The Impact Of Air-Flow Separation On The Drag Of The Sea Surface

An approach that allows assessment ofthe impact of air-flow separation (AFS) fromwave breaking fronts on the sea-surface drag is presented. Wave breaking fronts are modelled by the discontinuities of the sea-surface slope. It is assumedthat the dynamics of the AFS from wave breaking crests is similar to thatfrom the backward facing step. The form drag supported by an individualbreaker is described by the action of the pressure drop distributed alongthe forward face of the breaking front. The total stress due to the AFS isobtained as a sum of contributions from breaking fronts of different scales.Outside the breaking fronts the drag of the sea surface is supported by theviscous surface stress and the wave-induced stress. To calculate the stressdue to the AFS and the wave-induced stress a physical model of the wind-wavespectrum is used. Together with the model of the air flow described in termsof surface stresses it forms a self-consistent dynamical system for the seasurface-atmosphere where the air flow and wind waves are strongly coupled.Model calculations of the drag coefficient agree with measurements. It is shownthat the dimensionless Charnock parameter (roughness length normalized onthe square of the friction velocity and the acceleration of gravity)increases with the increase of the wind speed in agreement with fieldmeasurements. The stress due to the AFS normalized on the square of thefriction velocity is proportional to the cube of wind speed. At low windsthe viscous surface stress dominates the drag. The role of the form drag,which is the sum of the stress due to the AFS and the wave-induced stress, isnegligible. At moderate and high winds the form drag dominates. At windspeeds higher than 10 m s^-1 the stress supported by the AFS becomescomparable to the wave-induced stress and supports up to 50% of the totalstress.     

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.     

Phase-Averaged Flow Properties Beneath Microscale Breaking Waves

The phase-averaged characteristics of the turbulent velocity fields beneath steep short wind waves are investigated. A scheme was developed to compute the phase of individual wind waves using spatial surface displacement data. This information was used to analyze the two-dimensional velocity data acquired using particle image velocimetry (PIV) in a wind-wave tank. The experiments were conducted at a fetch of 5.5m and at wind speeds that ranged from 4 to 10ms⁻¹. Under these conditions previous studies have shown that a significant percentage of the waves are microscale breaking waves. An analysis of the phase-averaged results suggests under these conditions (short fetches and moderate wind speeds) a wind-driven water surface can be divided into three regions based on the intensity of the turbulence. These are the crests of microscale breaking waves, the crests of non-breaking waves and the troughs of all waves. The turbulence is most intense beneath the crests of microscale breaking waves. In the crest region of microscale breaking waves coherent structures were observed that were stronger and occurred more frequently than beneath the crests of non-breaking waves. Beneath the crests of non-breaking waves the turbulence is a factor of two to three times weaker and beneath the wave troughs it is a factor of six weaker. These findings provide additional support for the hypothesis that approximately two-thirds of the gas and heat fluxes occur across the turbulent wakes produced by microscale breaking waves.     

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.     

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.     

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).     

Visualization of airflow separation over wind-wave crests under moderate wind

An intermittently-smoking smoke-wire was devised to visualize the airflow structure over individual crests of actual wind waves. The device was used under a moderate wind 6 m s^-1 (maximum speed in the vertical cross-section) at a fetch 3.8 m in a wind-wave tunnel. Airflow patterns with separation were clearly visualized over wind-wave crests which were not accompanied by wave breaking characterized by air entrainment. A classification of 41 samples of airflow structures showed that two distinct patterns (with and without separation) exist, with significant frequency of occurrence for each.     

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.     

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.     

Transport rate of drifting snow and the mean wind speed profile

Transport rates, measured by weighing snow blown into a filter fabric trap, were greater over hard snow or ice than for the same wind speed over soft, fresh snow surfaces. Analysis of wind speed profiles from nine blizzards showed that friction between moving particles and the surface was less, and particle speeds were greater over hard surfaces. Transport rates at a given wind speed increased rapidly as aerodynamic roughness decreased in the rough-smooth transition region. Bagnold's theory for bed load transport provided a useful framework for the analysis.     

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.     

海气界面动量通量算法的改进

COARE（Coupled Ocean-Atmosphere Response Experiment）算法是国际上较先进的计算海气界面通量的算法。最新的COARE 3.0算法包含TY01方案和O02方案两种考虑真实海浪状态的海面空气动力学粗糙度方案;当有效波高和谱峰周期缺省时,利用Taylor01风浪特征量参数化方案可对它们进行参数化。在此基础上引入自主设计的WHP（Wind-wave significant wave Height and dominant wave Period）风浪特征量参数化方案和三种海面空气动力学粗糙度方案,即SCOR方案、GW03方案、PYP07方案以及更简单的Andreas12、Vickers15摩擦速度算法,利用NDBC（National Data Buoy Center）浮标数据、解放军理工大学风浪流水槽实验数据,针对中高风速条件（10 m/s≤U₁₀≤25 m/s）比较上述方案对摩擦速度的预测效果。结果表明:WHP方案在COARE 3.0算法中的应用效果优于Taylor01方案,且新引入的SCOR、GW03、PYP07海面粗糙度方案对风浪特征量的观测误差敏感性更小、稳定度更高;水槽实测数据的对比结果表明,WHP方案结合SCOR海面粗糙度方案计算的摩擦速度与实测值最接近;引入其他三种实测数据的检验结果表明,原始COARE 3.0算法会低估摩擦速度,而WHP方案结合SCOR海面粗糙度方案能更准确地预测摩擦速度随10 m风速的增长趋势。      

Response of neutral boundary layers to changes of roughness

When air blows across a change in surface roughness, an internal boundary layer (IBL) develops within which the wind adapts to the new surface. This process is well described for short fetches, > 1 km. However, few data exist for large fetches on how the IBL grows to become a new equilibrium boundary layer where again the drag laws can be used to estimate the surface wind.To study this problem, data have been sampled for two years from four 30-m meteorological masts placed from 0 to 30 km inland from the North Sea coast of Jutland in Denmark. The present analysis is limited to neutral stratification, and the surface roughness is the main parameter. The analysis of wind data and two simple models, a surface layer and a planetary boundary layer (PBL) model, are described.Results from both models are discussed and compared with data analysis. Model parameters have been evaluated and the model sensitivity to those parameters has been investigated. Using the model parameters, a large-scale roughness length has been estimated.Istituto Di Fisica dell' Atmosfera I.F.A. — CNR, Rome, Italy.     

Impact Of Dominant Waves On Sea Drag

The impact of air-flow separation from breaking dominant waves is analyzed.This impact results from the correlation of the pressure drop with theforward slope of breaking waves. The pressure drop is parameterized via thesquare of the reference mean velocity. The slope of breaking waves isrelated to the statistical properties of the wave breaking fronts describedin terms of the average total length of breaking fronts. Assuming that thedominant waves are narrow and that the length of breaking fronts is relatedto the length of the contour of the breaking zone it is shown that theseparation stress supported by dominant waves is proportional to thebreaking probability of dominant waves. The breaking probability of dominantwaves, in turn, is defined by the dominant wave steepness. With thedominant wave steepness increasing, the breaking probability is increasedand so does the separation stress. This mechanism explains wave age (youngerwaves being steeper) and finite depth (the spectrum is steeper in shallowwater) dependence of the sea drag. It is shown that dominant waves support asignificant fraction of total stress (sea drag) for young seas due to theair-flow separation that occurs when they break. A good comparison of themodel results for the sea drag with several data sets is reported.     

On the impact of thermal stability on some rough flow effects over mobile surfaces

Calculations are made of the effects of thermal stability under a range of conditions, over the sea and land, on the physical factors (including the critical wind speed) affecting dust-storm generation, snow drift, and rough sea conditions. The computational procedure involves the surface friction velocity, u _*, and its relation with the aerodynamic roughness over aerodynamically rough, mobile surfaces. The results indicated that even at relatively high wind speeds, thermal effects under extreme advection situations may be significant, particularly for those properties of the agitated surface dependent on u _* ³ and u _* ⁴.     

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。     

Impact of waves on air-sea exchange of sensible heat and momentum

The impact of sea waves on sensible heat and momentum fluxes is described. The approach is based on the conservation of heat and momentum in the marine atmospheric surface layer. The experimental fact that the drag coefficient above the sea increases considerably with increasing wind speed, while the exchange coefficient for sensible heat (Stanton number) remains virtually independent of wind speed, is explained by a different balance of the turbulent and the wave-induced parts in the total fluxes of momentum and sensible heat.Organised motions induced by waves support the wave-induced stress which dominates the surface momentum flux. These organised motions do not contribute to the vertical flux of heat. The heat flux above waves is determined, in part, by the influence of waves upon the turbulence diffusivity.The turbulence diffusivity is altered by waves in an indirect way. The wave-induced stress dominates the surface flux and decays rapidly with height. Therefore the turbulent stress above waves is no longer constant with height. That changes the balance of the turbulent kinetic energy and of the dissipation rate and, hence the diffusivity.The dependence of the exchange coefficient for heat on wind speed is usually parameterized in terms of a constant Stanton number. However, an increase of the exchange coefficient with wind speed is not ruled out by field measurements and could be parametrized in terms of a constant temperature roughness length. Because of the large scatter, field data do not allow us to establish the actual dependence. The exchange coefficient for sensible heat, calculated from the model, is virtually independent of wind speed in the range of 3–10 ms^-1. For wind speeds above 10 ms^-1 an increase of 10% is obtained, which is smaller than that following from the constant roughness length parameterization.The investigation was in part supported by the Netherlands Geosciences Foundation (GOA) with financial aid from the Netherlands Organization for Scientific Research (NWO).     

On the growth rate of wind‐generated waves

Abstract

A new approach to fetch‐limited wave studies is taken in this paper. Using data from five towers arranged along a line from the eastern shore of Lake St Clair, the differential growth between towers is explored as a function of local wave age. It is argued that this method avoids the usual fetch‐limited pitfall of inhomogeneity over long fetches and, in particular, the changes in wind speed downfetch of an abrupt roughness change. It is found that the growth rate decreases uniformly downfetch as the waves approach full development. This differential method leads to a smooth transition from rapidly growing short fetch waves to the asymptotic invariant state of full development. When the variation in wind speed after an abrupt (land to water) roughness change is taken into account, the idea of a universal fetch‐limited growth curve is called into question.     

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.