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.     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

Vertical velocity field in the convective boundary layer as observed with an acoustic Doppler sodar

The morning development of the daytime convective boundary layer (CBL) during fine weather has been observed with an acoustic Doppler sodar of the C.R.P.E. In particular, the vertical profile of the vertical velocity third-order statistic W* ³ has been obtained. This quantity is a maximum near 0.3z _I where z _I, is the height of the CBL. The histogram of vertical velocity in the CBL shows a relationship between W ³ and the convective velocity W _* and is useful for convective plume determination.     

A generalized scaling for convective shear flows

During the last two decades, different scalings for convective boundary layer (CBL) turbulence have been proposed. For the shear-free regime, Deardorff (1970) introduced convective velocity and temperature scales based on the surface potential temperature flux,Q _s , the buoyancy parameter, , and the time-dependent boundary-layer depth,h. Wyngaard (1983) has proposed decomposition of turbulence into two components, bottom-up (b) and top-down (t), the former characterized byQ _s , the latter, by the potential temperature flux due to entrainment,Q _h . Sorbjan (1988) has devised height-dependent velocity and temperature scales for both b- and t-components of turbulence.Incorporating velocity shear, the well known similarity theory of Monin and Obukhov (1954) has been developed for the atmospheric surface layer. Zilitinkevich (1971, 1973) and Betchov and Yaglom (1971) have elaborated this theory with the aid of directional dimensional analysis for a particular case when different statistical moments of turbulence can be alternatively attributed as being of either convective or mechanical origin.In the present paper, we attempt to create a bridge between the two approaches pointed out above. A new scaling is proposed on the basis of, first, decomposition of statistical moments of turbulence into convective (c), mechanical (m) and covariance (c&m) contributions using directional dimensional analysis and, second, decomposition of these contributions into bottom-up and top-down components using height-dependent velocity and temperature scales. In addition to the statistical problem, the scaling suggests a new approach of determination of mean temperature and velocity profiles with the aid of the budget equations for the mean square fluctuations.Notation ATL alternative turbulence layer - CBL convective boundary layer - CML convective and mechanical layer - FCL free convection layer - MTL mechanical turbulence layer     

SURFACE-LAYER SCALING FOR THE CONVECTION-INDUCED STRESS REGIME

The Prandtl, Obukhov, and Monin andObukhov similarity theories are widely used todescribe the structure of turbulence in theatmospheric surface layer. Currently it isunderstood that in strong convection with no or veryweak mean wind the traditional theory breaks down.In particular, the traditional theory implies asingle-valued correspondence between localturbulence statistics and local properties ofthe flow. In very strong convection, this is nottrue because of large-scale ( 10 3 m) coherentstructures, embracing the entire convective boundarylayer (CBL). These structures produce random guststhat crucially affect surface-layer turbulence andmake it dependent on global properties of theflow, such as the CBL depth. In the present paperthe limits of validity of the traditional surface-layer similarity theory are determined and a revisedtheory of fair weather convection in the surface layeris developed by considering the effect of gustiness. It is shownthat the theoretical predictions are consistent withfield data from the TOGA COARE and SCOPEexperiments.     

风切变对边界层对流影响的大涡模拟研究

利用"西北干旱区陆-气相互作用野外观测实验"加密观测期间在敦煌站的观测资料以及大涡模式,模拟了对流边界层的发展,以及示踪物从混合层向残留层传输的时空变化。模拟的对流边界层的结构及演变特征与实测结果基本一致。进一步通过有风切变和无风切变的敏感性数值试验,研究了风切变对垂直速度、位温和示踪物浓度的水平分布以及示踪物传输高度的影响。研究结果表明,在有风切变的试验中(甚至风切变仅存在于近地层中),对流边界层的增长加强,而且示踪物被传输的高度也较高。与浮力驱动的对流边界层相比,由浮力和风切变共同驱动的边界层中上升气流较弱而下沉气流较强,但前者的上升气流与下沉气流的分布在垂直方向上更为倾斜。由于夹卷作用的增强,浮力和风切变共同驱动的对流边界层较浮力驱动的对流边界层暖。在夹卷层,浮力和风切变共同驱动的边界层对流的上升气流和下沉气流都比浮力驱动的边界层对流中的强,而且垂直速度的概率密度函数分布也较对称,其位温和示踪物浓度的概率密度函数分布也比浮力驱动的边界层中的平直。对湍流动能收支的分析也表明风切变对湍流动能有重要影响,尤其对夹卷层中的湍流动能切变产生项影响较大。示踪物浓度的概率密度函数垂直分布显示,浮力驱动的边界层中示踪物浓度随高度变化较小,而浮力和风切变共同驱动的边界层中示踪物浓度随高度递减,但是示踪物传输的高度比较高。     

A Simple Mixing Length Formulation for the Eddy-Diffusivity Parameterization of Dry Convection

In this paper a simple mixing length formulation for the eddy-diffusivityparameterization of dry convection is suggested. The new formulation relates the mixinglength to the square root of the turbulent kinetic energy (e) and a time scale ( ):l = e. To close the parameterization the time scale is calculated as a functionof the boundary-layer height (h) and the convective velocity scale (w_*), h/w_*. Thesimpler approach of a constant time scale is also studied. The simulation of a case of dry atmosphericconvection with a one-dimensional boundary-layer model shows that the model with the new formulationreproduces quite well the main properties of the convective boundary layer. In particular,the entrainment is realistically represented by the new mixing length, which has the advantage of naturallydecreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapserate, in the context of a simplified situation, show the robustness of the new formulation.     

A saline laboratory model of the planetary convective boundary layer

A laboratory water-analog of clear-air penetrative convection in the atmosphere has been constructed to continue studies of the turbulent dispersion of buoyant plumes in the convective boundary layer (CBL). A unique feature is the utilization of saline rather than thermal convection, which has been made possible by the development of a reliable method for delivering a controllable buoyancy flux through a porous membrane. It has been shown in an earlier paper that at typical laboratory scales, a saline convection tank is well suited to modelling buoyant plume dipersion under strongly convective (light wind) conditions.A range of experiments has clearly demonstrated the validity of the model. Results for density and velocity variances show much less scatter than most comparable measurements because of the greatly improved sampling that is possible in the tank. The results are generally in good agreement with field data and other laboratory simulations but the improved accuracy of the data has highlighted the anomalously low values for the horizontal velocity variances produced by large-eddy simulations of the CBL. The cause of this apparent underprediction remains unresolved.     

Numerical simulation of turbulent convective flow over wavy terrain

By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude up to 0.15H and wavelength ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz _o=10^–4 H. The mean wind is varied between zero and 5w _*, wherew _* is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with /H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w _*>2.     

论边界层中的大气扩散PDF模式

基于大气扩散Ｋ理论，用作为风速脉动均方差和拉氏时间尺度函数的湍流交换系数，得到了直接利用风速脉动几率密度而不用扩散参数的大气扩散ＰＤＦ模式。分别研究了对流边界层上升气流区与下降区垂直速度的统计特征，求得双正态ＰＤＦ模式。在给定ＣＢＬ自身参数如对流特征速度ｗ＊，顶高ｈｉ和源高度上的平均风速时，该模式计算出的无量纲浓度分布与室内外测试结果一致。     

Similarity scaling applied to sodar observations of the convective boundary layer above an irregular hill

Nine profiles of the temperature structure parameter C _T ² and the standard deviation of vertical velocity fluctuations ( _w) in the convective boundary layer (CBL) were obtained with a monostatic Doppler sodar during the second intensive field campaign of the First ISLSCP Field Experiment in 1987. The results were analyzed by using local similarity theory. Local similarity curves depend on four parameters: the height of the mixed layer (z _i ), the depth of the interfacial layer (), and the temperature fluxes at the top of the mixed layer (Q _i ) and the surface (Q _o). Values of these parameters were inferred from sodar data by using the similarity curve for C _T ² and observations at three points in its profile. The effects of entrainment processes on the profiles of C _T ² and _wnear the top of the CBL appeared to be described well by local similarity theory. Inferred estimates of surface temperature flux, however, were underestimated in comparison to fluxes measured by eddy correlation. The measured values of _wappeared to be slightly smaller than estimates based on available parmeterizations. These discrepancies might have been caused by experimental error or, more likely, by the distortion of turbulence structure above the site by flow over the nonuniform terrain at the observation site.     

Parameterization of Sheared Entrainment in a Well-developed CBL.Part Ⅱ:A Simple Model for Predicting the Growth Rate of the CBL

Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. (2016), the present study aims to further investigate the characteristics of entrainment, and develop a simple model for predicting the growth rate of a well-developed and sheared CBL. The relative stratification, defined as the ratio of the stratification in the free atmosphere to that in the entrainment zone, is found to be a function of entrainment flux ratio (A _e). This leads to a simple expression of the entrainment rate, in which A _e needs to be parameterized. According to the results in Liu et al. (2016), A _e can be simply expressed as the ratio of the convective velocity scale in the sheared CBL to that in the shear-free CBL. The parameterization of the convective velocity scale in the sheared CBL is obtained by analytically solving the bulk model with several assumptions and approximations. Results indicate that the entrainment process is influenced by the dynamic effect, the interaction between mean shear and environmental stratification, and one other term that includes the Coriolis effect. These three parameterizations constitute a simple model for predicting the growth rate of a well-developed and sheared CBL. This model is validated by outputs of LESs, and the results show that it performs satisfactorily. Compared with bulk models, this model does not need to solve a set of equations for the CBL. It is more convenient to apply in numerical models.     

日间对流边界层中的非局地动量混合

日间对流边界层最显著的结构特征是在热力作用下所形成的组织化对流。与小尺度湍涡不同的是,组织化对流具有边界层尺度的垂直相干性,可实现垂直贯穿边界层的非局地物质和能量传输。本文针对对流边界层中的动量混合,探究组织化对流对动量输送的贡献。以高精度大涡模拟数据为研究资料,通过傅里叶变换、本征正交分解和经验模态分解3种滤波方法,分离组织化对流和背景湍涡,计算与两者相关的非局地和局地动量通量,发现与组织化对流相关的非局地动量通量是总通量的重要组成部分,并主导混合层中的垂直动量输送。而后,基于协谱和相位谱分析,探究组织化对流的空间结构对动量传输的影响,发现在热力主导的不稳定环境中,单体型环流结构对动量的传输效率较低。而在风切较强的近中性环境中,滚涡型组织化结构可使垂直和水平流向扰动速度的相位差减小,从而提升动量传输效率。研究结果表明,边界层方案需要包含非局地动量通量项,其参数化应考虑整体稳定度对传输效率的影响。     

Interaction between the atmospheric and oceanic boundary layers

The two-layer system of an atmosphere over water bodies is reduced to a single-layer problem. Values of the interfacial quantities, such as the friction velocity, the surface velocity, the angles, and , between the surface shear stress and the geostrophic wind velocity and the surface wind velocity, respectively, and the surface roughness, all of which depend upon external parameters, such as the geostrophic wind and stratifications, are obtained. The geostrophic drag coefficient C _d, the geostrophic wind coefficient C _f, and the angles , and , of the turbulent flow at the sea-air interface are functions of a dimensionless number, mfG/kg, with S ₁ and S ₂ as two free stratification parameters. The surface roughness is uniquely determined from the geostrophic wind rather than from the wind profile in the boundary layer.Formerly Visiting Research Associate, Applied Physics Branch, Earth Observations Division, NASA-Manned Spacecraft Center, Houston, Texas.     

Airflow over a mountain and the convective boundary layer

In this paper, the analytical model coupling the convective boundary layer (CBL) with the free atmosphere developed by Qi and Fu (1992) is improved. And by this improved model, the interaction between airflow over a mountain and the CBL is further discussed. The conclusions demonstrate: (1) The perturbation potential temperatures in the free atmosphere can counteract the effect of orographic thermal forcing through entraining and mixing in the CBL. If _M > _F , the feedback of the perturbation potential temperatures in the free atmosphere is more important than orographic thermal forcing, which promotes the effect of interfacial waves. If _M < _F , orographic thermal forcing is more important, which makes the interfacial height and the topographic height identical in phase, and the horizontal speeds are a maximum at the top of the mountain. (2) The internal gravity waves propagating vertically in the free atmosphere cause a strong downslope wind to become established above the lee slope in the CBL and result in the hydraulic jump at the top of the CBL. (3) With the CBL deepening, the interfacial gravity waves induced by the potential temperature jump at the top of the CBL cause the airflow in the CBL to be subcritical.     

A laboratory study of the turbulent velocity characteristics in the convective boundary layer

Based on the measurement of the velocity field in the convective boundary layer （CBL） in a convection water tank with the particle image velocimetry （PIV） technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal＇s motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity wi^2/w＊^2. at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity （w＊）.     

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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Parameterization of sheared entrainment in a well-developed CBL. Part I: Evaluation of the scheme through large-eddy simulations

The entrainment flux ratio A _e and the inversion layer (IL) thickness are two key parameters in a mixed layer model. A _e is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of A _e is derived from the TKE budget in the firstorder model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness. The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized A _e and IL thickness agree well with the LES outputs.     

Convective Profile Constants Revisited

This paper examines the interpolation betweenBusinger–Dyer (Kansas-type) formulae,_u = (1 -1 6 )^-1/4 and_t = (1 - 16 )^-1/2, and free convection forms. Based on matching constraints, the constants, a_u and a_t, in the convective flux-gradient relations, _u = (1 - a_u )^-1/3 and _t = (1 - a_t )^-1/3, are determined. It isshown that a_u and a_t cannot be completely independent if convective forms are blended with theKansas formulae. In other words, these relationships already carryinformation about a_u and a_t. This follows because the Kansas relations cover a wide stability range (up to = - 2), which includes a lower part of the convective sublayer (about 0.1 < - < 2). Thus, there is a subrange where both Kansas and convective formulae are valid. Matching Kansas formulae and free convection relations within thesubrange 0.1 < - < 2 and independently smoothing ofthe blending function are used to determine a_u and a_t. The values a_u = 10 for velocity and a_t = 34for scalars (temperature and humidity) give a good fit. This new approacheliminates the need for additional independent model constants and yields a`smooth' blending between Kansas and free-convection profileforms in the COARE bulk algorithm.     

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.