从湍流经典理论到大气湍流非平衡态热力学理论

湍流是日常生活中一种普遍的自然现象,也是经典物理学仍未完全解决的难题。湍流更是大气运动的最基本特征。本文系统地回顾了大气湍流经典理论发展简史,进一步详细介绍了大气湍流非平衡态热力学理论。大气湍流非平衡态热力学理论在熵平衡方程中引入动力过程,进而统一推导出大气湍流输送的Fourier定律、Flick定律和Newton定律,证明了Dufour效应、Soret效应、可逆动力过程与热力不可逆湍流输送过程之间的交叉耦合效应,以及湍流强度定理。这些定律和定理中得到了观测的事实验证,同时它们的唯象系数也由观测资料所确定。湍流强度定理揭示,湍流发展的宏观原因是速度和温度的剪切效应,Reynolds湍流和Rayleigh-Bénard湍流共存于大气湍流中。热力过程和动力过程间耦合效应现象的发现突破了传统湍流输送理论,即Fourier定律、Flick定律和Newton定律的观点——一个宏观量的输送通量等价于这个宏观量的梯度湍流输送通量。热力和动力过程间的耦合原理认为,一个宏观量的输送通量包括这个量的梯度湍流输送通量和速度耦合输送通量两部分。因此,能量和物质的垂直输送通量除了相应物理量梯度造成的湍流输送外,还应包括垂直速度耦合效应,即辐散或辐合运动造成的耦合效应。在一个很宽的尺度范围内,地表面的空间特征是非均匀的。下垫面非均匀性造成的对流运动将引起大气的辐散或辐合运动。这可能是导致地表能量收支不平衡的重要原因之一。垂直速度对垂直湍流输送的交叉耦合效应为非均匀下垫面大气边界层理论的发展,并为克服地表能量收支不平衡问题及非均匀下垫面大气边界层参数化遇到的困难提供了可能的线索。     

The influence of convergence movement on turbulent transportation in the atmospheric boundary layer

Classical turbulent K closure theory of the atmospheric boundary layer assumes that the vertical turbulent transport flux of any macroscopic quantity is equivalent to that quantity‘s vertical gradient transport flux. But a cross coupling between the thermodynamic processes and the dynamic processes in the atmospheric system is demonstrated based on the Curier-Prigogine principle of cross coupling of linear thermodynamics. The vertical turbulent transportation of energy and substance in the atmospheric boundary layer is related not only to their macroscopic gradient but also to the convergence and the di-vergence movement. The transportation of the convergence or divergence movement is important for the atmospheric boundary layer of the heterogeneous underlying surface and the convection boundary layer.Based on this, the turbulent transportation in the atmospheric boundary layer, the energy budget of the heterogeneous underlying surface and the convection boundary layer, and the boundary layer parameteri-zation of land surface processes over the heterogeneous underlying surface are studied. This research offers clues not only for establishing the atmospheric boundary layer theory about the heterogeneous underlying surface, but also for overcoming the difficulties encountered recently in the application of the atmospheric boundary layer theory.     

Vertical and Horizontal Transport of Energy and Matter by Coherent Motions in a Tall Spruce Canopy

In the framework of the EGER (ExchanGE processes in mountainous Regions) project, the contribution of coherent structures to vertical and horizontal transports in a tall spruce canopy is investigated. The combination of measurements done in both the vertical and horizontal directions allows us to investigate coherent structures, their temporal scales, their role in flux transport, vertical coupling between the sub-canopy, canopy and air above the canopy, and horizontal coupling in the sub-canopy layer. The temporal scales of coherent structures detected with the horizontally distributed systems in the sub-canopy layer are larger than the temporal scales of coherent structures detected with the vertically distributed systems. The flux contribution of coherent structures to the momentum and sensible heat transport is found to be dominant in the canopy layer. Carbon dioxide and latent heat transport by coherent structures increase with height and reach a maximum at the canopy height. The flux contribution of the ejection decreases with increasing height and becomes dominant above the canopy level. The flux fraction transported during the sweep increases with height and becomes the dominant exchange process at the upper canopy level. The determined exchange regimes indicate consistent decoupling between the sub-canopy, canopy and air above the canopy during evening, nighttime and morning hours, whereas the coupled states and coupled by sweep states between layers are observed mostly during the daytime. Furthermore, the horizontal transport of sensible heat by coherent structures is investigated, and the heterogeneity of the contribution of coherent events to the flux transport is demonstrated. A scheme to determine the horizontal coupling by coherent structures in the sub-canopy layer is proposed, and it is shown that the sub-canopy layer is horizontally coupled mainly in the wind direction. The vertical coupling in most cases is observed together with streamwise horizontal coupling, whereas the cross-stream direction is decoupled.     

浪花和飞沫水滴在海面大风边界层中的垂直传输

对我们在南海海域建立的大气边界层观测站的资料进行分析表明,在冷涌和热带气旋（包括强台风）过境的大风期间,在边界层底层10 min平均的水平风速u基本不随高度而变,甚至大都伴随有明显的上升气流w。而且风场脉动中含有强相干性的阵风扰动（ v _g,频率位于1/60~1/600 Hz频段）,以及近于随机性的高频湍流脉动（ v _t,频率大于1/60 Hz）,它们的特性以及w都可以很好地用水平风速u来参数化表示。取实测的（u,w）和脉动 v '= v _g+ v _t,或取实测的u与参数化的 v _g、 v _t和w,应用拉格朗日随机模式作数值模拟,结果表明:由破头浪发射出来的浪花和飞沫水滴（半径r_p为10~500 μm）有相当大的一部分可以飞离大气底层而进入100 m高以上的大气中,继而对进入大气中的海盐气溶胶通量有重要贡献,不可以被忽略。在水滴的垂直传输过程中,阵风扰动起了极重要的作用,而在w>0且较显著时w更起重要作用。我们对上扬率（可上升至100 m以上高度的水滴数与由海面发射出的水滴数之比）作出了初步的参数化公式,有很高的精度,主要的参量是无量纲量u2/（r_qg）,其中r_p和g分别是水滴半径和重力加速度。     

Inertial Effects on the Vertical Transport of Suspended Particles in a Turbulent Boundary Layer

In many atmospheric flows, a dispersed phase is actively suspended by turbulence, whose competition with gravitational settling ultimately dictates its vertical distribution. Examples of dispersed phases include snow, sea-spray droplets, dust, or sand, where individual elements of much larger density than the surrounding air are carried by turbulent motions after emission from the surface. In cases where the particle is assumed to deviate from local fluid motions only by its gravitational settling (i.e., they are inertialess), traditional flux balances predict a power-law dependence of particle concentration with height. It is unclear, however, how particle inertia influences this relationship, and this question is the focus of this work. Direct numerical simulations are conducted of turbulent open-channel flow, laden with Lagrangian particles of specified inertia; in this way the study focuses on the turbulent transport which occurs in the lowest few meters of the planetary boundary layer, in regions critical for connecting emission fluxes to the fluxes felt by the full-scale boundary layer. Simulations over a wide range of particle Stokes number, while holding the dimensionless settling velocity constant, are performed to understand the role of particle inertia on vertical dispersion. It is found that particles deviate from their inertialess behaviour in ways that are not easily captured by traditional theory; concentrations are reduced with increasing Stokes number. Furthermore, a similarity-based eddy diffusivity for particle concentration fails as particles experience inertial acceleration, precluding a closed-form solution for particle concentration as in the case of inertialess particles. The primary consequence of this result is that typical flux parametrizations connecting surface emission models (e.g., saltation models or sea-spray generation functions) to elevated boundary conditions may overestimate particle concentrations due to the reduced vertical transport caused by inertia in between; likewise particle emission may be underestimated if inferred from concentration measurements aloft.     

The Characteristics of Turbulence Structure and Transfer over the Middle Area of the Tibetan Plateau

In this paper, turbulent data obtained from the Damxung site during the Secondary Tibetan Plateau Science Experiment (TIPEX) in 1998 are used to study the characteristics of the turbulent spectra, turbulence transport, and the dissipation rates of turbulent kinetic energy, temperature variance, and humidity variance in the middle area of the Tibetan Plateau. The turbulent spectra of wind velocity, potential temperature, and humidity satisfy the-2/3 power law in the high frequency range. Horizontal transportation of heat and water vapor is negligible compared with vertical transportation under strong unstable conditions, and as the stability parameter z/L increases (where z is the observational height, and L is the Monin Obukhov length), horizontal transportation becomes dominant under near-neutral, neutral, and stable conditions. The non-dimensional temperature and humidity variances are 20% less than the temperature and humidity gradient variances. These deficits appear to increase as the absolute stability parameter increases. Moreover, the effects of turbulence transportation and pressure variance exist throughout the entire stability region.     

适用于GRAPES模式C-P边界层方案的设计和实现

基于K廓线闭合方案,通过考虑不稳定边界层和稳定边界层中热量交换系数在半层上求取及下边界条件的设置,将温湿倾向在整层上直接计算,设计了Charney-Phillips跳点（简称C-P跳点）的边界层方案,使之与GRAPES全球模式的C-P跳点相协调,解决了Lorenz跳点物理过程与C-P跳点动力框架耦合时插值造成的不协调问题,同时避免了耦合时反复插值造成的误差,提高了边界层物理过程参数化方案及其反馈的准确性和合理性。试验表明:C-P跳点边界层方案因为避免了温度和湿度在垂直方向上的插值,消除了温湿变量在垂直方向上的锯齿状抖动,使温湿廓线分布更合理,减小了模式预报误差,形势场的预报效果也得到一定改善。C-P边界层方案的应用提升了GRAPES全球模式的总体预报性能。     

绿洲灌溉对垂直湍流热通量影响的大涡模拟研究

为了研究湍涡对中尺度绿洲灌溉的响应,利用WRF模式大涡模拟模块（WRF-LES）在西北半干旱区绿洲区开展灌溉前和灌溉后两个大涡模拟试验（分别简称为BI和AI）,其中灌溉可能会改变绿洲非均匀强度。利用面积平均的办法计算湍流热通量并利用小波分析将湍流热通量模态分解到不同的尺度。结果表明灌溉增加了土壤湿度,引起绿洲内部非均匀强度增加,灌溉对垂直热通量以及通量频散都有较大影响。AI中的湍涡为网状,与BI中一致。AI与BI中的感热通量的频散高度都随着感热通量的减小而减小。AI与BI中感热通量小波能量谱尺度一致,但是BI中强度比AI小。潜热通量的频散高度依赖于感热通量,且潜热通量能量谱随高度减小。空间滞后相关系数的结果表明由于灌溉前地表加热较强,感热通量对地表热通量的响应高度在灌溉之前（BI）比灌溉后（AI）更高。灌溉后的通量模态的飘移距离小于灌溉前的。     

青藏高原五道梁地区湍流输送特征的研究

根据１９９４年６－７月在青藏高原五道梁地区的湍流脉动观测资料，分析了该地区近地层能量平衡、感热和谱热的日变化及湍流强度和端流谱特征。结果表明：晴天该地区近地层能量基本平衡，各能量分量的日变化与常情况相同；白天感热通量的输送占主导地位，潜热通量占次要地位，符合半干旱的一般特征。     

Vertical transport of turbulent kinetic energy in the surface layer over a paddy field

Turbulent kinetic energy and its vertical flux were measured at two heights over a paddy field. The vertical transport of turbulent kinetic energy was always downward right above the paddy field and was frequently downward at higher levels within a few metres above the crop. Contributions to the downward transport arise mainly from the turbulent kinetic energy of horizontal wind velocity components. It is shown from the analysis of probability distributions that appreciable transport takes place intermittently in a few large downward bursts and that these downdrafts are efficient for downward energy transport.In the budget of turbulent kinetic energy, the flux divergence term and the energy dissipation term are the main loss terms under unstable conditions. These terms increase in magnitude with increasing instability. Buoyant production is insufficient to balance these losses. The imbalance term involving the pressure-work term is probably one of the main energy sources in unstable conditions.     

Application of Linear Thermodynamics to the Atmospheric System. Part Ⅰ: Linear Phenomenological Relations and Thermodynamic Property of the Atmospheric System

从一般的热力学原理或其它自然原理对唯象关系所强加的限制，能够演绎出大气系统的一系列热力学性质。利用非平衡态线性热力学导出了湍流K闭合理论中湍流交换系数同唯象系数的关系，从理论上证明大气系统热量湍流输送同水泡之间存在交叉耦合，还导出了湍流强度同速度和位温梯度的关系，从而证明速度和位温空间分布的非均匀性是湍流之源。并证明湍流强度定理，不可压缩气体和各向同性湍流大气中，湍流强度正比于速度与位温梯度的标积。进而证明大气涡旋定理，位温的切变将导致涡旋运动或各种环流运动，速度涡度等于速度同位温相对梯度的矢积。展现了线性热力学在大气系统的应用前景。     

A scheme for computing surface fluxes from mean flow observations

A computational scheme is developed for estimating turbulent surface stress, sensible heat flux and humidity flux from mean velocity, temperature and humidity at a single height in the atmospheric surface layer; conditions at this reference level are presumed known from observations or from a numerical atmospheric circulation model. The method is based on coupling a Monin-Obukhov similarity profile to a force-restore formulation for the evolution of surface soil temperature to yield the local values of shear stress, heat flux and surface temperature. A self-contained formulation is presented including parameterizations for solar and infrared radiant flux at the surface.In addition to reference-level mean flow properties, the parameters needed to implement the scheme are thermal heat capacity of the soil, surface aerodynamic roughness, latitude, solar declination, surface albedo, surface emissivity and atmospheric transmissivity.Sample calculations are presented for (a), constant atmospheric forcing at the reference level, and (b) variable atmospheric forcing corresponding to Kahle's (1977) measurements of windspeed, air temperature and radiometer soil surface temperature under dry vegetatively sparse conditions in the Mohave Desert in California. The latter case simulated the observed diurnal variations resonably well for the parameters used.Consultant, Atmospheric Sciences Division, Department of Energy and Environment, Brookhaven National Laboratory, Upton, N.Y., pc11973, U.S.A.     

Helicopter-Borne Flux Measurements in the Nocturnal Boundary Layer Over Land – a Case Study

This case study introduces measurements of turbulent fluxes in a nocturnal boundary layer in North Germany with the new helicopter-borne turbulence measurement system HELIPOD, a detailed data analysis and examination in regard of systematic errors of the instrument, and some comparison with local similarity theory and experiments of the past, in order to confirm the occurrence of small vertical turbulent fluxes. The examined nocturnal boundary layer offered excellent conditions to analyse the quality of the measurement system. In this connection, a detailed look at a strong ground-based inversion disclosed small turbulent fluxes with a spectral maximum at ten metres wavelength or less, embedded in intermittent turbulence. For verification of these fluxes, the measurements were compared with well established results from past experiments. Local similarity theory was applied to calculate dimensionless variances of the turbulent quantities, which were found in good agreement with other observations. Since shear and stratification varied significantly on the horizontal flight legs due to global intermittency, a method was developed to determine vertical gradients on a horizontal flight pattern, by use of small fluctuations of the measurement height. With these locally determined gradients, gradient transport theory became applicable and the turbulent diffusivities for heat and momentum, the Richardson number, and the flux Richardson number were estimated within isolated strong turbulent outbursts. Within these outbursts the flux Richardson number was found between 0.1 and 0.2. The functional relationship between the gradient Richardson number and the turbulent Prandtl number agreed well with observations in past experiments and large eddy simulation. The impact of the stratification on the vertical turbulent exchange, as already described for the surface layer using Monin–Obukhov similarity, was analogously observed in the very stably stratified bulk flow when local scaling was applied.     

Surface energy balance,parameterizations of boundary-layer heights and the application of resistance laws near an Antarctic Ice Shelf front

A study of the surface energy balance with turbulent fluxes obtained by the Monin-Obukhov similarity theory and a comparison with results for resistance laws are presented for the strong baroclinic conditions in the vicinity of the Filchner/Ronne Ice Shelf front. The data are taken from a field experiment in the Antarctic summer season 1983/84. For the first time in the coastal Antarctic region, this data set comprises synchronous energy balance measurements over the polynya and the ice shelf together with soundings of the boundary layer, yielding vertical profiles of the wind velocity and temperature over the ice shelf, at the ice shelf front and over the polynya.Over the ice shelf, the radiation balance is the largest component of the energy fluxes and is mainly compensated by the subsurface energy flux and the turbulent heat flux in the daily mean. Over the polynya, turbulent fluxes of sensible and latent heat lead to large energy losses of the water surface in the night-time and in situations of very low air temperatures.Different parameterizations for boundary-layer height are compared using tethered sonde and energy balance measurements. With the height of the inversion base over the polynya and the height of the critical bulk Richardson number over the ice shelf, external parameters for the application of resistance laws were determined. The comparison of turbulent surface fluxes obtained by the energy balance measurements and by the resistance laws shows good agreement for the convective conditions over the polynya. For the stably stratified boundary layer over the ice shelf with small amounts of the turbulent heat flux, the deviation is large for the case of a cold air outflow with a superposed inertial oscillation.     

Measuring Vertical Heat Flux with RASS

Summary A wind‐profiling Doppler radar equipped with a radio acoustic sounding system (RASS) may be used to estimate the vertical profile of the vertical flux of heat in the atmosphere. Simultaneous measurements of the time‐varying temperature and vertical air velocity are combined to give the convective heat flux using the eddy‐correlation method. The accuracy of the estimates depends on the fundamental accuracy of the temperature and vertical velocity measurements. Also, in common with all eddy‐correlation methods, uncertainties are introduced by the need to define a suitable averaging time and to remove trends. A problem unique to RASS is the possible presence of ground and intermittent clutter at close ranges, which can cause errors in the vertical air velocity measurements. These considerations are discussed with particular reference to observations using a UHF radar wind profiler situated in an urban environment, where clutter is a serious problem. A Rank‐Order Signal Processing Algorithm (ROSPA) for recognizing and eliminating outliers in the vertical velocity, is introduced. It is explained how ROSPA uses both a minimum filter and a median filter on the velocity data. It is shown, using a comparison with nearly clutter free data from a rural site, that the filtering substantially improves the quality of the noisy urban data. The paper then compares RASS‐measured urban and rural heat flux profiles, along with the heat flux profile measured by an instrumented airplane. It is concluded that the main obstacles to RASS heat flux measurements are the effects of winds and turbulence in the boundary layer, rather than clutter. Received September 24, 1998 Revised January 27, 1999     

线性热力学对大气系统的应用(I)大气系统的线性唯象关系和热力学性质(英文)

从一般的热力学原理或其它自然原理对唯象关系所强加的限制,能够演绎出大气系统的一系列热力学性质。利用非平衡态线性热力学导出了湍流K闭合理论中湍流交换系数同唯象系数的关系,从理论上证明大气系统热量湍流输送同水汽之间存在交叉耦合,还导出了湍流强度同速度和位温梯度的关系,从而证明速度和位温空间分布的非均匀性是湍流之源。并证明湍流强度定理,不可压缩气体和各向同性湍流大气中,湍流强度正比于速度与位温梯度的标积。进而证明大气涡旋定理,位温的切变将导致涡旋运动或各种环流运动,速度涡度等于速度同位温相对梯度的矢积。展现了线性热力学在大气系统的应用前景。     

Turbulent transport from an arctic lead: A large-eddy simulation

The upward transfer of heat from ocean to atmosphere is examined for an Arctic lead, a break in the Arctic ice which allows contact between the cold atmosphere and the relatively warm ocean. We employ a large-eddy model to compute explicitly the three-dimensional turbulent response of the atmosphere to a lead of 200 m width. The surface heat flux creates a turbulent plume of individual quasi-random eddies, not a continuous updraft, which penetrate into the stable atmosphere and transport heat upward.Maximum updraft velocities and turbulence occur downwind of the lead rather than over the lead itself, because the development time of an individual thermal eddy is longer than its transit time across the lead. The affected vertical region, while shallow over the lead itself, grows to a height of 65m at 600 m downwind of the lead; beyond that, the depth of the turbulent region decreases as the eddies weaken. The maximum vertical turbulent heat flux occurs at the downwind edge of the lead, beyond which a relative maximum extends upward into the plume. Negative surface heat flux immediately downwind of the lead creates a growing stable layer, but above that internal boundary layer the turbulent heat flux is still positive. Updraft maxima are typically 28 cm/s, but compensating downdrafts result in time-averaged vertical velocities of less than 1 cm/s in the plume. Conditional sampling separates the updraft and downdraft contributions. Formulas for the horizontal eddy development distance and for the vertical plume penetration height are presented. The relative importance of mean and turbulent transport is compared for both vertical and horizontal heat transfer: turbulence dominates the vertical heat transport whereas mean advection dominates the horizontal transport, these offsetting transports producing a quasi-stationary state.     

对流边界层湍流通量及逆梯度输送参数化分析

"K"理论是众多气象预报模式中运用最广泛的湍流参数化方案之一,但无法解释"逆梯度"的输送,必须进行修正。最具代表性的修正方案有三种:方案Ⅰ(Deardroff方案)、方案Ⅱ(Holtslag和Moeng方案)和方案Ⅲ(刘烽方案)。本文利用香河的边界层观测资料对上述三种方案进行验证和比较,发现方案Ⅰ的结果在整个对流边界层(Convective Boundary Layer,CBL)呈系统性偏低,与观测不符;方案Ⅱ在CBL中上部能够再现逆梯度输送现象,基本能给出合理的湍流通量垂直分布,但在CBL的下部和上部与观测不符;方案Ⅲ的逆梯度项与高度有关,并在CBL中部达到最大,而其他两个方案中逆梯度项随高度不变。该方案不但在CBL中上部与方案Ⅱ的结果一致,并能合理表达整个CBL内的湍流通量分布,更接近观测结果。     

On the interaction of turbulent and radiative transfers in the surface layer

The turbulent heat flux is usually assumed constant with height in the atmospheric surface layer. The validity of this hypothesis is known to be questionable, due to a possible variation along the vertical of the infrared radiative heat flux.This problem is approached theoretically, using semi-empirical expressions for emissivities, and assuming logarithmic temperature and humidity profiles. A first approximation of the radiative heat flux divergence is thus obtained analytically, as a function of the surface layer parameters. Numerical application to the case of an underlying water surface reveals appreciable variations of the radiative and turbulent heat fluxes in the first ten meters of the atmosphere, especially when wind velocity is low and humidity is high.These preliminary results are presented here for discussion. If accepted, they could lead to a reinterpretation of some experimental data, and should permit an extension of turbulent transfer theories to the case of a variable heat flux.Chargé de Recherches au C.N.R.S.Assistant I.N.R.A., Station de Bioclimatologie de Montfavet.Contributed paper to IUGG-IAMAP-AMS Conference on Planetary Boundary Layers, Boulder (Colorado), March 18–21, 1970.     

Characteristics of turbulent structures in the unstable atmospheric surface layer

An atmospheric surface-layer (ASL) experiment conducted at a meteorological site in the Oostelijk-Flevoland polder of the Netherlands is described. Turbulent fluctuations of wind velocity, air temperature and static pressure were measured, using three 10 m towers.Simultaneous turbulent signals at several heights on the towers were used to investigate the properties of the turbulent structures which contribute most significantly to the turbulent vertical transports in the unstable ASL. These turbulent structures produce between 30 and 50% of the mean turbulent vertical transport of horizontal alongwind momentum and they contribute to between 40 and 50% of the mean turbulent vertical heat transport; in both cases this occurs during 15 to 20% of the total observation time.The translation speed of the turbulent structures equals the wind speed averaged over the depth of the ASL, which scales on the surface friction velocity. The inclination angle of the temperature interface at the upstream edge of the turbulent structures to the surface is significantly smaller than that of the internal shear layer, which is associated with the temperature interface. The turbulent structures in the unstable ASL are determined by a large-scale temperature field: Convective motions, which encompass the whole depth of the planetary boundary layer (PBL), penetrate into the ASL. The curvature of the vertical profile of mean horizontal alongwind velocity forces the alignment of the convective cells in the flow direction (Kuettner, 1971), which have an average length of several hundreds of metres and an average width of a few tens of metres. This mechanism leads to the formation of turbulent structures, which extend throughout the depth of the ASL.