Fetch Limited Drag Coefficients

Measurements made at a tower located 2 km off the coast of Denmark inshallow water during the Risø Air Sea Experiment (RASEX) are analyzedto investigate the behaviour of the drag coefficient in the coastal zone.For a given wind speed, the drag coefficient is larger during conditions ofshort fetch (2-5 km) off-shore flow with younger growing waves than it isfor longer fetch (15-25 km) on-shore flow. For the strongest on-shorewinds, wave breaking enhances the drag coefficient. Variation of the neutral drag coefficient in RASEX is dominated byvariation of wave age, frequency bandwidth of the wave spectra and windspeed. The frequency bandwidth is proportional to the broadness of the waveheight spectra and is largest during conditions of light wind speeds. Usingthe RASEX data, simple models of the drag coefficient and roughness length are developed in terms of wind speed, wave age and bandwidth. An off-shoreflow model of the drag coefficient in terms of nondimensional fetch isdeveloped for situations when the wave state is not known.     

Drag of the sea surface

It is shown how the drag of the sea surface can be computed from the wind speed and the sea state. The approach, applicable both for fully developed and for developing seas, is based on conservation of momentum in the boundary layer above the sea, which allows one to relate the drag to the properties of the momentum exchange between the sea waves and the atmosphere.The total stress is split into two parts: a turbulent part and a wave-induced part. The former is parameterized in terms of mixing-length theory. The latter is calculated by integration of the wave-induced stress over all wave numbers. Usually, the effective roughness is given in terms of the empirical Charnock relation. Here, it is shown how this relation can be derived from the dynamical balance between turbulent and wave-induced stress. To this end, the non-slip boundary conditions is assigned to the wave surface, and the local roughness parameter is determined by the scale of the molecular sublayer.The formation of the sea drag is then described for fully developed and developing seas and for light to high winds.For the Charnock constant, a value of about 0.018–0.030 is obtained, depending on the wind input, which is well within the range of experimental data.It is shown that gravity-capillary waves with a wavelength less than 5 cm play a minor role in the momentum transfer from wind to waves. Most of the momentum is transferred to decimeter and meter waves, so that the drag of developing seas depends crucially on the form of the wave spectrum in the corresponding high wavenumber range.The dependence of the drag on wave age depends sensitively on the dependence of this high wavenumbertail on wave age. If the tail is wave-age independent, the sea drag appears to be virtually independent of wave age. If the tail depends on wave age, the drag also does. There is contradictory evidence as to the actual dependence. Therefore, additional experiments are needed.The investigation was in part supported by the Netherlands Geosciences Foundation (GOA) with financial aid from the Netherlands Organization for Scientific Research (NWO).     

TESTING DRAG COEFFICIENT APPROACHES BY USING THE BUOY DATA COLLECTED IN MODERATE TO HIGH WIND UNDER FOLLOWING, CROSSING AND OPPOSING SWELL CONDITIONS

Hurricane intensity and track are strongly affected by air-sea interactions. Classified as following swells, crossing swells, and opposing swells, the observed wave height was parameterized by using the 10-m wind speed collected on 5 buoys by the National Buoy Data Center during 13 hurricane events. The path information of these 13 hurricanes was obtained from the National Hurricane Center Best Track (NHC-BT). Results show that the wave height increases exponentially with the 10-m wind speed, and the wave height reaches the maximum value, 11.2 m (8.1 m), when 10-m wind speed is 40 m s-1 under the following and crossing (opposing) swell conditions. We find that the wave steepness (the ratio of wave height to wave length) is proportional to the -2/3 power of the wave age (the ratio of wave phase velocity to 10-m wind speed). The parameterizations of friction velocity and drag coefficient are tested using the buoy data collected in moderate to high wind under following, crossing and opposing swell conditions. A wave age dependent equation for drag coefficient is found more accurate and suggested for future usage in numerical models. Further, these algorithms also suggest that wind-swell orientation needs to be considered to retrieve accurate surface drag under high winds and strong swells.     

A Note on Velocity Spectra in the Marine Boundary Layer

Spectra of longitudinal and vertical velocity have been studied at a marine site, östergarnsholm, in the Baltic Sea during a period of six days with near-neutral or slightly unstable conditions, when the wave state gradually changed from pure wind sea to strong swell having approximately the same direction as the wind. During the pure wind sea phase, spectra are shown to adhere closely to general forms for the neutral atmospheric surface layer obtained from a new theory. As soon as the wave age goes slightly beyond that representative of pure wind sea conditions, the spectra deviate in shape from the ideal forms. The spectral modification appears to start at a frequency typical of the swell component. As the wave age increases, it progresses in frequency as a downscale cascade, which is particularly prominent in the spectrum of the vertical component but which is also observed in the longitudinal component. In addition, there is a strong effect in the low-frequency part of the spectra. It is interpreted as an indirect effect of large-scale inactive turbulence, which becomes progressively more important as wave-age increases. It is found that the ratio of the spectrum of the vertical component and the spectrum of the corresponding longitudinal component attains the theoretically predicted value of 4/3 for cases of developing sea (gale force wind) for frequencies above approximately 4 Hz but never much exceeds unity for cases with swell. It is argued that this is an indication of local anisotropy and that the inertial-dissipation method for determination of the momentum flux is inappropriate in the case of mixed seas or swell.     

Aerodynamic roughness of the sea surface at high winds

The role of the surface roughness in the formation of the aerodynamic friction of the water surface at high wind speeds is investigated. The study is based on a wind-over-waves coupling theory. In this theory waves provide the surface friction velocity through the form drag, while the energy input from the wind to waves depends on the friction velocity and the wind speed. The wind-over-waves coupling model is extended to high wind speeds taking into account the effect of sheltering of the short wind waves by the air-flow separation from breaking crests of longer waves. It is suggested that the momentum and energy flux from the wind to short waves locally vanishes if they are trapped into the separation bubble of breaking longer waves. At short fetches, typical for laboratory conditions, and strong winds the steep dominant wind waves break frequently and provide the major part of the total form drag through the air-flow separation from breaking crests, and the effect of short waves on the sea drag is suppressed. In this case the dependence of the drag coefficient on the wind speed is much weaker than would be expected from the standard parameterization of the roughness parameter through the Charnock relation. At long fetches, typical for the field, waves in the spectral peak break rarely and their contribution to the air-flow separation is weak. In this case the surface form drag is determined predominantly by the air-flow separation from breaking of the equilibrium range waves. As found at high wind speeds up to 60 m s⁻¹ the modelled aerodynamic roughness is consistent with the Charnock relation, i.e. there is no saturation of the sea drag. Unlike the aerodynamic roughness, the geometrical surface roughness (height of short waves) could be saturated or even suppressed when the wind speed exceeds 30 m s⁻¹.     

Turbulence intensities and bulk coefficients in the surface layer above the sea

The structure of the atmospheric surface layer above the sea is analysed from aircraft turbulence measurements. The data are issued from two experiments performed in 1990 above the Mediterranean sea: Crau and PYREX, and correspond to moderately unstable conditions and to wind velocities ranging from 6 to 20 m/s. Low-altitude straight and level runs were used to compute the variances of the wind components, as well as of the temperature and moisture. Their dependence on the stability index —z/L is analysed. The turbulent fluxes of momentum, sensible heat and latent heat, calculated by the eddy-correlation technique, are used to estimate the neutral bulk coefficients: drag coefficient, Stanton number and Dalton number. The neutral drag coefficient clearly exhibits a dependence on the windspeed, which could be well fitted by the Charnock relation, with a constant of 0.012.     

Air–Sea Interaction Features in the Baltic Sea and at a Pacific Trade-Wind Site: An Inter-comparison Study

A systematic comparison of wind profiles and momentum exchange at a trade wind site outside Oahu, Hawaii and corresponding data from the Baltic Sea is presented. The trade wind data are to a very high degree swell dominated, whereas the Baltic Sea data include a more varied assortment of wave conditions, ranging from a pure growing sea to swell. In the trade wind region swell waves travel predominantly in the wind direction, while in the Baltic, significant cross-wind swells are also present. Showing the drag coefficient as a function of the 10-m wind speed demonstrates striking differences for unstable conditions with swell for the wind-speed range 2 m s^?1 < U ₁₀ < 7 m s^?1, where the trade-wind site drag values are significantly larger than the corresponding Baltic Sea values. In striking contrast to this disagreement, other features studied are surprisingly similar between the two sites. Thus, exactly as found previously in Baltic Sea studies during unstable conditions and swell, the wind profile in light winds (3 m s^?1) shows a wind maximum at around 7–8 m above the water, with close to constant wind speed above. Also, for slightly higher wind speeds (4 m s^?1 < U ₁₀ < 7 m s^?1), the similarity between wind profiles is striking, with a strong wind-speed increase below a height of about 7–8 m followed by a layer of virtually constant wind speed above. A consequence of these wind-profile features is that Monin–Obukhov similarity is no longer valid. At the trade-wind site this was observed to be the case even for wind speeds as high as 10 m s^?1. The turbulence kinetic energy budget was evaluated for four cases of 8–16 30- min periods at the trade-wind site, giving results that agree very well with corresponding figures from the Baltic Sea.     

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 <Emphasis Type="SmallCaps">int</Emphasis>OA Experiment: A Study of Ocean-Atmosphere Interactions Under Moderate to Strong Offshore Winds and Opposing Swell Conditions in the Gulf of Tehuantepec,Mexico

The Gulf of Tehuantepec air–sea interaction experiment (intOA) took place from February to April 2005, under the Programme for the Study of the Gulf of Tehuantepec (PEGoT, Spanish acronym for Programa para el Estudio del Golfo de Tehuantepec). PEGoT is underway aiming for better knowledge of the effect of strong and persistent offshore winds on coastal waters and their natural resources, as well as performing advanced numerical modelling of the wave and surface current fields. One of the goals of the intOA experiment is to improve our knowledge on air–sea interaction processes with particular emphasis on the effect of surface waves on the momentum flux for the characteristic and unique conditions that occur when strong Tehuano winds blow offshore against the Pacific Ocean long period swell. For the field campaign, an air–sea interaction spar (ASIS) buoy was deployed in the Gulf of Tehuantepec to measure surface waves and the momentum flux between the ocean and the atmosphere. High frequency radar systems (phase array type) were in operation from two coastal sites and three acoustic Doppler current profilers were deployed near-shore. Synthetic aperture radar images were also acquired as part of the remote sensing component of the experiment. The present paper provides the main results on the wave and wind fields, addressing the direct calculation of the momentum flux and the drag coefficient, and gives an overview of the intOA experiment. Although the effect of swell has been described in recent studies, this is the first time for the very specific conditions encountered, such as swell persistently opposing offshore winds and locally generated waves, to show a clear evidence of the influence on the wind stress of the significant steepness of swell waves.     

0801号台风风浪场和涌浪场的数值模拟

利用美国国家海洋大气总局/美国国家环境预报中心（NOAA/NCEP）发布的最新版WAV-EWATCHⅢ（version3.14）海浪模式对0801号台风＂浣熊＂进行数值模拟,并在此基础上对台风浪的发展过程和台风影响下的海面有效波高、风浪场及涌浪场的分布特征进行分析。结果表明：海面有效波高的分布和演变受台风系统强度和移动的影响;台风过程中所产生的大浪主要为风浪;涌浪场的分布与风浪场的分布几乎相反,涌浪场基本分布在远离台风中心的外围海域;涌浪场波高比风浪场波高要小。     

全球海洋海浪要素季节变化研究

本文使用欧洲中期天气预报中心（European Center for Medium Range Weather Forecasting,ECMWF）近30年（1982～2011年）全球再分析资料（ECMWF 40 Year Re-analysis Interim）中的风场及海浪场资料,对全球海表10 m风场、有效波高、平均周期和平均波向进行了统计分析,并定义了一种计算季节变率的方法。研究发现,有效波高和平均周期均存在明显的季节变化,且北半球大洋比南半球大洋季节变化更为明显,印度季风区则例外。另外尝试用波龄揭示风浪、涌浪的分布特征,证实了全球海洋为涌浪占主导及太洋东部存在涌浪强化,同时发现了涌浪的分布在春夏季变化明显的特征。     

ANALYSIS OF SEA-SURFACE DRAG PARAMETERIZATIONS IN OPEN OCEAN CONDITIONS

Data from the Surface Waves and Processes Program (SWAPP) are employed to test current sea-surface drag parameterizations in open ocean conditions. General trends in the data indicate that drag increases with increasing wind speed and wave height, and decreases with wave age. However, scatter in the data limits the use of these parameters and other wave dependent parameterizations for modelling efforts. Upon close inspection, it is found that during the onset of three wind events analyzed separately, each of these parameters correlate well with the drag coefficient. However, the dependence of the drag coefficient on each of these parameters varies markedly from event to event. The disparity appears most closely linked to the turning rate of the wind, indicating that temporal and directional effects may play an important role. A temporal lag of O(4) hours between the rise of the wind and subsequent rise in the drag coefficient is also noticed, further pointing out the complexity of the wind-stress system.     

西北太平洋海域风浪、涌浪、混合浪波浪能资源特征

用ECMWF的ERA-40海浪再分析资料,应用波浪能流密度计算方法,对西北太平洋海域的风浪能、涌浪能、混合浪能展开研究。结果表明:(1)波浪能流密度呈现出显著季节性差异。混合浪能流密度表现为冬高夏低;春、夏、秋季的涌浪能流密度明显大于风浪能流密度,冬季相反;(2)混合浪能流密度的大值区主要分布于阿留申群岛附近海域,高值中心可达60 kW/m以上;近海的大值区主要分布于琉球群岛—巴士海峡—传统的南海大风区一带,年平均值在4 kW/m以上,南海北部可达12 kW/m以上;(3)黄渤海的涌浪和混合浪能流密度峰值出现在8—9月,波谷出现在6月。风浪能流密度峰值出现在11月—次年3月,波谷出现在6—8月,均呈现双峰型月变化特征。东海、南海北部、南海中南部海域能流密度的月变化特征相似,都为双峰型,12月—次年4月的能流密度整体较高,波峰出现在12月,波谷出现在5—7月;(4)2 kW/m以上混合浪能流密度出现的频率较高,近海低于大洋;(5)0.5 m以上有效波高出现的频率都非常高,中国近海稍低于大洋;(6)涌浪能流密度的稳定性明显好于风浪能流密度;大洋的能流密度稳定性明显强于近岸。1月份能流密度的稳定性最好,4月和7月次之,10月的稳定性最差。     

A Note on a Parameterization of the Sea Drag

A new parameterization of the sea drag is based on a wind-over-wavescoupling theory. The parameterization accounts for the wind speed, wave ageand finite depth dependencies of the sea drag. The latter two are introducedthrough the integral parameters of the wind-wave field: the dominant waveheight and the wavenumber at the spectral peak, and the water depth. Theparameterization is checked against the wind-over-waves model results andtwo field datasets obtained in a wide range of the wind speed and wave age.The comparison is encouraging. The parameterization is aimed for use inoperational ocean-state and atmosphere models.     

The influence of sea waves on the wind profile

From wind profile and wave measurements performed during the JONSWAP II experiment, relations between the dimensionless profile slope and the significant wave height are derived. It is shown that the wind profile is distorted by the waves especially in the vicinity of the water surface. The wave influence on the profile seems to be restricted to heights below about three wave heights. Above this level, the dimensionless profile slope is an approximately constant value corresponding to a drag coefficient of about 1.15 × 10^–3.     

A Note on Wind Speed and sea State Dependence of the Heat Exchange Coefficient

Both mean and wave-induced motions generate turbulence in the air flow above sea waves. Assuming a local balance between production of turbulent kinetic energy and its dissipation, an explicit relation for the heat exchange coefficient CH is obtained. It is shown that CH follows a square-root dependence on the drag coefficient CD. However, the proportionality coefficient appears to depend on the sea state, expressed in terms of the coupling parameter. Dependence on the sea state suppresses the CD1/2 wind-speed dependence, and results in a marginal increase of CH with increase in the wind speed.     

Impact of Surface Exchange Coefficients and Sea Surface Cooling on Tropical Cyclone Simulation

The surface flux exchange associated with the exchange coefficients and upper ocean conditions is essential to the development of tropical cyclones (TCs). Using the Weather Research and Forecasting (WRF) model, the present study has investigated the impact of exchange coefficients and ocean coupling during Super Typhoon Saomai (2006). Firstly, two experiments with different formula of roughness are conducted. The experiment with the Donelan formula for drag coefficient (Cd) and ramped formula for enthalpy coefficient (Ck) can simulate stronger intensity compared to other experiments due to the increased surface wind and enthalpy fluxes. That is because the new formulas allows for a smaller Cd and larger Ck in the high wind regime than the former formulas did. Moreover, two coupled simulations between WRF and a one-dimensional ocean model are conducted to examine the feedback of sea surface cooling to the TC. In the experiments with a horizontal uniform mixed layer depth of 70 m, the sea surface cooling is too weak to change the evolution of TC. While in the experiment with an input mixed layer calculated using the Hybrid Coordinate Ocean Model (HYCOM) data, the significant sea surface cooling induces obvious impact on TC intensity and structure. Under the negative feedback of sea surface cooling, the sensible and latent heat fluxes decreases, especially in the right part of Saomai (2006). The negative feedback with coupled ocean model plays a vital role in simulating the intensity and structure of TC.     

Effects of Bubbles and Sea Spray on Air–Sea Exchange in Hurricane Conditions

The lower limit on the drag coefficient under hurricane force winds is determined by the break-up of the air–sea interface due to Kelvin–Helmholtz instability and formation of the two-phase transition layer consisting of sea spray and air bubbles. As a consequence, a regime of marginal stability develops. In this regime, the air–sea drag coefficient is determined by the turbulence characteristics of the two-phase transition layer. The upper limit on the drag coefficient is determined by the Charnock-type wave resistance. Most of the observational estimates of the drag coefficient obtained in hurricane conditions and in laboratory experiments appear to lie between the two extreme regimes: wave resistance and marginal stability.