuming the eddy viscosity coefficient varied linearly with height above the sea surface. The wave-induced component was evaluated using a directional wave spectrum and growth rate. Spray force was described using interactions between ocean-spray droplets and wind-velocity shear. Wind profiles and sea-surface drag coefficients were calculated for low to high wind speeds for wind-generated sea at different wave ages to examine surface-wave and ocean-spray effects on MABL momentum distribution. The theoretical solutions were compared with model solutions neglecting wave-induced stress and/or spray stress. Surface waves strongly affected near-surface wind profiles and sea-surface drag coefficients at low to moderate wind speeds. Drag coefficients and near-surface wind speeds were lower for young than for old waves. At high wind speeds, ocean-spray droplets produced by wind-tearing breaking-wave crests affected the MABL strongly in comparison with surface waves, implying that wave age affects the MABL only negligibly. Low drag coefficients at high wind caused by ocean-spray production increased turbulent stress in the sea-spray generation layer, accelerating near-sea-surface wind. Comparing the analytical drag coefficient values with laboratory measurements and field observations indicated that surface waves and ocean spray significantly affect the MABL at different wind speeds and wave ages.     

THE LYAPUNOV STABILITY OF NONLINEAR WAVE MOTION IN THE BAROTROPIC NONDIVERGENT ATMOSPHERE

Introducing the concept of pseudo-momentum, a generalized Arnold-Dikii functional is established, and then thesufficient condition for stability of nonlinear wave motion in the barotropic nondivergent atmosphere is derived by useof variational principle. It is found that the stability of nonlinear wave motion depends not only on its streamfield distri-bution, but also on its phase speed for the propagating nonlinear wave motion. Moreover, the stability criterion of trav-elling modon is also obtained, and it is shown that the travelling modon is stable if the scale of disturbance superimposedon the travelling modon remains to be less than that of the travelling modon.     

热带平流层多尺度波动分离方案的研究：多站点高分辨率无线电探空联合分析

利用太平洋地区台风过境期间6个热带气象站的高分辨率无线电探空资料,结合扩展经验正交函数（EEOF）展开,对热带下平流层行星波和重力波扰动进行了分离,给出了一种热带地区提取重力波扰动的新方案。对观测数据做EEOF展开后,选择表征行星尺度波动模态的特征向量和相应权重进行气象要素场的重建。结果显示,在不同的台风过程期间,温度、纬向风和经向风的重建扰动量显示出不同的动力学偏振关系:在准两年振荡（QBO）东风位相时与赤道开尔文波的偏振关系一致,而在准两年振荡西风位相时与混合罗斯贝-重力波（MRG）的偏振关系一致。把行星尺度波动模态从原始观测中剔除,得到新的扰动廓线,对其进行重力波垂直波数谱的谱型拟合。结果发现,与以往方法提取的重力波扰动相比,新方法所得谱型参数中特征垂直波长λ*在不同时期不同站点变化很小,稳定在1.7 km左右,且低频波数段谱斜率s的数值与理论假设1十分接近。综合其研究结果可以推测,用新方法提取的热带重力波扰动更加符合当前的理论垂直波数谱模型。      

Comments on the Phillips'-Miles' theory of wind wave generation

Some ambiguities and omissions in the Phillips'-Miles' theory of wind wave generation are discussed. The details of the theory are revised on the basis of the coupled system of equations for water and air. The results are then applied to a consideration of the statistical properties of the problem. The wavenumber spectrum, corresponding to this model of wind wave generation, is different from the spectrum corresponding to the theories proposed by Phillips (1966) and Miles (1960). The well-known qualitative physical conclusions of the Phillips'-Miles' theory remain unchanged and therefore are not discussed. Only a formal treatment of the problem is presented.     

On the Dependence of the Equilibrium Range of Sea Wave Spectra with Wave Age

Donelan and Pierson have proposed a semiphysical model of the equilibrium sea wave spectrum, based upon a parameterization of wave growth and dissipation terms. Their model is applicable for fully developed seas only. In the framework of Donelan and Pierson's approach, this paper explores the dependence of the equilibrium spectrum upon wave age. To this end, we examine how the dissipation through wave breaking is expected to vary with wave age, according to the approach proposed by Longuet-Higgins in 1969. The constraint imposed by Longuet-Higgins' theory requires an increase of the equilibrium spectrum F(k,0) in the wind direction with increasing inverse wave age U/C_p. This is in accordance with Banner's empirically deduced statement that F(k,0) is proportional to (U/C_p)^0.5 in the equilibrium range. Our inferred F(k,0) tends to increase more or less linearly with U/C_p (we find F(k,0) proportional to 1 + 0.25(U/C_p - 0.83), rather than through a power law. If a power law is fitted we obtain F(k,0) approximately proportional to (U/C_p)^0.35 for the range 0.83 < U/C_p > 5. Finally, the roughness length of the air-sea interface is inferred from our modelled spectrum through integration of the form drag over wave number under rough conditions. This shows a wave age dependence that is compatible with measurements of wind stress performed in the field at various wave ages.     

基于Weierstrass-Mandelbrot函数的分形风速脉动仿真

实际风速脉动普遍具有自相似分形特征,而传统的谐波合成法和线性滤波法仿真的风速脉动均不具有自相似分形特征.因此,基于随机型Weierstrass-Mandelbrot函数,设计了一种能够仿真自相似风速脉动的方案.其中,表征风速脉动自相似特征的重要参数分形维度可与湍流惯性区能谱的幂指数建立联系.将该方案仿真的风速脉动与实际风速脉动一些重要的统计特征,如功率谱和概率密度函数等,进行了比较,结果表明提出的新方案能有效仿真风速脉动的中高频变化及其概率分布特征.     

Drag coefficient modeling for the near coastal zone

Using the JONSWAP spectrum for describing the surface wave state in the near coastal zone, models for the roughness length and the drag coefficient are used to simulate the dependence of the wind stress on fetch and depth. The results of each model are then compared with a compiled set of past investigations of the neutral drag coefficient over a variety of conditions. It is found that the models of Donelan, Hsu, and Kitaigorodskii correctly predict the trends in the drag coefficient with fetch and depth. Although it did not account for all the observed variations in the neutral drag coefficient. Kitaigorodskii's model, when incorporating the JONSWAP spectrum, more accurately simulated the slopes of the various C_DN regressions against windspeed.     

The second order approximation to the nonlinear wave in barotropic atmosphere

A kind of technique of computer extension of perturbation series is presented and used in seeking for the second-order approximation to a large-scale travelling wave solution of the barotropic primitive equations. Numerical experiments show that the second-order approximation keeps major characters of the travelling wave solution and is indeed more exact than the zero-order and the first order approximations.