Impact of the Diurnal Cycle of the Atmospheric Boundary Layer on Wind-Turbine Wakes: A Numerical Modelling Study

The wake characteristics of a wind turbine for different regimes occurring throughout the diurnal cycle are investigated systematically by means of large-eddy simulation. Idealized diurnal cycle simulations of the atmospheric boundary layer are performed with the geophysical flow solver EULAG over both homogeneous and heterogeneous terrain. Under homogeneous conditions, the diurnal cycle significantly affects the low-level wind shear and atmospheric turbulence. A strong vertical wind shear and veering with height occur in the nocturnal stable boundary layer and in the morning boundary layer, whereas atmospheric turbulence is much larger in the convective boundary layer and in the evening boundary layer. The increased shear under heterogeneous conditions changes these wind characteristics, counteracting the formation of the night-time Ekman spiral. The convective, stable, evening, and morning regimes of the atmospheric boundary layer over a homogeneous surface as well as the convective and stable regimes over a heterogeneous surface are used to study the flow in a wind-turbine wake. Synchronized turbulent inflow data from the idealized atmospheric boundary-layer simulations with periodic horizontal boundary conditions are applied to the wind-turbine simulations with open streamwise boundary conditions. The resulting wake is strongly influenced by the stability of the atmosphere. In both cases, the flow in the wake recovers more rapidly under convective conditions during the day than under stable conditions at night. The simulated wakes produced for the night-time situation completely differ between heterogeneous and homogeneous surface conditions. The wake characteristics of the transitional periods are influenced by the flow regime prior to the transition. Furthermore, there are different wake deflections over the height of the rotor, which reflect the incoming wind direction.     

On eddy convection velocity in the atmospheric boundary layer

Lumley's model is extended to predict the effect of convection velocity fluctuations on eddy convection velocity for the high-frequency region of the longitudinal, transverse and scalar phase spectra in the atmospheric boundary layer. The resulting model predicts that the eddy convection velocity will be higher than the mean wind speed. The increase over the mean wind speed is largest for the longitudinal spectrum.     

中国冷季高架对流个例初步分析

通过对3个中国冷季高架对流个例进行详细分析,试图揭示中国冷季不同类型高架对流在环境背景、雷达回波结构、产生的天气类型和主要形成机理方面的主要特征,包括共同点和差异。利用常规高空和地面观测、NCEP分析和雷达回波资料,采用对不同类型多个典型个例分析的方法进行研究。首先给出了中国冷季高架对流的定义,然后分别仔细分析了3个不同类型冷季高架对流个例,探讨他们各自的环境背景特征,生成与发展机理,对他们的相同点和差异进行了对比。3个个例的共同特点是斜压性和深层风垂直切变都很强,对流发生区在地面锋面冷区一侧数百千米。不同点是前2个个例为条件不稳定结合水汽和抬升触发等条件导致的垂直对流,低层暖平流都很强,但对流有效位能差异很大,对流强度和导致的天气差异很大。第3个个例为条件对称不稳定结合水汽等条件形成的倾斜对流个例,倾斜对流区在地面锋面以北500-600 km处,冷垫非常深厚。第1个例子于2012年2月27日发生在华南,最不稳定气块对流有效位能只有100 J/kg左右,深层风垂直切变很强,850-700 hPa的辐合切变线触发了该高架对流,对流较弱,最强反射率因子在40-45 dBz,只产生了雷电、霰和小冰雹。第2个例子于2007年3月30日晚上出现在山东半岛,最不稳定气块对流有效位能达1400 J/kg,0-6 km风垂直切变（风矢量差）达32 m/s,形成数个结构类似超级单体的对流风暴,多个多单体强风暴,和大量多单体风暴,最强反射率因子将近70 dBz,导致6个站出现冰雹,其中1个站观测到直径23 mm的大冰雹,另1个站点出现21 m/s对流大风。其最有可能的触发机制是以泰山为中心的山地激发出来,在低层为稳定层,以上为深层条件不稳定层和强风垂直切变环境下形成的较大振幅俘获中尺度重力波。该俘获重力波可能还对对流生成后对流的组织形态和对流群的整体结构具有显著调制作用。最后1个例子是发生在2008年1月中国南方大范围冰冻雨雪期间1月27日安徽、江苏和浙江的区域性大暴雪,分析表明,条件对称不稳定导致的倾斜对流是产生此次大暴雪的主要原因之一。      

经典Ekman流,Ekman层的平衡风场及其扰动稳定性

本文首先利用变分方法,考察了边界层运动能量的变化,指出经典Ekman流是在不可压缩条件下,能量积分达最小值时的一种平衡运动。这对Ekman层运动的物理本质有了进一步的认识。其次,讨论了Ekman动量近似下的Ekman层的平衡风场特征,研究了该平衡风场附近扰动的稳定性问题,结果表明,在自由大气气压场不发生扰动条件下,Ekman层中存在一类新的与惯性不稳定相类似的动力不稳定,且其不稳定性可与Ekman抽吸相联系,还讨论了一般性条件下的扰动不稳定性问题。     

Turbulence Structure of Stable Boundary Layers with a Near-Linear Temperature Profile

By using a thermally stratified wind tunnel, we have successfullysimulated stably stratified boundary layers (SBL), in which the meantemperature increases upward almost linearly. We have investigated the flow structure and the effects of near-linearstable stratification on the transfer of momentum and heat. Thevertical profiles of turbulence quantities exhibit different behaviour in two distinct stability regimes of the SBLflows with weak and strong stability. For weak stability cases, theturbulent transfer of momentum and heat is basically similar to that for neutral turbulent boundary layers, although it is weakenedwith increasing stability. For strong stability cases, on the other hand,the time-mean transfer is almost zero over the whole boundary-layer depth.However, the instantaneous turbulent transfer frequently occurs in bothgradient and counter-gradient directions in the lower part of the boundary layer. This is due to the Kelvin–Helmholtz (K–H) shear instability and therolling up and breaking of K–H waves. Moreover, the internal gravity wavesare observed in the middle and upper parts of all stable boundary layers.     

Ekman动量近似下中间边界层模式中的风场结构

发展了一个准三维的、中等复杂的边界层动力学模式，该模式包含了EKman动量近似下的惯性加速度和Blackadar的非线性湍流粘性系数，它进一步改进了Tan和Wu(1993）提出的边界层理论模型。该模型在数值计算复杂性上与经典Ekman模式相类似，但由于包含了Ekman动量近似下的惯性项，使得该模式比传统Ekman模式更近于实际过程。中详细地比较了该模式与其他简化边界层模式在动力学上的差异，结果表明：在经典的Ekman模式中，由于忽略了流动的惯性项作用，导致在气旋性切变气流（反气旋性切变气流）中风速和边界层顶部的垂直速度的高估（低估），而在半地转边界层模式中，由于高估了流动惯性项的作用，结果与经典Ekman模式相反。同样，该模式可以应用于斜压边界层，对于Ekman动量下的斜压边界层风场同时具有经典斜压边界层和Ekman动量近似边界层的特征。     

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。     

Observations of mesoscale cellular convection from the marine stratocumulus phase of “fire”

A common mode of convection within the atmospheric boundary layer, mesoscale cellular convection (MCC), assumes the form of an organized array of three-dimensional polygonal cells. This study employs aircraft data, collected off the coast of California during the marine stratocumulus phase of the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment (FIRE), to investigate the closed cell variety of MCC. Forty-five transects of closed marine mesoscale convective cells are utilized in this study. Data from these transects are used to calculate first-order and scale-dependent second-order kinematic, thermodynamic, and radiation statistics. From these statistics, a conceptual model of closed MCC is constructed detailing the horizontal and vertical structure of the cells in coupled as well as decoupled boundary-layer environments.Mesoscale convective cells not only have a profound influence on the radiation budget of their environment, but also play a key role in governing the exchange of heat, moisture, and momentum between the atmosphere and the surface. During FIRE, the MCC-scale structures were found to be buoyantly-driven above cloud base and driven by perturbation pressure forces below. Microscale eddies generally worked in tandem with these MCC-scale structures to transport heat and moisture vertically throughout the cells. Microscale eddies were responsible for most of this transport within the surface layer, while MCC-scale structures performed most of the transport at mid-levels within the cells.     

Buoy and satellite observations of mesoscale cellular convection during AMTEX 75

Buoy and satellite observations of mesoscale cellular convection (MCC) over the East China Sea in the vicinity of the Kuroshio current have been made during 14–18 February 1975, as a part of the Air Mass Transformation Experiment (AMTEX). Surface observations of solar radiation from spar buoys indicate the distinct passage of open and closed MCC that formed and continued for three consecutive days during an outbreak of cold polar air over the much warmer Kuroshio. A critical air-sea temperature of –5 °C for the occurrence of MCC has been substantiated. The time required for the passage of solar radiation peaks coupled with the buoy wind speed gave a computed closed cell diameter of 28 km, comparable to estimates from satellite photographs.The horizontal component of wind beneath the cloudy portion of a closed cell, due to convection, has been estimated as 0.6 m s^–1. This represents the speed at which air near the sea surface moves from the edge toward the center of a closed cell. Also, the temperature difference obtained near the sea surface between the relatively cold descending branch and the warm ascending branch is 0.2°C. Similarly, the specific humidity difference of the less moist descending air near the edge and the moist ascending air near cell center is 9% (0.4 g/kg). Some indications were also found in the variation of horizontal wind direction with the passage of closed cells, since wind variations at the edge of passing cells exceeded the mean sequential variability (10.6 ° compared to 9.4 °).Sensible heat flux calculations associated with closed MCC suggest that strong surface heating can be associated with closed cells, previously reported by Hubert (1966) to be a characteristic of only open cells.Finally, the results of this study should remove any disclaimers that MCC appear in satellite photography simply because of a resolution bias and that the consideration of all visible clouds actually present would remove any periodicity one might expect to see in surface observations.     

Observations of the barotropic Ekman layer over an urban terrain

Data from low-level soundings over Cambridge, U.S.A. were selected on the basis of an Ekman-like variation of the wind vector with altitude combined with evidence of a barotropic atmosphere. The method of geostrophic departure was used to determine the shear-stress distribution. The analysis yields the dimensionless properties of the barotropic Ekman layer under neutral and stable stratification. Some important results include: the geostrophic drag coefficient displays no dependence on the degree of static stability; the dimensionless height of the boundary layer decreases with increasing stability in agreement with the prediction of Zilitinkevich; the properties of the urban surface layer, where the roughness elements are multistory buildings, show no dependence on atmospheric stability under the moderate wind conditions which display the Ekman-like wind profile; and the directions of the horizontal shear stress and the vertical derivative of the velocity vector usually tend to be parallel only near the surface layer. Values of the two constants of the Rossby number similarity theory are found for the neutral barotropic Ekman layer at a surface Rossby number equal to 2 × 10⁵. The implications of the work with respect to wind-tunnel simulation of the flow over models of urban areas are discussed.     

SIMULATION OF BOUNDARY LAYER EFFECTS ON A HEAVY RAINFALL EVENT CAUSED BY A MESOSCALE CONVECTIVE SYSTEM OVER THE YELLOW RIVER MIDSTREAM AREA

A heavy rainfall event caused by a mesoscale convective system (MCS), which occurred over the Yellow River midstream area during 7–9 July 2016, was analyzed using observational, high-resolution satellite, NCEP/NCAR reanalysis, and numerical simulation data. This heavy rainfall event was caused by one mesoscale convective complex (MCC) and five MCSs successively. The MCC rainstorm occurred when southwesterly winds strengthened into a jet. The MCS rainstorms occurred when low-level wind fields weakened, but their easterly components in the lower and boundary layers increased continuously. Numerical analysis revealed that there were obvious differences between the MCC and MCS rainstorms, including their three-dimensional airflow structure, disturbances in wind fields and vapor distributions, and characteristics of energy conversion and propagation. Formation of the MCC was related to southerly conveyed water vapor and energy to the north, with obvious water vapor exchange between the free atmosphere and the boundary layer. Continuous regeneration and development of the MCSs mainly relied on maintenance of an upward extension of a positive water vapor disturbance. The MCC rainstorm was triggered by large range of convergent ascending motion caused by a southerly jet, and easterly disturbance within the boundary layer. While a southerly fluctuation and easterly disturbance in the boundary layer were important triggers of the MCS rainstorms. Maintenance and development of the MCC and MCSs were linked to secondary circulation, resulting from convergence of Ekman non-equilibrium flow in the boundary layer. Both intensity and motion of the convergence centers in MCC and MCS cases were different. Clearly, sub-synoptic scale systems in the middle troposphere played a leading role in determining precipitation distribution during this event. Although mesoscale systems triggered by the sub-synoptic scale system induced the heavy rainfall, small-scale disturbances within the boundary layer determined its intensity and location.     

边界层对流对示踪物抬升和传输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"加密观测期间敦煌站的实测资料以及大涡模式, 通过一系列改变地表热通量和风切变的敏感性数值试验, 分析了地表热通量和风切变对边界层对流的强度、形式, 以及对对流边界层结构和发展的影响。模拟结果显示风切变一定, 增大地表热通量时, 由于近地层湍流运动增强, 向上输送的热量也较多, 使对流边界层变暖增厚, 而且边界层对流的强度明显增强, 对流泡发展的高度也较高。当地表热通量一定, 增大风切变时, 由于风切变使夹卷作用增强, 将逆温层中的暖空气向下卷入混合层中, 使对流边界层增暖增厚, 但是对流泡容易破碎, 对流的强度也较弱。另外通过在模式近地层释放绝对浓度为100的被动示踪物方法, 用最小二乘法定量地分析了地表热通量和风切变分别与示踪物抬升效率和传输高度的关系。分析结果表明, 风切变小于10.5×10-3 s-1时, 增大地表热通量加强了上层动量的下传, 使示踪物的抬升效率也线性增大;地表热通量小于462.5 W m-2时, 增大风切变减弱了边界层对流的强度, 从而使示踪物的抬升效率减弱。当风切变一定时, 示踪物的平均传输高度随地表热通量增加而增大, 而地表热通量一定, 只有风切变大于临界值时, 示踪物平均传输高度才随风切变的增加而增大, 而临界风速的大小由地表热通量决定。     

大气静力稳定度的铅直分布和不同风速铅直廓线对天气系统发展的影响

采用一个准地转三层模式,对于高低空不同层结及不同风速铅直廓线下的斜压不稳定性问题进行了分析和讨论。指出:(1)大气层结特征对斜压不稳定的影响不仅表现在对不稳定临界波长和临界风速切变的制约上,而且其铅直分布的不均一性决定了大气的各个层次对斜压不稳定的贡献大小;扰动的斜压发展主要取决于静力稳定度较小的那些层次内的热力、动力学条件,在这些层次内,扰动也最为明显。(2)高低空风速比中空为大的“高低空强风型”风速铅直分布最有利于扰动的不稳定发展,在这种风速铅直廓线下,不稳定波波谱较宽,不稳定波临界波长和最不稳定波波长也较短。     

Inertially coupled Ekman layers

The inertial coupling model of the surface shear stress at the sea surface (Bye, 1995) which takes account of the surface wavefield, has been applied to couple the Ekman layers of the ocean and atmosphere. We determine the surface shear stress and geostrophic drag coefficient, under barotropic conditions. The results are expressed in terms of the shear between the inertially weighted (i.e. velocity×square root of the density) relative geostrophic velocities in the two fluids, in which the reference velocity need not be specified, a priori. We find, in particular, that the deflection of the relative surface geostrophic wind to the surface shear stress in naturally occurring seastates, is about 9°. In the application of the analysis to general circulation models, it is argued that, since the inertially weighted relative geostrophic velocities in air and water are of similar magnitude, this implies that the surface shear stress can be significantly reduced by the current component of the inertially weighted geostrophic shear, with a corresponding reduction in importance of the Ekman transport.     

一次东北冷涡暴雨过程中尺度及云物理特征分析

本文利用WRF数值模式对2019年7月16日发生在东北冷涡底部的暴雨过程进行数值模拟,使用常规观测资料、卫星云图和数值模拟结果对此次暴雨过程的中尺度及云物理特征进行分析。结果表明：东西两个暴雨区分别由MCC和MCS活动造成的。MCC发展的环境具有低层更暖湿高层更干冷,对流不稳定更强,垂直风切变更大的特点,有利于酝酿更强的风暴。降水回波与地面辐合线同时出现,共同移动,两者有正反馈作用。与西部回波相对应的辐合线辐合更强,北侧偏北风风速更大,移动更快,对应的强降水范围更小、时段更集中。而东部暴雨区相对应的辐合线两侧风速均较小,呈准静止态,回波长时间在辐合线附近维持,列车效应形成暴雨,对应的强降水范围较大、持续时间更长。降水过程中霰和雪是对流云中主要的降水粒子,并通过冷云增长；雨水的增长主要依赖于霰和雪的融化,其次还有暖云中云水的碰并增长。     

A parameterization of the stable atmospheric boundary layer

Two formulations of the stable atmospheric boundary layer are proposed for use in weather forecasting or climate models. They feature the log-linear profile near the surface, but are free from the associated critical Richardson number. The diffusion coefficients in the Ekman layer are a natural extension of the surface layer. They are locally determined using wind shear in one case and turbulent kinetic energy in the other. The parameterizations are tested in a one-dimensional model simulating the evolution of the nocturnal boundary layer with and without radiative cooling. Both formulations give very similar results, except near the top of the boundary layer where the transition to the free atmosphere is smoother with the wind shear formulation. A distinctive feature of these schemes is that they retain their simulating skill when resolution is reduced. This is verified for a wide range of situations. In practice, this means that there is no need for a large-scale model to have a level below 50 m or so.     

Numerical Simulation of Roll Vortices in the Convective Boundary Layer

Roll vortices,which often appear when cold air outbreaks over warm ocean surfaces,are an important system for energy and substance exchange between the land surface and atmosphere.Numerical simulations were carried out in the study to simulate roll vortices in the convective boundary layer(CBL).The results indicate,that with proper atmospheric conditions,such as thermal instability in the CBL,stable stratification in the overlying layer and suitable wind shear,and a temperature jump between the two layers in a two-layer atmosphere,convective bands appear after adding initial pulses in the atmosphere.The simulated flow and temperature fields presented convective bands in the horizontal and roll vortices in the crosswind section. The structure of the roll vortices were similar to those observed in the cloud streets,as well as those from analytical solutions.Simulations also showed the influence of depth and instability strength of the CBL, as well as the stratification above the top of the CBL,on the orientation spacing and strength of the roll vortices.The fluxes caused by the convective rolls were also investigated,and should perhaps be taken into account when explaining the surface energy closure gap in the CBL.     

Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift

Recent technological advances in current measuring devices has resulted in a large observational database related to wind-driven motions in the upper ocean mixed layer. This has served to highlight the fact that transient motions make up a substantial contribution of the resulting Ekman currents. At the same time, certain discrepancies have emerged between the observed angular deflections of the steady-state currents from the surface wind stress, both at the surface and at sub-surface depths, which cannot be reconciled using the classical Ekman model. This paper seeks to tackle these two issues.First a general analytical method is presented for solving the time dependent horizontal momentum Ekman equations. Analysis of the unsteady terms that arise from simple special cases shows how the evolution proceeds through three stages. At early times, the Coriolis acceleration is insignificant, and the current is unidirectional and deepens through downward diffusion of momentum. Later Coriolis acceleration deflects the current vectors in the upper layers, whilst downward diffusion of momentum continues to deepen the layer. Finally, once diffusion has penetrated down to the depth of the steady-state current, then the transients decay on the inertial or diffusive timescale, depending upon the boundary conditions of the particular problem.In the second half of the paper, a new steady-state model is developed that includes the effects of wind-generated waves, through the action of their Stokes drift on the planetary vorticity. Comparisons between observations and the theoretical predictions, demonstrate that inclusion of the Stokes drift is the key to reconciling the discrepancies in the angular deflections of the steady-state currents. This leads to the conclusion that Ekman layer currents are significantly influenced by the surface waves.     

An Approximate Analytical Solution For The Baroclinic And Variable Eddy Diffusivity Semi-Geostrophic Ekman Boundary Layer

The WKB method has been used to develop an approximate solutionof the semi-geostrophic Ekman boundary layer with height-dependenteddy viscosity and a baroclinic pressure field. The approximate solutionretains the same simple form as the classical Ekman solution. Behavioursof the approximate solution are discussed for different eddy viscosityand the pressure systems. These features show that wind structure inthe semi-geostrophic Ekman boundary layer depends on the interactionbetween the inertial acceleration, variable eddy viscosity and baroclinicpressure gradient. Anticyclonic shear has an acceleration effect on theair motion in the boundary layer, while cyclonic shear has a decelerationeffect. Decreasing pressure gradient with height results in a super-geostrophicpeak in the wind speed profile, however the increasing pressure gradient withheight may remove the peak. Anticyclonic shear and decreasing the variableeddy viscosity with height has an enhanced effect on the peak.Variable eddy viscosity and inertial acceleration has an important role in thedivergence and vorticity in the boundary layer and the vertical motion at the top of the boundary layer that is called Ekman pumping. Compared to the constanteddy viscosity case, the variable eddy diffusivity reduces the absolute value ofEkman pumping, especially in the case of eddy viscosity initially increasing with height. The difference in the Ekman pumping produced by different eddy diffusivity assumptions is intensified in anticyclonic flow and reduced in cyclonic flow.     

The wind in the baroclinic boundary layer with three sublayers incorporating the weak non-linear effect

In considering the weak non-linear effect, and using the small parameter expansion method, the analyt-ical expressions of the wind distribution within PBL (planetary boundary layer) and the vertical velocity at the top of the PBL are obtained when the PBL is divided into three layers and different eddy transfer coefficients K are adopted for the three layers. The conditions of barotropy and neutrality for the PBL are extended to that of baroclinity and non-neutral stratification. An example of a steady circular vortex is used to display the characteristics of the horizontal wind within the PBL and the vertical velocity at the top of the PBL. Some new results have been obtained, indicating that the magnitude of the speed in the lower height calculated by the present model is larger than that by the model in which k is a constant within the whole boundary layer, for example, in the classical Ekman boundary layer model and the model by Wu (1984). The angle between the wind at the top of the PBL and the wind near the surface calculated by the present model is less than that calculated by the single K model. These results are in agreement with the observations.