A nonlinear dynamical model for atmospheric boundary layer turbulence

Using the qualitative theory of nonlinear dynamical systems and the ergodic theory of chaos and strange attractors, we study a truncated-spectrum model of dynamical equations of the atmosphere. In the parameter plane (Re, Ri), the atmospheric motion states can be divided into four regions: O (basic), P (periodic), T (turbulent or chaotic), and T-P (transition of T and P). We analyze the routes to turbulence during the day and at night. Finally, we discuss the physical aspects of the occurrence of turbulence.     

Near-surface turbulence in the atmospheric boundary layer

Measurements of the near-surface turbulence in the atmospheric boundary layer have been made using hot-wire probes above the salt flats of northwestern Utah, where the momentum thickness Reynolds number, R_θ, is O(10⁶), and the surface is smooth and nearly devoid of flow obstructions. The measurements were made with arrays of up to 24 parallel straight sensors and with a modular 12-sensor probe capable of measuring all of the components of the instantaneous velocity vector and velocity gradient tensor. Measurements were also made in a laboratory wind tunnel at R_θ=1730 using 22 straight sensors. The data analysis focuses on the effects of the Reynolds number on turbulence properties and on the physics of the dissipation rate of turbulent kinetic energy.Some properties are found to be dependent on the Reynolds number when normalized with inner variables, while others are not. Among those that show the significant Reynolds number dependence are the rms and the skewness factor of the streamwise velocity fluctuations.Significant differences in flow structure, particularly those related to high rates of dissipation, are implied by the data. The joint PDF and covariance integrand of streamwise and wall normal vorticity fluctuations show less preferred orientation of the vorticity vector in the buffer layer at R_θ of O(10⁶) than at R_θ=1070. The largest contribution to the dissipation rate, at O(10⁶) is by the ∂w/∂z velocity gradient, while this term makes a quite small contribution to the dissipation rate at low R_θ. Here w and z are the spanwise velocity fluctuations and direction, respectively. Conditional analysis in the streamwise-wall normal (x−y) plane based on high instantaneous dissipation rate shows that the typical high dissipation rate events are generally similar at high and low Reynolds numbers, but display some significant differences.     

Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer

A stability correction function φ(m)(ζ) that accounts for distortions to the logarithmic mean velocity profile (MVP) in the lower atmosphere caused by thermal stratification was proposed by Monin and Obukhov in the 1950s using dimensional analysis. Its universal character was established from many field experiments. However, theories that describe the canonical shape of φ(m)(ζ) are still lacking. A previous link between the spectrum of turbulence and the MVP is expanded here to include the effects of thermal stratification on the turbulent kinetic energy dissipation rate and eddy-size anisotropy. The resulting theory provides a novel explanation for the power-law exponents and coefficients already reported for φ(m)(ζ) from numerous field experiments.     

Study of local scaling in the stable atmospheric boundary layer for the evaluation of turbulence parameters

Summary A renewed interest in the dynamic and thermal structure of the atmospheric boundary layer (ABL) has recently revived, due to the contribution that this layer can provide to the improvement of skill of weather prediction and climate simulation in the most advanced general circulation models. The attention is particularly focused on non-stationary and non-homogeneous turbulent structures of this transition layer, for which many parametrization schemes, based on local-and non-local-closure assumptions, have been proposed. However, also stationary, non-homogeneous, continous-turbulence conditions can give rise to some complication in the ABL parametrization when air stability becomes stronger and stronger. In this situation, the governing scales of the classical non-local Monin-Obukhov similarity theory are no more representative, and new local scales must be derived from local forcings of the flux. This paper summarizes a few relevant points of the local-similarity theory and shows the results of a local-scaling analysis obtained by observation data of wind and temperature profiles in the ABL in the northern Po Valley Paper presented at the IX Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 8–10, 1992, Rome.     

Eddy diffusivities derived from a numerical model of the convective planetary boundary layer

Summary Functional forms for the vertical eddy diffusivityK _z (z) are sought that optimize the performance of theK-theory diffusion equation. The method developed to determine the optimal diffusivity is first tested by applying it to analytic solution of the diffusion equation in which the functional form of the diffusivity is known precisely. In all test cases performed, the technique yields the correctK _z profile regardless of the initial estimate ofK _z from which the technique’s search procedure begins. When applied to “observed” mean, cross-wind-integrated point source concentration fields derived from Lagrangian diffusion theory and data from a numerical turbulence model jointly, the technique yields optimal diffusivities that make the solution of the diffusion equation agree within ±20% of the “observed” values within the core of point source plumes. Expressed in terms of the convective-velocity scalew _* and the mixed-layer depthz _i , the optimal diffusivity has a quasiuniversal form for atmospheric stabilities in the rangez _i /L⪯-10 whereL is the Monin-Obukhov length. The optimal diffusivity is found to be strongly dependent on the source hight. TheK _z profiles derived for the two source heightsz _s∼-0.025z _i andz _s ∼-0.25z _i are of opposite shape, but they have comparable maximum values ofK _z ∼-0.25w _* z _i .

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Riassunto Si cercano forme funzionali per la diffusibilità turbolenta verticaleK _z (z) che rendano ottimale l’efficacia dell’equazione di diffusione della teoriaK. II metodo sviluppato per determinare la diffusibilità ottimale è dapprima controllato applicandolo a soluzioni analitiche dell’equazione di diffusione in cui la forma funzionale della diffusibilità è nota esattamente. In tutti i casi di prova la tecnica dà il profilo corretto diK _z qualunque sia la stima iniziale diK _z da cui prende inizio il procedimento di ricerca della tecnica. Quando è applicata contemporaneamente ai campi di concentrazione medi “osservati”, a sorgente puntiforme integrati sui venti trasversali, derivati dalla teoria di diffusione lagrangiana ed ai dati presi dal modello di turbolenza numerico, la tecnica dà diffusibilità ottimali per le quali la soluzione dell’equazione di diffusione è in buon accordo entro il ±20% dei valori “osservati” nel nocciolo di pennacchi della sorgente puntiforme. Espressa in termini della scala di velocità di convezionew _* e della profondità dello strato mistoz _i , la diffusibilità ottimale dipende fortemente dall’altezza della sorgente. I profili diK _z derivati per due altezze di sorgentez _s ∼-0.025z _s ez _s ∼-0.25z _i sono di forma opposta ma hanno valori massimi diK _z paragonabili,K _z ∼-0.25w _* z _i .

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Резюме Определяются функциональные выражения для вертикального вихревого козффициента диффузииK _z (Z), которые оптимизируют получение уравнения диффузии вK-теории. Развитый метод для определения оптимального коэффициента диффузии сначала проверяется на аналитических решениях уравнения диффузии, в которых функциональное выражение козффициента диффузии известно точно. Во всех исследованных случаях предложенный метод дает правильный профильK _z . Предложенный метод дает оптимальные козффициенты диффузии, при которых решение уравнения дуффузии согласуется, в пределах ±20%, с ≪наблюдаемыми≫ величинами. Выраженный через масштаб конвекционной скоростиw _* и глубину смешанного слояz _i оптимальный коэффициент диффузии имеет квази-универсальную форму для атмосферных устойчивостей в областиz _i /L≤10, гдеL есть длина Монина-Обухова. Обнаружено, что оптимальный козффнциент диффузии сильно зависит от высоты источника. ПрофилиK _z , выведенные для двух высот источниковz _i ≅0.025z _i иz _i ≅0.25z _i , имеют противоположную форму, но они имеют сравнимые максимальные значенияK _z ≅0.25w _* z _i .

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To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

An analytical model with temporal variable eddy diffusivity applied to contaminant dispersion in the atmospheric boundary layer

In this work, we present a new analytical model for the prediction of pollutant dispersion in the atmospheric boundary layer incorporating either the spatial and temporal continuous dependence of the eddy diffusivity. For such, we solve the time-dependent three-dimensional advection–diffusion equation combining the Decomposition and GILTT approaches. In fact, applying the idea of Decomposition method, we reduce the advection–diffusion equation with temporal dependence of the eddy diffusivity into a set of recursive advection–diffusion equations with eddy diffusivity just depending on the spatial variable z$z$, which is then directly solved by the GILTT method. To our knowledge this sort of model has not been part of the literature yet.     

大气边界层模式中随机参数的反演与不确定性分析

在大气边界层气象中湍流黏性系数是一个很重要的参数,通过直接观测往往无法得到其准确值,仅能通过间接观测获得大致范围.本文选用随机广义Ekman动力近似模式中的湍流黏性系数进行反演研究与不确定性分析.首先利用风速观测数据,并采用基于混沌多项式的集合Kalman滤波方法对系数进行反演,降低其不确定性,缩小可能取值的范围,该方法的核心思想是将集合Kalman滤波方法中求解模式不确定性传播的方法由蒙特卡罗法改为混沌多项式展开,从而避免大规模采样带来的计算资源耗费.然后进行数值实验,结果表明该方法能够有效且快速地求解出湍流黏性的后验概率分布,从而达到降低系数不确定性的目的.根据系数的先验分布计算出风速的先验分布,从而找到风速不确定性大的区域,且揭示了在不确定性大的区域内的观测数据进行系数反演可得到十分明显的效果,这对于观测点位置的选择提供了重要的指导.     

Millimetric flux densities as a test of atmospheric turbulence

In this paper it is shown how submillimetre and millimetre flux density measurements of sky fluctuations can be used to infer the characteristics of atmospheric turbulence.Two different approaches have been followed: first, by considering the observed process as due to the atmospheric turbulence, we used the r.m.s. sky fluctuations to derive some physical parametres characterizing the phenomenon; second, by investigating the power spectrum and the autocorrelation function, we derive an empirical model (the AR model) to try to deduce the physical process. In this case, the fitted power spectrum agrees strikingly with that predicted by the theory of a stationary turbulent flow for the atmosphere in the sampled frequency range. This kind of modeling can help to disentangle the atmospheric fluctuations from the extraterrestrial signal in ground-based astrophysical measurements.Measurements of the water vapour content and atmospheric transmission at the Italian Base in Antarctica, where the data have been taken, at the wavelengths of 350 μm, 1 and 2mm are also reported.     

Aspect sensitivity of sound backscattering in the atmospheric boundary layer

The dependence of backscatter intensity on the inclination of a SODAR beam was measured in the nocturnal boundary layer. The aspect sensitivity was revealed, but the angular dependence was not so strong as that of radiowave backscattering in the upper atmosphere. The mechanism of the phenomenon is under discussion as well as its influence on the accuracy of SODAR measurements of C _T ² values which are very useful for air-pollution meteorology.     

Level-crossing statistics of the horizontal wind speed in the planetary surface boundary layer

The probability density of the times for which the horizontal wind remains above or below a given threshold speed is of some interest in the fields of renewable energy generation and pollutant dispersal. However there appear to be no analytic or conceptual models which account for the observed power law form of the distribution of these episode lengths over a range of over three decades, from a few tens of seconds to a day or more. We reanalyze high resolution wind data and demonstrate the fractal character of the point process generated by the wind speed level crossings. We simulate the fluctuating wind speed by a Markov process which approximates the characteristics of the real (non-Markovian) wind and successfully generates a power law distribution of episode lengths. However, fundamental questions concerning the physical basis for this behavior and the connection between the properties of a continuous-time stochastic process and the fractal statistics of the point process generated by its level crossings remain unanswered. (c) 2001 American Institute of Physics.     

大气边界层各向异性的室内模拟研究

边界层的各向异性研究对于了解实际大气的湍流特性和经典理论的适用范围均具有较大的意义。利用室内水槽实验模拟了实际大气边界层,使用小波变换方法分析了对数光强起伏谱的特征,将获得的标度指数与理论值进行比较,结果表明混合层在水平方向较为接近各向同性,而垂直方向则呈现一定的各向异性。     

Lunar tides in the electric field of the atmospheric boundary layer

Investigations are aimed at a search for and an estimation of a correlation between the electric field in the atmospheric boundary layer (ABL) and the lunar tides. The lunar tides and their correlation with the electric field in the ABL can be studied either by accumulation of a large experimental data arrays or by the method of signal reception at spatially separated points. The problem of investigating lunar tide manifestations in the electric field in the ABL is solved using a network of stations for monitoring the vertical electric field strength component, specially constructed models and their consequences, and procedures developed for experimental data processing.     

大气边界层各向异性的室内模拟研究

 边界层的各向异性研究对于了解实际大气的湍流特性和经典理论的适用范围均具有较大的意义。利用室内水槽实验模拟了实际大气边界层,使用小波变换方法分析了对数光强起伏谱的特征,将获得的标度指数与理论值进行比较,结果表明混合层在水平方向较为接近各向同性,而垂直方向则呈现一定的各向异性。     

AML-1车载测污激光雷达探测大气边界层气溶胶

介绍了自行研制用于环境监测的车载式激光雷达(AML-1)系统及典型特点,其在测量气溶胶时不但可以全天候探测,还可以从不同仰角进行测量,对实现连续、实时、大范围监测大气污染有着重要的意义。结合该激光雷达的特点,从垂直、斜程、二维扫描等方面分别给出了该系统探测气溶胶时的典型结果和时空分布图,总结了AML-1车载测污激光雷达系统在测量气溶胶时的优越性和意义。     

AML-1车载测污激光雷达探测大气边界层气溶胶

 介绍了自行研制用于环境监测的车载式激光雷达(AML-1)系统及典型特点，其在测量气溶胶时不但可以全天候探测，还可以从不同仰角进行测量，对实现连续、实时、大范围监测大气污染有着重要的意义。结合该激光雷达的特点，从垂直、斜程、二维扫描等方面分别给出了该系统探测气溶胶时的典型结果和时空分布图，总结了AML-1车载测污激光雷达系统在测量气溶胶时的优越性和意义。     

The improvement of turbulence modeling for the aerothermal computation of hypersonic turbulent boundary layers

The engineering computation of turbulent flows is mainly based on turbulence modeling,however,accurate aerothermal computation of hypersonic turbulent boundary layers is still a not well-solved problem. Aerothermal computation for turbulent boundary layers on a supersonic or hypersonic blunt cone with small bluntness is done firstly by using both direct numerical simulation and BL model,and seven different cases are investigated. Then the results obtained by the two methods are compared,and the reason causi...     

Continuous transformation computation of boundary layer equations between similarity regimes

Consideration is given to the computation of boundary layer flows displaying evolution between similarity regimes. A continuous transformation is introduced which reflects the associated evolution. When applied in conjunction with recent developments involving extrapolation on crude nets an efficient, accurate and straightforward algorithm ensues.     

Acoustic sounding of diurnal variations and gravity waves in the planetary boundary layer

In the introductory part the paper presents some SODAR results on diurnal variations of different boundary layer structures from measurements during the KOPEX-experiment at a city station and a suburban station. In Sect. 1 the investigations about wave processes in the planetary boundary layer are discussed. The SODAR measurements were carried out in different international cooperations at the Kopisty Atmospheric Observatory of the Institute of Physics of the Atmosphere Prague (northern Czechoslovakia) in the year 1986 (KOPEX-86), at the Observatory Juliusruh of the Heinrich-Hertz-Institut Berlin at the island of Rügen (JULEX-87) and at the Meteorological Observatory of the nuclear power plant Jaslovske Bohunice in Slovakia, about 60 km north-east of Bratislava (JABEX-88).Formerly: Heinrich-Hertz-Institute, Berlin-Adlershof, Germany