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.     

The roughness of wind waves

In this paper, a new dynamic roughness equation for airflow over wind waves is proposed, based on relationships of dimensionless parameters and the 1986 HEXMAX field data. The equation can be considered as a modification of the Charnock formula. The data are also compared with the parameterizations of Toba and Koga, and of Hsu, and the consequences of the new equation for aerodynamic drag are discussed. In the new equation, the drag coefficient is expressed as a function of both wind speed and wave age c _p/u_*. This testifies to the strong wave-age dependence of the drag, found in several experimental studies. It is also in good agreement with results of a theoretical model of the airflow-seawave interaction, proposed by Janssen (1989).Also: Dept. of Applied Physics, Techn. Univ. Delft, the Netherlands.     

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.     

Impact of waves on the sea drag: measurements in the Baltic sea and a model interpretation

Measurements from the Baltic Sea and a wind-over-wave coupled model are used to study the wave impact on the sea drag. The study has been carried out for different wave conditions, namely a pure wind-sea, following-swell/ mixed sea and cross-swell/ mixed sea. Measurements reveal the fact that the sea drag is dependent on the sea-state. In stationary conditions and in the absence of severe cross-swell, swell reduces drag compared to wind-sea at the same wind speed. The cross-swell enhances the drag as compared to the following-swell case and the magnitude of the drag coefficient is increased with increasing the angle of swell propagation to the wind. It is shown that the agreement between the model results and measurements is good for pure wind-sea and stationary mixed-sea cases. Discrepancies occur at light winds, where most of the data represent pure swell conditions. During these pure swell conditions the data are characterized by a large variation of the drag coefficient. The variation is caused by mesoscale variability in the stress co-spectra, wind-cross-swell effects and nonstationarity in the wave and wind fields not represented in the model.     

Nonlinear Formulation of the Bulk Surface Stress over Breaking Waves: Feedback Mechanisms from Air-flow Separation

Historically, our understanding of the air-sea surface stress has been derived from engineering studies of turbulent flows over flat solid surfaces, and more recently, over rigid complex geometries. Over the ocean however, the presence of a free, deformable, moving surface gives rise to a more complicated drag formulation. In fact, within the constant-stress turbulent atmospheric boundary layer over the ocean, the total air-sea stress not only includes the traditional turbulent and viscous components but also incorporates surface-wave effects such as wave growth or decay, air-flow separation, and surface separation in the form of sea-spray droplets. Because each individual stress component depends on and alters the sea state, a simple linear addition of all stress components is too simplistic. In this paper we present a model of the air-sea surface stress that incorporates air-flow separation and its effects on the other stress components, such as a reduction of the surface viscous stress in the separated region as suggested by recent measurements. Naturally, the inclusion of these effects leads to a non-linear stress formulation. This model, which uses a variable normalized dissipation rate of breaking waves and normalized length of the separation bubble, reproduces the observed features of the drag coefficient from low to high wind speeds despite extrapolating empirical wave spectra and breaking wave statistics beyond known limits. The model shows the saturation of the drag coefficient at high wind speeds for both field and laboratory fetches, suggesting that air-flow separation over ocean waves and its accompanying effects may play a significant role in the physics of the air-sea stress, at least at high wind speeds.     

A Dynamic Urban Canopy Parameterization for Mesoscale Models Based on Computational Fluid Dynamics Reynolds-Averaged Navier–Stokes Microscale Simulations

Urban canopy parameterizations (UCPs) are necessary in mesoscale modelling to take into account the effects of buildings on wind and turbulent structures. This study is focused on the dynamical part of UCPs. The main objective is twofold: first, computing important UCP input parameters (turbulent length scales and the sectional drag coefficient) by means of Reynolds-averaged Navier–Stokes (RANS) simulations of turbulent flow; and second, comparing UCP variables with spatially-averaged properties obtained from RANS simulations for the same configurations. The results show the importance of using a suitable parameterization of the drag force for different packing densities. An urban canopy parameterization that is a compromise between simplicity and accuracy is proposed. This scheme accounts for the variation of drag coefficients with packing densities, and has a parameterization of turbulent length scales. The technique adopted ensures that, at least for the simple configurations studied, the urban canopy parameterization gives values of spatially-averaged variables similar to those computed from a more complex simulation, such as RANS that resolves explicitly the flow around buildings.     

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.     

Characteristics of over-water surface stress during strex

Surface stress values obtained from the NOAA Ship OCEANOGRAPHER during STREX indicate that wind speed and stability dependent bulk derived stress values are two to three times too low in surface pre-frontal, pre-trough and pre-ridge regions of transiting synoptic systems. The measured stress values were based on calculations of turbulent kinetic energy dissipation rates using hot film measured velocity variances. Bulk stress values obtained with wind speed (neutral drag coefficient) and stability dependencies in the Large and Pond derivation agreed very well with the measured values in other regions of the synoptic systems. In situ wave information was not adequate to relate differences to coupled vector wind and wave fields. However, analyses and interpretation of wind and stability effects suggest that wind wave interaction was the reason for the observed sub-synoptic (mesoscale) stress enhancements.     

Wave disturbances associated with the red river valley severe weather outbreak of 10–11 April 1979

Summary An analysis of mesoscale gravity wave events during the severe weather outbreak in the Red River Valley on 10–11 April 1979 is presented utilizing surface pressure data and the 3 h rawinsonde data from the AVE-SESAMEI special network. The unique data set provided by the SESAME field experiment makes it possible to relate the wavelike characteristics observed at the surface to the variability of the temperature, humidity, and wind fields over a deep tropospheric layer that act to initiate and sustain the waves over long distances and time periods.Three different wave events (A, B, and C) were identified via spectral analysis and cross-correlation techniques. They all have similar periods, approximately 3 h, but different phase velocities. All three wave events are generated and propagate in the exit region or anticyclonic side of upperlevel jet streaks. Convection and wind shear are shown to be unlikely contributors to the generation of event A, which is probably related to the development of a strong divergent field in association with an upper-tropospheric jet streak and to the ensuing mass adjustment process. Events B and C also appear in a region of strong ageostrophic motion associated with an upper-level jet streak. However, the low values of the Richardson number (Ri) at the critical levels of these two waves suggest vertical wind shear as a likely contributor to their generation and/or maintenance. A linear stability analysis confirms, with unprecedent spatial and temporal resolution, that a modal structure is present in the atmosphere whose characteristics are consistent with those of waves B and C.Three-hourly rawinsonde data show strong temporal and spatial variability throughout the troposphere in the wind, temperature, and humidity fields when the waves are present. Convective systems, as detected by radar, are closely linked to the waves, although not in a consistent manner: cells intensify or develop at the passage of a wave trough in event A, at the passage of a wave ridge in event C, and at the passage of a wave trough or ridge in event B, depending on the geographic location of the cells. For all three events, maximum rainfall recorded at the surface is associated with a wave ridge with a time lag of approximately 1 h.With 20 Figures     

Wave-dependence of friction velocity,roughness length,and drag coefficient over coastal and open water surfaces by using three databases

The parameterization of friction velocity, roughness length, and the drag coefficient over coastal zones and open water surfaces enables us to better understand the physical processes of air-water interaction. In context of measurements from the Humidity Exchange over the Sea Main Experiment (HEXMAX), we recently proposed wave-parameter dependent approaches to sea surface friction velocity and the aerodynamic roughness by using the dimensional analysis method. To extend the application of these approaches to a range of natural surface conditions, the present study is to assess this approach by using both coastal shallow (RASEX) and open water surface measurements (Lake Ontario and Grand Banks ERS-1 SAR) where wind speeds were greater than 6.44 m s^-1. Friction velocities, the surface aerodynamic roughness, and the neutral drag coefficient estimated by these approaches under moderate wind conditions were compared with the measurements mentioned above. Results showed that the coefficients in these approaches for coastal shallow water surface differ from those for open water surfaces, and that the aerodynamic roughness length in terms of wave age or significant wave height should be treated differently for coastal shallow and open water surfaces.     

GRAPES中地形重力波拖曳物理过程的引进和应用试验

在中国新一代全球中期/区域中尺度同化与预报系统(GRAPES)模式中引进了ECMWF地形重力波拖曳物理过程,填补了GRAPES全球中期数值预报系统中物理过程的空白。重新计算了地形重力波过程需要的地形静态资料数据,并与原ECMWF模式的地形静态参数进行了对比分析,验证了模式地形参数的正确性。利用GRAPES模式,进行了地形重力波拖曳物理过程影响的敏感性数值试验;结果表明:引进地形重力波拖曳过程以后,在存在大地形的区域,风场会发生变化,当纬向风遇到青藏高原时,一部分气流会产生爬坡效应而越过高原,使高原上空的西风气流减弱;另一部分气流会绕过高原,在高原的南侧产生绕流;随着模式积分时间的延长,风场变化会越来越明显,地形越复杂,风场的变化也越复杂;连续的模式积分试验结果显示,引进地形重力波过程,可以延长GRAPES模式的可用预报时效,提高了全球形势预报的准确率。通过对一次降水过程的模拟,对地形重力波过程影响降水预报的原因进行了简单分析。结果显示:引进地形重力波拖曳过程后,改变了大气流场的分布,使预报的流场更接近于大气真实状态,从而提高了降水预报的准确率。     

New evidence for a relation between wind stress and wave age from measurements during ASGAMAGE

Data from the 1996 ASGAMAGE experiment, performed in the southern North Sea at research platform Meetpost Noordwijk (MPN), are analysed for the parameters affecting the momentum flux. The stress turns out to be quadratically related to the 10-m wind speed and linearly to the wind speed at a wavelength related level. The Charnock parameter (dimensionless roughness length) shows a pronounced correlation with wave age. This implies, due to a coupling between wave age and the steepness of the waves, a connection between the stress and the steepness. We find that our North Sea results are consistent withopen ocean observations. For a given wind speed the mean stress at MPN turns out to be higher because the wave age there is in general lower. We define and give an expression for a drag coefficient at a wavelength related level that can be calculated straightforwardly from the wave age and then reduced to a standard level.     

荒漠戈壁大气总体曳力系数和输送系数观测研究

利用“我国西北干旱区陆一气相互作用观测试验”在甘肃敦煌进行的陆面过程野外试验的观测资料,依据三种不同方法确定了干旱戈壁区动量输送的曳力系数Cd、感热和潜热交换的总体输送系数Ch和Cq。结果表明：尽管这三种方法计算的曳力系数和总体输送系数有一定的差别,但在量级上相当,尤其是Cd和Ch的平均值比较接近。本文还通过对风向的分析,剔除了附近建筑物干扰和来自绿洲湿平流的影响,得到了荒漠戈壁总体输送系数的特征及其与理查孙数的关系。     

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.     

Building morphological characteristics and their effect on the wind in Beijing

An urban boundary layer model (UBLM) is improved by incorporating the effect of buildings with a sectional drag coefficient and a height-distributed canopy drag length scale. The improved UBLM is applied to simulate the wind fields over three typical urban blocks over the Beijing area with different height-to-width ratios. For comparisons, the wind fields over the same blocks are simulated by an urban sub-domain scale model resolving the buildings explicitly. The wind fields simulated from the two different methods are in good agreement. Then, two-dimensional building morphological characteristics and urban canopy parameters for Beijing are derived from detailed building height data. Finally, experiements are conducted to investigate the effect of buildings on the wind field in Beijing using the improved UBLM.     

辽东湾东海岸近地层特性探讨

采用离岸800m高100m的气象铁塔观测所得的资料,利用粗糙度、阻力系数及幂指数公式,计算了辽东湾东海岸地区的粗糙度、阻力系数及风指数。结果表明：在向岸气流条件下,粗糙度值较大,可达0.18m,阻力系数最大值也可达0.025;在离岸气流条件下,粗糙度、阻力系数值较小。相同稳定度条件下,风指数值随着风速增大而减小。     

Aerodynamic drag coefficient and roughness length for three seasons over a tropical western Indian station

Land Surface Processes Experiment (LASPEX) was conducted over semi-arid region of western India in 1997. As a part of this program, wind and temperature observations were taken using slow as well as fast response sensors over a semi-arid station Anand (22°35′N, 72°55′E) situated in Gujarat state of India. Turbulent parameters such as drag coefficient and sensible heat flux were estimated using eddy correlation method and aerodynamic roughness length was estimated using wind profiles. The analysis has been carried out for the data representing summer, monsoon and winter seasons. It was found that the wind speed does not exceed 5 ms^− 1 during the observational period considered in this study. Relationship of aerodynamic drag coefficient and roughness length with wind speed and stability has been investigated. Aerodynamic roughness length was greater in the stable conditions when the wind speed was low and it reduced drastically during convective conditions. The resulting values of aerodynamic roughness length and drag coefficient for the monsoon period agree well with values reported in literature over Indian subcontinent for homogeneous grass covered surfaces.     

Determination Of The Surface Drag Coefficient

This study examines the dependence of the surface drag coefficienton stability, wind speed, mesoscale modulation of the turbulent flux and method of calculation of the drag coefficient. Data sets over grassland, sparse grass, heather and two forest sites are analyzed. For significantly unstable conditions, the drag coefficient does not depend systematically on z/L but decreases with wind speed for fixed intervals of z/L, where L is the Obukhov length. Even though the drag coefficient for weak wind conditions is sensitive to the exact method of calculation and choice of averaging time, the decrease of the drag coefficient with wind speed occurs for all of the calculation methods. A classification of flux calculation methods is constructed, which unifies the most common previous approaches.The roughness length corresponding to the usual Monin–Obukhovstability functions decreases with increasing wind speed. This dependence on wind speed cannot be eliminated by adjusting the stability functions. If physical, the decrease of the roughness length with increasing wind speed might be due to the decreasing role of viscous effectsand streamlining of the vegetation, although these effects cannot be isolated from existing atmospheric data.For weak winds, both the mean flow and the stress vector often meander significantly in response to mesoscale motions. The relationship between meandering of the stress and wind vectors is examined. For weak winds, the drag coefficient can be sensitive to the method of calculation, partly due to meandering of the stress vector.     

One-dimensional theory of the wave boundary layer

Results obtained in a 2-D modeling of the statistical structure of the wave boundary layer (WBL) are used for elaboration of the general approach to 1-D modeling taking into account the spectral properties of wave drag for an arbitrary wave field. In the case of the wave field described by the JONSWAP spectrum, the momentum and energy spectral density exchange, vertical profiles of the wave-induced momentum flux and dependence of total roughness parameter and drag coefficient on peak frequency are given. The reasons that the total roughness parameter increases with decreasing fetch are explained. The role of wind waves as an active element of the ocean-atmosphere dynamic system is also discussed.