A model of turbulence spectra in the atmospheric surface layer

The spectral equations of turbulent kinetic energy and temperature variance have been solved by using Onsager's energy cascade model and by extending Onsager's model to closure of terms that embody the interaction of turbulent and mean flow.The spectral model yields the following results: In a stably stratified shear flow, the peak wave numbers of the spectra of energy and temperature variance shift toward larger wave numbers as stability increases. In an unstably stratified flow, the peak wave numbers of energy spectra move toward smaller wave numbers as instability increases, whereas the opposite trend is observed for the peak wave numbers of temperature variance spectra. Hence, the peak wave numbers of temperature spectra show a discontinuity at the transition from stable to unstable stratification. At near neutral stratification, both spectra reveal a bimodal structure.The universal functions of the Monin-Obukhov similarity theory are predicted to behave as _m ~ _H ~ (- Z/L)^-1/3 in an extremely unstable stratification and as _m ~ _H ~ z/L in an extremely stable stratification. For a stably stratified flow, a constant turbulent Prandtl number is expected.     

Characteristics of atmospheric turbulence in the surface layer over Antarctica

This paper presents meteorological measurements made during the antarctic summer period, on two 9 m and 3 m towers, on the rocky and ice shelf terrains of the Indian antarctic stations Maitri and Dakshin Gangotri, respectively. The measurements of fluctuations in temperature and wind speed made with relatively lesser precision instrumentation pertain to smaller wave numbers ~10^-2 m^-1 appropriate to outer scale L ₀ of the atmospheric turbulence spectrum. Autocorrelation analysis of the fluctuations in temperature and wind speed has been performed. A new autoregressive scheme has been developed to represent the computed autocorrelation functions by a Yule statistical model, and to estimate the correlation period T ₀ of the turbulent medium. Height profiles of outer scale L ₀ of turbulence may be given in terms of T ₀ and mean wind speed u. Further, the similarity theory of Monin-Obukhov has been used to compute height profiles of temperature structure parameter C _T ². At Maitri, values of L ₀ and C _T ² are higher between 03–22 h local time than between 22–03 h. Values of L ₀ and C _T ² are smaller over the ice shelf terrain of the Dakshin Gangotri station, compared to those over the rocky terrain of the Maitri station.     

The Theoretical Model of Atmospheric Turbulence Spectrum in Surface Layer

It is shown that the slope of energy spectrum obtained from the velocity solution of Kdv-Burgers equation lies between -5/3 and -2 in the dilogarithmic coordinates paper. The spectrum is very close to one of Kolmogorov’s isotropic turbulence and Frisch’s intermittent turbulence in inertial region. In this paper, the Kdv-Burgers equation to describe atmospheric boundary layer turbulence is obtained. In the equation, the 1 / Re, corresponds to dissipative coefficient v, to dispersive coefficient β, then (v/ 2β)2 corresponds to .We prove that the wave number corresponding to maximum energy spectrum decreases with the decrease of stability (i.e., the increase of in eddy-containing region. And the spectrim amplitude decreases with the increase of (i.e., the decrease of stability). These results are consistent with actual turbulence spectrum of atmospheric surface layer from turbulence data.     

大气边界层湍流相干结构的识别

首先利用数字滤波方法对淮河流域试验的大气边界层湍流观测资料进行三项分解，将大气边界层湍流的风速信号分解为近似各项同性的小尺度涡和各向异性的大尺度涡。然后再将大尺度涡信号进行离散正交小波分解，寻求相干结构的主要特征尺度。对于大气边界层湍流垂直脉动风速来说，其相干结构的主要特征尺度为16s；对径向与纬向脉动来说，其相干结构的主要特征尺度为32－64s。在此基础上，利用小波的反变换提取出相干结构的信号与非相干结构的信号，并计算两间的相关系数，最大仅有0．02。此外，对原始大气湍流观测信号不进行数字滤波，直接利用本中子波分析法提取湍流相干结构所得结果作比较研究；并探讨了采用对称或似对称离散正交小波对此研究的影响。     

Characterizing atmospheric surface layer turbulence using chaotic return map analysis

Nonlinear time series analysis methods are used to investigate the dynamics of mechanical and convective turbulences in the atmospheric surface layer flow. Using dynamical invariant analysis (e.g. correlation dimension, Lyapunov exponent and mutual information) along with recurrence quantification analysis (e.g. recurrent rate, determinism, average diagonal length of recurrence plot, etc.) of the vertical wind component data, it is confirmed that a convective turbulence is a lower order manifold in its phase space exhibiting higher degree of organization than a mechanical turbulence. Applying a quasi-one-dimensional chaotic return map technique, the topological differences between the mechanical and convective turbulences are explored. These quasi-one-dimensional return maps are produced using the local maxima of the first principal component of the reconstructed turbulence data. A comparison of the probability distribution of the local maxima of a forced Lorenz model with the turbulence data indicates the possible existence of a stable fixed point for both type of turbulences. Furthermore, dynamically the mechanical turbulence is found to resemble an unforced Lorenz model whereas the convective turbulence resembles a forced Lorenz model.     

Forward Lagrangian stochastic simulation of a transient source in the atmospheric surface layer

We show that a forward Lagrangian stochastic (LS) model simulates well the ensemble-averaged concentration transient due to a short time (5 min) point source in the uniform atmospheric surface layer. In LS models, computational particles, which may not descend below ground level, are necessarily reflected at an imposed (artificial) boundary above ground. Model results were rather insensitive to the placing of the lower reflection boundary, and no definite benefit stemmed from including a parametrization for unresolved delays/displacements beneath the lower boundary.     

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.     

Experimental investigation of atmospheric boundary layer turbulence

This paper describes how to measure turbulence in the atmospheric boundary layer (ABL) in order to address certain problems in modern atmospheric physics. These problems mainly relate to the Earth's energy budget (including the hydrological cycle) and biogeochemical cycles. Starting from the main characteristic numbers and the basic equations of atmospheric turbulent flow, we show what turbulence parameters are important to measure. Special attention is given to the various methods used to compute the turbulent fluxes. We analyse the range of scales which has to be measured to properly capture the eddies contributing to the turbulent transfers. This range of scales determines what sensors can be used in the atmospheric surface layer and in the ABL. We describe the most widely used instruments and their performances. The principal platforms used to deploy these instruments are examined. Aircraft are described in more details, because they allow a thorough exploration of the ABL. In the last section, some examples of ABL turbulence signals measured in various conditions are presented. These examples illustrate horizontally homogeneous turbulence as well as inhomogeneous signals for which standard analysis techniques cannot be used. We show how some recent techniques, like wavelet transforms, can help to investigate this kind of signal. At the end, we present what would be interesting to do in the near future for the study of ABL turbulence.     

Numerical simulation of particle trajectories in inhomogeneous turbulence,III: Comparison of predictions with experimental data for the atmospheric surface layer

It is shown that predictions of a numerical trajectory-simulation method agree closely with the Project Prairie Grass observations of the concentrations 100 m downwind of a continuous point source of sulphur dioxide if the height (z) dependence of the Lagrangian length scale Λ _L is chosen as: whereL is the Monin-Obukhov length. The value of 0.5 for Λ _L /z in neutral conditions is consistent with the findings of Reid (1979) for the Porton experiment, and is also shown to be the best choice for simulation of an experiment in which concentration profiles were measured a short distance (< 40 m) downwind of an elevated point source of glass beads (40 μn diameter). $$\begin{gathered} \Lambda _L = 0.5z\left( {1 - 6\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} L< 0 \hfill \\ \Lambda _L = 0.5z/\left( {1 + 5\frac{z}{L}} \right)L > 0 \hfill \\ \end{gathered} $$      

The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering

Townsend's attached eddy hypothesis states that the turbulent structure in the constant stress layer can be decomposed into attached and detached eddy motion. This paper proposes and tests a methodology for separating the attached and detached eddy motion from time series measurements of velocity and temperature. The proposed methodology is based on the time-frequency localization and filtering capabilities of the orthonormal wavelet transforms. Using a relative entropy statistical measure, the optimal wavelet basis is identified first. The turbulence time series measurements are then transformed into the wavelet domain where the contribution of specific events in the time-frequency domain is identified. The filtering scheme utilizes a recently constructed Lorentz thresholding methodology that successfully eliminates all wavelet coefficients associated with the detached eddy motion. While this filtering scheme lacks the compression efficiency of the classical Donoho and Johnstone's universal thresholding model, it conserves the higher-order statistics and important turbulence interactions related to the Reynolds stresses. Following the filtering scheme, the attached eddy motion time series is re-constructed by an inverse wavelet transform of the non-zero wavelet coefficients. The proposed partitioning methodology for attached and detached eddy motion is tested using 56 Hz triaxial sonic anemometer velocity and temperature measurements above a uniform dry lake bed in Owens valley, California, for a wide range of atmospheric stability conditions. Validation that the wavelet filtered time series represents the attached eddy motion is also discussed in the context of conservation of turbulence energy and surface fluxes.     

Thermal plumes and turbulence spectra in the atmospheric boundary layer

Experimental observations on the temperature and wind fields above flat grassy terrain have been obtained with an instrumented 92-m tower during intervals of strong insolation about midday. The turbulence characteristics of the air confirm that free convection prevailed at heights between 16 and 48 m, with some tendency for departure at higher levels. The spectra of temperature and vertical velocity contain gaps at wave numbers in the range 0.01–0.025 m^–1. These are attributed to natural thermal plumes that act as sources of extra energy input to the Kolmogorov-Obukhov-Corrsin scheme of turbulence in or at the low-wave number limit of the inertial subrange. Modified forms of the K-O-C spectral laws for thermally unstable air are derived which agree with the observed spectra over the whole range of wave numbers examined, and which contain the spectral gap at wave numbers corresponding to the thermal plume diameters.     

Turbulent dispersion in the atmospheric surface layer

By non-dimensionalizing a trajectory-simulation (TS) model of turbulent dispersion, it is shown that the dimensionless concentration z ₀cu_*/kQ (cu _*/kQ) due to a continuous line (area) source of strength Q in the atmospheric surface layer depends only on z/z ₀, x/z ₀, z ₀/L and z _s/z₀, where z _s is the source height. The TS model is used to tabulate concentration profiles due to ground-level line and area sources. Concentration profiles generated by the TS model for elevated sources are shown to be inconsistent with the Reciprocal Theorems of Smith (1957) and it is suggested that this is because the flux-mean gradient closure scheme inherent in the Reciprocal Theorem is invalid for an elevated source.     

Temperature structure in the atmospheric surface layer

Production, transport and dissipation terms in the temperature variance equation have been measured in the atmospheric surface layer. The transport term is, within the experimental uncertainty, negligible. The dissipation term, determined by assuming local isotropy, is approximately equal to production under near-neutral conditions. For moderately unstable conditions, the ratio of production to dissipation is 1.4. The resulting imbalance in the budget is attributed to the inequality between the three components of the dissipation term. The Kolmogorov constant for temperature is found to be about 0.8.     

Two-point coherence in the atmospheric surface layer

Two-point, one-dimensional coherence in horizontally homogeneous atmospheric turbulence is studied, both by experiment and analysis. Measurements are carried out using horizontally spaced sensors with the separation perpendicular to the mean velocity. Two-dimensional spectral models and three-dimensional inertial-range spectral tensors are used in the coherence calculations. The one-dimensional coherence for both velocity and scalar fluctuations is found to roll off at a wavenumber much smaller than we would expect from the classical notion of eddy correlation. This is a consequence of the cancellation of Fourier components aliased from the direction of the sensor separation into the streamwise direction. However, the coherence for the three velocity components behaves somewhat differently, reflecting the relative orientations of the velocity component, sensor separation and the mean velocity. These features are well predicted by the calculation. The analysis is also extended to calculate the two-point scalar-vertical velocity cospectrum and the results are in good agreement with our experimental data. The ratio of two- to one-point cospectra decreases at slightly larger wavenumber than the two-point scalar coherence does.     

Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer

Boundary-layer measurements conducted at the Marsta site in Sweden from a winter-time situation (23–25 Feb.) with stable stratification have been analysed. The data comprise wind and temperature profile measurements up to 30 m, turbulence measurements at 2, 6 and 30 m and Doppler acoustic sounder data up to about 150 m. The upwind fetch at the site is flat and free from obstacles to a distance of ca 5 km for the particular sector chosen for the experiment.During the night, a two-layer vertical structure developed. Analysis of power spectra, co-spectra and variances in a shallow and very stable turbulent boundary layer near the ground show that the turbulence is fully developed and follow the universal behaviour.Above, at a height of 30 m, another turbulent layer is produced by increased wind shear near a low-level jet. This turbulent upper layer can be regarded as a layer of free shear flow. At this height, there also exist wave-turbulence interactions at low frequencies which sometimes cause a countergradient heat flux.     

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。     

An investigation of the turbulence balance equations in the atmospheric boundary layer

Three Cardington turbulence probes were operated at heights of 61, 91, and 152 m over a 5-h period in an unstable boundary layer. The results have been used to assess (at the middle level) the relative importance of the terms in the turbulence equations for kinetic energy, temperature variance, stress, and the vertical and total horizontal heat fluxes.Now at the Building Research Station, Garston, Watford, England.     

Stably stratified flow in a marine atmospheric surface layer

Data from the marine atmospheric surface layer have been analysed. The data set consists of about two weeks with tower measurements up to 31 m of mean profiles of wind, temperature, and humidity, together with 20 Hz turbulence data. Mean wind, temperature, and humidity profiles up to 2000 m are also available from pibal trackings and radio soundings. Wave height was measured at 2 Hz, using an inverted echo-sounder.It was found from pibal wind profiles that low level jets were present during 2/3 of the measurements, having their maxima in the height interval 40 to 300 m. Here only data from the remaining 1/3 of the measurements, without low level jets, have been analysed.Non-dimensional wind and temperature gradients agree with results over homogeneous land surfaces as regards stability dependence during stable conditions that prevailed during this experiment. Linear regression gave _m = 1 + 6.8z/L and _m = 1 + 8.3z/L. No significant sea wave influence was found. The same was vrue for me dimensionless standard deviations of the three wind components, except for the vertical component. The expected wind speed dependence was found for the neutral drag coefficient, givingC _dN = 0.109U + 0.33 at 10 m, and a dependence on the wave parameter,C/u _*, was confirmed. Note, however, that the data set was restricted to low and moderate wind speeds and that stratification was mainly stable.Power spectra, non-dimensionalized according to suface-layer theories, do not follow the expected stability dependence. It was shown that this may be a consequence of the presence of gravity waves in the stable marine boundary layer. Indicators of gravity waves were found in most runs. The TKE budget agrees with findings over homogeneous land areas. The pressure transport term was found to be a source of energy also for near neutral conditions.     

Measurements of turbulence structure in the boundary layer on a rough surface

Mean products of velocity fluctuations up to fourth order have been measured in a wind tunnel at the trailing edge of a flat plate, one side of which was covered with floor-sanding paper to produce a fully rough surface. This set-up permits easy comparison of structural parameters in smooth-wall and rough-wall boundary layers. The Reynolds-stress profiles and second-order parameters are closely the same on the rough and smooth surfaces; in particular the decrease in Reynolds shear stress near the rough surface, encountered by several other laboratory workers, was not found in the present results. The triple products are spectacularly altered for a distance of up to 10 roughness heights from the rough surface, and imply a large net rate of transport of turbulent energy and shear stress towards the surface. Comparison with other published data shows that the behaviour of this modified region depends on roughness geometry as well as on the roughness height itself; for example, the mean cube of the normal-component fluctuation remains positive (energy transport away from the surface) over sand or gravel roughness but goes negative, like the other energy-transport terms, over crop canopies.     

The atmospheric boundary layer over a wavy surface

The wavy area of north-west Bohemia (Czechoslovakia) is simulated by a cylindrical surface model. A curvilinear orthogonal system of coordinates along the model surface is introduced. The hydrodynamical equations of motion are transformed into this system of coordinates. By applying boundary-layer assumptions, the equations of motion for the atmospheric boundary layer (ABL) above the model are derived. The equations and boundary conditions show an equivalence of the ABL above the model with that above a flat surface with external pressure gradient.