Estimation of the Exchange Coefficient of Heat During Low Wind Convective Conditions

For the first time, the exchange coefficient of heat C_H has been estimated from eddy correlation of velocity and virtual temperature fluctuations using sonic anemometer measurements made at low wind speeds over the monsoon land atJodhpur (26°18' N, 73°04' E), a semi arid station. It shows strong dependence on wind speed, increasing rapidly with decreasing wind speed, and scales according to a power law C_H = 0.025U₁₀ ^-0.7 (where U₁₀ is the mean wind speed at 10-m height). A similar but more rapid increase in the drag coefficient C_Dhas already been reported in an earlier study. Low winds (<4 m s^-1) are associated with both near neutral and strong unstable situations. It is noted that C_H increases with increasing instability. The present observations best describe a low wind convective regime as revealed in the scaling behaviour of drag, sensible heat flux and the non-dimensional temperature gradient. Neutral drag and heat cofficients,corrected using Monin–Obukhov (M–O) theory, show a more uniform behaviour at low wind speeds in convective conditions, when compared with the observed coefficients discussed in a coming paper.At low wind convective conditions, M-O theory is unable to capture the observed linear dependence of drag on wind speed, unlike during forced convections. The non-dimensional shear inferred from the present data shows noticeable deviations from Businger's formulation, a forced convection similarity. Heat flux is insensitive to drag associated with weak winds superposed on true free convection. With heat flux as the primary variable, definition of new velocity scales leads to a new drag parameterization scheme at low wind speeds during convective conditionsdiscussed in a coming paper.     

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

Although the bulk aerodynamic transfer coefficients for sensible (C _H ) and latent (C _E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C _H and C _E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C _E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s^–1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10^–3 and 1.5 × 10^–3.     

Air-sea bulk transfer coefficients in diabatic conditions

On the basis of recent data for the roughness Reynolds number of the sea surface, and using the Owen-Thomson theory on the transfers of heat and mass between a rough surface and the flow above it, the bulk transfer coefficients of the sea surface have been estimated. For a reference height of 10 m, the neutral-lapse transfer coefficient for water vapor is larger by only a few percent than that for sensible heat. When the wind speed at the 10-m height is u ₁₀>3 m s^–1, the coefficient for sensible heat C _H is larger by about 10% than that for momentum C _D . For u ₁₀<5 m s^–1, however, the value of C _D exceeds the value of C _H , and for u ₁₀=15 m s^–1 it is shown that C _H 0.8C _D . It may be also proposed that 10³ C _D =1.11 to 1.70, 10³ C _E =1.18 to 1.30, and 10³ C _H =1.15 to 1.26 for a range of u ₁₀=4 to 20 m s^–1. A plot of diabatic transfer coefficients versus wind speed is obtained by using a parameter of the sea-air temperature difference. For practical purposes, the coefficients are approximated by empirical formulae.     

Spatio-temporal Variability of Surface-layer Turbulent Fluxes Over the Bay of Bengal and Arabian sea During the ICARB Field Experiment

We report the spatio-temporal variability of surface-layer turbulent fluxes of heat, moisture and momentum over the Bay of Bengal (BoB) and the Arabian Sea (AS) during the Integrated Campaign for Aerosols, gases Radiation Budget (ICARB) field experiment. The meteorological component of ICARB conducted during March – May 2006 onboard the oceanic research vessel Sagar Kanya forms the database for the present study. The bulk transfer coefficients and the surface-layer fluxes are estimated using a modified bulk aerodynamic method, and then the spatio-temporal variability of these air-sea interface fluxes is discussed in detail. It is observed that the sensible and latent heat fluxes over the AS are marginally higher than those over the BoB, which we attribute to differences in the prevailing meteorological conditions over the two oceanic regions. The values of the wind stress, sensible and latent heat fluxes are compared with those obtained for the Indian Ocean Experiment (INDOEX) period. The variation of drag coefficient (C _D ), exchange coefficients of sensible heat and moisture (C _H = C _E ) and neutral drag coefficient (C _DN ) with wind speed is also discussed.

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Bulk transfer coefficient over a snow surface

The drag coefficient C _D and the bulk transfer coefficient for sensible heat C _H over a flat snow surface were determined experimentally. Theoretical considerations reveal that C _D depends on the friction velocity u _* as well as on the geometrical roughness h of the snow surface. It is found that C _D increases with increasing u _* and/or h. The dependency of C _H on u _* and h is so small that it is possible to consider C _H as a constant for practical purposes: C _{H, 1} = 2.0 × 10^–3 for a reference height of 1 m. The bulk transfer coefficient for water vapor is estimated at C _{E, 1} = 2.1 × 10^–3 for a reference height of 1 m.     

Momentum and sensible heat fluxes calculated by the dissipation technique during the Ocean Storms Project

High frequency measurements of wind velocity and temperature were made during the Ocean Storms Project in November 1987. The dissipation method was applied to the resulting time series in order to determine friction velocities,u _*, and the characteristic temperature scale,t _*, at 1-min intervals. These values were then compared to the 1-min mean wind speed and air-sea temperature differences to determine relationships for the drag coefficient (C _d ) and Stanton number (C _h ). The drag coefficient was comparable to other values reported in the literature, although the variation with wind speed was greater than reported by other investigators. An examination of the residual time series indicated a systematic low frequency periodicity of about 2-hr duration which was attributed to a fluctuating wind interacting with the surface gravity wave field. The temperature fluctuations did not produce meaningful estimates ofC _h for stable conditions. For unstable conditions, a value of 1.09±0.02×10^–3 was found.     

Geometric and aerodynamic roughness of sea ice

The aerodynamic drag of Arctic sea ice is calculated using surface data, measured by an airborne laser altimeter and a digital camera in the marginal ice zone of Fram Strait. The influence of the surface morphology on the momentum transfer under neutral thermal stratification in the atmospheric boundary layer is derived with the aid of model concepts, based on the partitioning of the surface drag into a form drag and a skin drag. The drag partitioning concept pays attention to the probability density functions of the geometric surface parameters. We found for the marginal ice zone that the form drag, caused by floe edges, can amount to 140% of the skin drag, while the effect of pressure ridges never exceeded 40%. Due to the narrow spacing of obstacles, the skin drag is significantly reduced by shadowing effects on the leeward side of floe edges. For practical purposes, the fractional sea-ice coverage can be used to parameterize the drag coefficientC _dn, related to the 10 m-wind. C _dnincreases from 1.2 · 10^-3 over open water to 2.8 · 10^-3 for 55% ice coverage and decreases to 1.5 · 10^-3 for 100% ice coverage.Aircraft turbulence measurements are used to compare the model values of C _dnwith measureents. The correlation between measured and modelled drag coefficients results in r ² = 0.91, where r is the correlation coefficient.     

A study of the planetary boundary layer over the polynya downwind of St. Lawrence Island in the Bering Sea using aircraft data

Turbulence data collected with the gust probe system on the NOAA P-3 aircraft over the polynya downwind of St. Lawrence Island in the Bering Sea are used to study the fluxes of heat, momentum, and moisture from the polynya. The data also allow study of the effect of the topography of St. Lawrence Island on the atmospheric boundary-layer flow over the polynya and ultimately on ice production in the polynya. Two cases are studied: one (Feb. 15, 1982) where the topographic effects are minimal and the other (Feb. 18, 1983) where the topographic effects are dominant. Calculation of the surface drag coefficient, C _D, for the Feb. 15, 1982 case over young grey/white ice gave a value of 1.2 × 10^-3, which is in close agreement with previous results. The value of the drag coefficient for the grey/white ice regime on Feb. 18, 1983, where the upstream topography on St. Lawrence Island had an important influence on the flow over the polynya, was 3.2 × 10^-3. It was determined that this higher value was related to the more efficient mixing of momentum downward by turbulent eddies generated by flow over and around the topography. The area-averaged heat transfer coefficient, C _H, over the polynya was on the order of 1.1 × 10^-3 for both days, but there were large variations in heat flux across the polynya due to variations in the flow caused by the topography. Conditional sampling techniques applied to the turbulence data showed that the fractional areas occupied by updrafts and downdrafts were 28% and 36%, respectively, and that these results were within the range of values found in previous studies for over-land and over-ocean conditions.     

Momentum and heat transfers in the surface layer over a frozen sea

Wind and temperature profiles from a 10-m mast were measured over the frozen Baltic Sea. The Monin-Obukhov similarity theory applies well to runs carefully selected according to stationarity criteria. This provides relatively low-scattered results with the roughness length z ₀ 0.04 cm, the drag coefficient C _D 1.5 × 10^-3 and the Stanton number C _H 1.00 × 10^-3 under near-neutral conditions. The roughness length, however, behaves in a peculiar way under intense stratification conditions. The reasons proposed for this could lead to an extension of the theory. The mechanisms for momentum and heat transfers are also examined, revealing that there are two different regimes, the smooth and the rough, for the wall friction but not for the heat transfer. Further, the scatter of the data for momentum and heat transfer under the aerodynamically rough regime can be explained by the distinction between the type of thermal stability conditions.     

Models for estimating offshore winds from onshore meteorological measurements

To understand and estimate wind speed differences across the coastal zone, two models, one theoretical and another semi-empirical, have been developed and verified by available data sets. Assuming that: (1) mean horizontal motion exists across the coastal zone; and (2) the geostrophic wind does not change appreciably at the top of the planetary boundary layer (PBL), the equation of motion in the direction of the wind can be reduced so that 341-01, where U, H, and C _D are wind speed, height of PBL, and drag coefficient over the sea and land, respectively. For practice, C _D SEA has been modified from a formula with U _LAND as the only input. H _SEA may be estimated routinely from known H _{D LAND LAND} and the temperature difference between land and sea, which can be provided by such means as remote sensing from meteorological satellites. For a given coast, Cmay be estimated also. This formula is recommended for weather forecasters. The semiempirical formula is based mainly on the power law wind distribution with height in the PBL. The formula states that 341-02. Simultaneous offshore and onshore wind measurements made at stations ranging from Somalia, near the equator, to the Gulf of Alaska indicated that values of a and b are 2.98 and 0.34 with a correlation coefficient of -0.95. For oceanographic applications, a simplified equation, i.e., 341-03, is also proposed.     

Atmospheric turbulent fluxes over snow

On March 26, 1971, eddy fluxes of momentum, sensible heat and water vapour were measured over Lake Mendota, Wisconsin, U.S.A., which was covered by an extensive snowfall. An evaporation rate of about 0.7mm day^–1 (2.2 mW cm^–2) was detected. Wind speeds were light and the atmosphere near the surface was highly stable. In these conditions, the average sensible heat transfer and Reynolds stress were -0.9 mW cm^–2 and 0.10 dyn cm^–2, respectively. Comparison with measured gradients of wind speed, temperature and humidity yield a drag coefficient of about 0.54 × 10^–3, and bulk transfer coefficients for sensible and latent heat of 0.41 × 10^–3 and 0.78 × 10^–3, respectively, applied to 10-m data. When corrected for the effect of atmospheric stability, these three coefficients become (in the same order) 1.2 × 10^–3, 0.9 × 10^–3 and 2.5 × 10^–3. The errors in these estimates are such that the drag coefficient is not significantly different from that corresponding to an aerodynamically smooth surface, while the heat coefficients are similar to those normally applied over liquid water surfaces.     

Turbulent fluxes of momentum,heat and water vapor in the atmospheric surface layer at sea during ATEX

The vertical turbulent fluxes have been determined during the Atlantic Trade Wind Experiment (ATEX) both by direct and profile methods. The drag coefficient obtained from direct measurements was c _D = 1.39 × 10^–3. A distortion of the wind profile due to wave action could be demonstrated, this produced an increased drag coefficient estimated by the profile method. The dissipation technique using the downwind spectrum gave a lower drag coefficient of 1.26 × 10^–3, probably due to non-isotropic conditions (the ratio of vertical to downwind spectrum at high frequencies scattered considerably with an average of 1 instead of 4/3).From direct measurements, the sensible heat flux showed a poor correlation with the bulk parameter product U, contrary to the heat flux obtained from profiles. It is shown that this is due to the higher frequency part of the cospectrum, say above 0.25 Hz, which contributes more than 50 % of the total flux. Determination of the heat flux from temperature fluctuations by the dissipation method would be in agreement with the direct determination only if the corresponding Kolmogoroff constant were 2.1 instead of 0.8.For the vertical flux of water vapor obtained from profiles, the bulk transfer coefficient was 1.28 × 10^–3.This work was supported by the Deutsche Forschungsgemeinschaft, Schwerpunktprogramm Meeresforschung and later the Sonderforschungsbereich Meeresforschung Hamburg.     

Eddy flux measurements over the ocean and related transfer coefficients

Eddy correlation measurements of vertical turbulent fluxes made during AMTEX 1975 are used to assess the reliability of flux prediction from established bulk transfer relations, using both surface-layer and planetary boundary-layer formulations. The surface-layer formulae predict momentum and latent heat fluxes to an accuracy comparable to the direct eddy correlation method, using transfer coefficients of C _DN (at 10m and in neutral conditions) increasing with wind speed, and a constant C _EN - 1.5 × 10 ^–3 . The data suggest C _CHN , for sensible heat, increases significantly with wind speed and is on average 30% lower than C _CEN The boundary-layer drag coefficient, C _GD , agrees within about 40% of recently published values using a vertically averaged geostrophic wind to the height of the lowest temperature inversion, corrected for trajectory curvature. Values of _* / from which C _CGH is derived, are in excellent agreement if the published values are modified to account for inappropriate surface temperatures used in their derivation. Preliminary values of C _GE are also presented.     

A comparison of airborne eddy correlation and bulk aerodynamic methods for ocean-air turbulent fluxes during cold-air outbreaks

Four bulk schemes (LKB, FG, D and DB), with the flux-profile relationships of Liuet al. (1979), Francey and Garratt (1981), Dyer (1974), and Dyer and Bradley (1982), are derived from the viscous interfacial-sublayer model of Liuet al. These schemes, with stability-dependent transfer coefficients, are then tested against the eddy-correlation fluxes measured at the 50 m flight level above the western Atlantic Ocean during cold-air outbreaks. The bulk fluxes of momentum (), sensible heat (H), and latent heat (E) are found to increase with various von Kármán constants (k _M for k _H forH, andk _E forE). Except that the LKB scheme overestimates by 28% (46Wm^–2), on the average, the fluxes estimated by the four bulk schemes appear to be in fairly good agreement with those of the eddy correlation method (magnitudes of biases within 10% for , 17% forH, and 13% forE). The results suggest that the overall fluxes and surface-layer scaling parameters are best estimated by FG and thatk _H <k _E . On the average, the FG scheme underestimates by 10% (0.032N m^–2) andE by 4% (12Wm^–2), and overestimatesH by 0.3% (0.5W m^–2). The equivalent neutral transfer coefficients at 10 m height of the FG scheme compare well with some schemes of those tested by Blanc (1985).The relative importance of various von Kármán constants, dimensionless gradients and roughness lengths to the oceanic transfer coefficients is assessed. The dependence of transfer coefficients on wind speeds and roughness lengths is discussed. The transfer coefficients for andE agree excellently between LKB and FG. However, the ratio of the coefficient forH of LKB to that of FG, increasing with decreasing stability, is very sensitive to stability at low winds, but approaches the neutral value of 1.25 at high winds.     

Discrepancy and Applicability of Various Similarity Functions in Flux Calculations Under Stable Conditions

Based on data obtained during the Hualhe River Basin Experiment （HUBEX） in 1999, this study intends to detect the quantitative discrepancies in the momentum （τ0）, sensible heat （H0） and latent heat （E0） fluxes among six sets of similarity functions with the aerodynamic method. It also aims to clarify the applicability of the functions under stable conditions. The relative discrepancy was studied with the normalized transfer coefficients for τ0, H0 and E0, namely CD, CH and CQ, respectively. Except for one set of functions that adopted a rather small von Kármán＇s constant （0.365）, the relative discrepancy in τ0 among the other functions was less than 10%, while that in H0（E0） sometimes reached 25% when the bulk Richardson number （R/B） was less than 0.07. The absolute discrepancy in the fluxes was studied with statistical computations. Among the six sets of functions, the discrepancy in τ0, H0 and E0 sometimes reached 0.03 kg m^-1 s^-2, 4 W m^-2 and 10 W m^-2, respectively, and the discrepancy in the energy balance ratio sometimes exceeded 0.1. Furthermore, when RiB exceeded the critical value （Ric） for a specific set of functions, no fluxes could be derived with the functions. It is therefore suggested that RiB be compared with Ric before computing the fluxes if RiB is less than Ric. Finally, two sets of nonlinear similarity functions are recommended, due to their unlimited applicability in terms of RiB.     

Convective heat transfer measurements of plants in a wind tunnel

Heat transfer was studied between intact leaves of various sizes and shapes in vivo under free and forced air conditions. Use of a wind tunnel and a microwave transmitter to heat the leaves facilitated measurements of convective, along with radiative and evaporative, heat losses from plant leaves. Knowledge of input energy, analysis of cooling curves, and established formulae, respectively, formed the basis of the steady-state, unsteady-state, and analytical methods for the determination of heat transfer coefficients.Typical values of steady-state free convection coefficients for Peperomia obtusifolia varied from 1.5 × 10^–4 to 1.9 × 10^–4 cal cm^–2 s^–1 C^–1 as the temperature difference was increased from 5.9 to 9.6°C, whereas the forced convection coefficient was found to be 4.2 × 10^–4 cal cm^–2 s^–1 C^–1 at 122 cm s^–1 wind velocity. For egg-plant, this value was about 9 × 10^–4 cal cm^–2 s^–1 C^–1 at 488 cm s^–1 wind velocity. Convection coefficients as determined under steady-state conditions are compared with those of the unsteady-state and with analytical values for a single leaf and leaves of three different plants. In general, experimental values were found to be higher than the analytical ones.     

The sea surface temperature deviation and the heat flow at the sea-air interface

The deviation of the sea surface temperature from the water temperature below is calculated as a function of the heat flow through the air-sea interface, using wind tunnel determinations of the effective thermal diffusivity in a boundary layer. The influence ofQ, shortwave radiation, andH, latent and sensible heat transfer plus effective back radiation, and U, wind speed, can be described by:T ₀ –T _w =C ₁ ·H/U +C ₂ ·Q/U. The calculated coefficients vary slightly with reference depth, Tables II and III. They are in good agreement with independent observations.On leave at Department of Oceanography, Oregon State University, Corvallis, Oregon in 1969–70.     

Kinetics of the reactions of hydroxyl radicals with aliphatic ethers studied under simulated atmospheric conditions

Rate coefficients have been measured for the reactions of hydroxyl radicals with a range of aliphatic ethers by a competitive technique. Mixtures of synthetic air containing a few ppm of nitrous acid, isobutene and an ether were photolyzed in a Teflon-bag smog chamber. From the rates of depletion of the ether and of the isobutene, and based on the value of the rate coefficient k(OH+i-C₄H₈)=5.26×10^-11 cm³ molecule^-1 s^-1, the following rate coefficients were obtained for the hydroxyl radical reactions at 750 Torr and at 294±2K in units of 10^-12 cm³ molecule^-1 s^-1: diethylether = 12.0±1.1, di-n-propylether = 15.3±1.6, di-n-butylether=17.1±0.9, ethyl n-butylether = 13.5±0.4, ethyl t-butyl-ether = 5.6±0.5, and di-isobutylether = 26.1±1.6. The quoted error limits correspond to 2 standard deviations but do not include any contribution from k(OH+i-C₄H₈) for which the error limits are estimated to be about ±10%. The results are discussed in relation to the available literature data and considered in terms of the structure-activity relation for hydroxyl radical reactions with organic molecules.     

珠海凤凰山森林下垫面干季和湿季气象要素的对比分析与动量和感热交换系数的参数化研究

利用珠海凤凰山陆气相互作用观测塔站2014年11月至2016年5月的观测数据,对比分析了干湿季森林下垫面能量通量和气象要素的变化特征,分析了在不同稳定度下3个风向范围（315°～45°、45°～135°和135°～225°）的动量和感热交换系数随冠层表面风速的变化特征,并对动量和感热交换系数进行了参数化研究。结果表明:干季感热和潜热通量值相当,湿季潜热远大于感热。干季和湿季的夜晚都出现负感热现象,感热从大气向森林输送。相对湿度的变化幅度大,与该地气象状况密切相关,相对湿度的垂直梯度夜晚较大,白天较小。干季的气温垂直梯度比湿季的明显。风速在冬季变化平缓,夏季变化剧烈,低层风速随高度变化梯度明显,高层较紊乱。各高度风向差异不大。中性和近中性状态下,在风向为315°～45°、45°～135°和135°～225°时,动量交换系数C_dn分别为0.05、0.0055和0.022,感热交换系数C_hn分别为0.0055、0.003和0.004。在稳定和不稳定状态下,动量交换系数C_d、感热交换系数C_h随冠层表面风速v明显发生变化,稳定条件下,C_d、C_h随v的增大而增大;不稳定条件下,C_d、C_h随v的增大而减小。分不同风向对森林冠层C_d、C_h在稳定和不稳定条件下与v的关系进行了拟合,得到了参数化公式。     

Etude experimentale d'une relation entre le coefficient de frottement et le facteur de rafales en regime de vent faible et au-dessus d'une surface d'eau

In usual aerodynamic bulk formulas, the drag coefficient C _d has been best estimated in the 5 to 16 m s^–1 range of mean wind velocity; a value of 1.3 × 10^–3 is often considered for operational use. However, in the 0 to 5 m s^–1 range of mean wind velocity, corresponding to meteorological conditions of very light wind, experimental results have not resulted in any convincing agreement between various authors (Hicks et al., 1974; Wu, 1969; Kondo and Fujinawa, 1972; Mitsuta, 1973; Brocks and Krugermeyer, 1970).In the present paper, the drag coefficient is experimentally determined in conditions of very light wind and limited fetch (about 250 m). Due to this limited fetch, we have to be cautious in the extrapolation of our results to other sites. Nevertheless, some of experimental results are worth describing, considering the paucity of data in light wind conditions.Mean value and standard deviation (respectively 1.84 × 10^–3 and 1.24 × 10^–3) are obtained from 70 runs of 10-min duration. Mean wind velocities observed at 2 m above water surface are found to lie between 1.2 and 3.6 m s^–1. Whereas this mean value is in fair agreement with C _{d 10} = 1.3 × 10^–3, usually given for the 5 to 16 m s^–1 range (Kraus, 1972), the above value for the standard deviation seems too large to be left without further analysis.A more exhaustive analysis of the 70 values obtained for C _d shows that it depends on a parameter characteristic of longitudinal fluctuations of the wind velocity. A similar idea was put forward earlier by Kraus (1972). Relations between the drag coefficient and wind fluctuations may be tentatively given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% igdacaGGUaGaaGimaiaaiEdacqGHRaWkcaaIXaGaaGinaiaac6caca% aIZaGaaGinamaalaaabaGaeq4Wdm3aaSbaaSqaaiaadwhacaGGNaaa% beaaaOqaaaaaaiaawIcacaGLPaaaruqqYLwySbacfaGaa8hEaiaa-b% cacaaIXaGaaGimamaaCaaaleqabaGaeyOeI0IaaG4maaaakiaabcca% caqGGaGaaeiiaiaabccacaqGXaGaaeOlaiaabAdacaqGGaGaaeyBai% aabccacaqGZbWaaWbaaSqabeaacaqGTaGaaeymaaaakiabgsMiJkqa% dwhagaqeamaaBaaaleaacaaIYaaabeaakiabgsMiJkaaiodacaGGUa% GaaGOnaiaab2gacaqGGaGaae4CamaaCaaaleqabaGaaeylaiaabgda% aaaaaa!634E!\[C_{d2} = \left( { - 1.07 + 14.34\frac{{\sigma _{u'} }}{{}}} \right)x 10^{ - 3} {\text{ 1}}{\text{.6 m s}}^{{\text{ - 1}}} \leqslant \bar u_2 \leqslant 3.6{\text{m s}}^{{\text{ - 1}}} \] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% iodacaGGUaGaaGioaiaaiAdacqGHRaWkcaaIZaGaaiOlaiaaiodaca% aI2aGaam4raaGaayjkaiaawMcaaerbbjxAHXgaiuaacaWF4bGaa8hi% aiaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaIZaaaaOGaaeilaa% aa!4B42!\[C_{d2} = \left( { - 3.86 + 3.36G} \right)x 10^{ - 3} {\text{,}}\] where _u/\-u ₂ and G, respectively, represent the standard deviation of u normalized with \-u ₂ and the longitudinal gust factor quoted in Smith (1974).We have established a relationship between these fluctuation parameters and the stability as given by a bulk layer Richardson number (between 0 and 2 m). These relations are given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHdpWCdaWgaaWcbaGaamyDaiaacEcaaeqaaaGcbaGabmyDayaaraWa% aSbaaSqaaiaaikdaaeqaaaaakiabg2da9iaaicdacaGGUaGaaGymai% aaikdacqGHRaWkcaaIZaGaaiOlaiaaiIdacaaI1aGaaeiiaiaabkfa% caqGPbWaaSbaaSqaaiaabcdacaqGTaGaaeOmaaqabaaaaa!4802!\[\frac{{\sigma _{u'} }}{{\bar u_2 }} = 0.12 + 3.85{\text{ Ri}}_{{\text{0 - 2}}} \] and G=1.35+14.56 Ri_0–2. The increase in gustiness with stability is in qualitative agreement with Goptarev (1957)'s experimental results.In spite of the high-level correlation between C _d and _u/\-u ₂(G) on the one hand and between _u/\-u ₂(G) and Ri_0–2on the other hand, we found a poor relationship between C _d and Ri_0–2. It is worth noting too that the trend observed here for C _d to increase with stability is in complete disagreement with the usual theoretical expectation for C _d to decrease with increasing layer stability above water.

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E.R.A. du C.N.R.S. n 259.