ENERGY-INERTIAL SCALE INTERACTIONS FOR VELOCITY AND TEMPERATURE IN THE UNSTABLE ATMOSPHERIC SURFACE LAYER

Triaxial sonic anemometer velocity and temperature measurements were used to investigate the local structure of the velocity and temperature fluctuations in the unstable atmospheric surface layer above a grass-covered forest clearing. Despite the existence of a 2/3 power law in the longitudinal velocity (2 decades) and temperature (1 decade) structure functions, local isotropy within the inertial subrange was not attained by the temperature field, although a near-isotropic state was attained by the velocity field. It was found that sources of anisotropy were due to interactions between the large-scale and small-scaleeddy motion, and due to localvelocity-thermal interactions. Statistical measures were developed and used to quantify these types of interactions. Other types of interactions were also measured but were less significant. The temperature gradient skewness was measured and found to be non-zero in agreement with other laboratory flow types for inertial subrange scales. Despite these interactions and anisotropy sources in the local temperature field, Obukhovs 1949hypothesis for the mixed velocity-temperature structure functions was found to be valid. Finally, our measurements show that while a 2/3 power-law in the longitudinal velocity structure function developed at scales comparable to five times the height from the ground surface (z), near-isotropic conditions wereachieved at scales smaller than z/2.     

Wavelet Analysis of Intermittent Turbulent Transport in the Atmospheric Surface Layer over a Monsoon Trough Region

The structure of the turbulence in the atmospheric surface layer over a monsoon trough region has been studied using structural analysis based on wavelet transform. The observational site is located at the eastern (wet) end of the monsoon trough region, characterized by high moisture in the atmospheric surface layer. On the average relative humidity varied from 70% to 100% during the experiment. The wind and temperature data, collected at Kharagpur (22°25' N, 87°18' E) at six observational hours of a day in June 1990 during the Monsoon Trough Boundary Layer Experiment (MONTBLEX), have been utilized in the study. The wind and instantaneous momentum flux time series were decomposed into 12 scales using the Haar wavelet transform. The eddies exhibited a large temporal variability generating intermittency in the energy and flux distributions. A criterion based on the isotropy has been suggested for separating the large eddies from the small eddies. At the separation scale the isotropy coefficient drops sharply. It is shown that the intermittency in the small eddies resulted from the spatial variation of energy, and deviation of velocity statistics from the Gaussian distribution known as flatness. The deviation from the -5/3 power law has been attributed to the increased mean values of, (i) the coefficient of variation of energy, and (ii) the flatness factor, in the inertial subrange. The decomposition of the instantaneous momentum flux time series reveals that the major contribution to the total flux arises from the large eddies. The quadrant analysis of the momentum flux shows that ejections and sweeps account for a substantial part of the total flux, and quantifies the relative importance of the various spatial scales that contribute to the transport of momentum.     

Spectral scaling in a high reynolds number laboratory boundary layer

Spectra and co-spectra of the streamwise (u) and normal or vertical (w) velocity fluctuations have been measured in the inner region of a large Reynolds number laboratory boundary layer over a rough wall. There is reasonable evidence of ak ₁ ^–1 range in theu spectrum (wherek ₁ is the streamwise wavenumber). Such a range results from an overlap between a spectral region dominated by largescale, inactive motion, which scales on the boundary-layer thickness, and a region dominated by smaller-scale, active motion which scales on the distance from the wall. Spectra ofw, anduw cospectra, scale in a manner consistent with the dominance by active motion. The present spectral data do not support local isotropy over the inertial subrange. A comparison between measuredw spectra and calculations based on isotropy indicates that the inertial subrange anisotropy is only slightly affected by the magnitude of the non-dimensional mean shear.     

Local isotropy and anisotropy in the sheared and heated atmospheric surface layer

Longitudinal velocity and temperature measurements above a uniform dry lakebed were used to investigate sources of eddy-motion anisotropy within the inertial subrange. Rather than simply test the adequacy of locally isotropic relations, we investigated directly the sources of anisotropy. These sources, in a daytime desert-like climate, include: (1) direct interaction between the large-scale and small-scale eddy motion, and (2) thermal effects on the small-scale eddy motion. In order to explore these two anisotropy sources, we developed statistical measures that are sensitive to such interactions. It was found that the large-scale/small-scale interaction was significant in the inertial subrange up to 3 decades below the production scale, thus reducing the validity of the local isotropy assumption. The anisotropy generated by thermal effects was also significant and comparable in magnitude to the former anisotropy source. However, this thermal anisotropy was opposite in sign and tended to counteract the anisotropy generated by the large-scale/smallscale interaction. The thermal anisotropy was attributed to organized ramp-like patterns in the temperature measurements. The impact of this anisotropy cancellation on the dynamics of inertial subrange eddy motion was also considered. For that purpose, the Kolmogorov-Obukhov structure function equation, as derived from the Navier-Stokes equations for locally isotropic turbulence, was employed. The Kolmogorov-Obukhov structure function equation in conjunction with Obukhov's constant skewness closure hypothesis reproduced the measured second- and third-order structure functions. Obukhov's constant skewness closure scheme, which is also based on the local isotropy assumption, was verified and was found to be in good agreement with the measurements. The accepted 0.4 constant skewness value derived from grid turbulence experiments overestimated our measurements. A suggested 0.26 constant skewness value, which we derived from Kolmogorov's constant, was found to be adequate.     

Some Thoughts On Local Isotropy And The 4/3 Lateral To Longitudinal Velocity Spectrum Ratio

Applications of Kolmogorov's universal equilibrium hypothesis and the Taylor transform to velocity spectra derived from measurements within the low frequency portion of the atmospheric surface layer (ASL) inertial subrange are examined. The measured ratios of lateral to longitudinal velocity component spectra exhibit considerable scatter, but suggest convergence towards 1.0 rather than towards the 4/3 expected from theory. Shear and buoyancy introduce anisotropy to the inertial subrange, thereby contributing to the observed scatter. The apparent discrepancy between the 4/3 velocity component spectrum ratio expected from theory and the measurements could arise as a consequence of the processing used to produce spectra. These processing effects must be considered from the perspective of the propagating eddy. Spectral averaging used with sonic anemometer data is done over time periods that are large with respect to inertial subrange eddy correlation decay times. This averaging causes energy from larger scale eddies to appear as `local convection' that dominates the Taylor transform. Spectrum ratio convergence and cospectra approaching zero are necessary, but not sufficient, conditions for onset of local isotropy. Measurements of spectrum ratios and cospectra over the entire inertial subrange are needed to determine whether or not local isotropy might occur within the ASL.     

Statistical properties of optical refractive index fluctuations in the marine boundary layer

The optical refractive index fluctuation has been determined from measurements of turbulent temperature and humidity fluctuations in the atmospheric surface layer over the ocean. Probability density, spectral density and even- and odd-order structure functions of the refractive index fluctuation are presented. The spectral density exhibits a significant -5/3 inertial subrange as a result of the existence of a -5/3 subrange in the spectra of temperature and humidity fluctuations and in the temperature-humidity co-spectrum. The behaviour in the inertial subrange of fourth- and sixth-order structure functions of the refractive index is in reasonable agreement with that predicted by the analysis of Antonia and Van Atta (1975, 1978). The third-order structure functions of the refractive index exhibit an approximately linear dependence on separation in the inertial subrange, in agreement with a ramp model for the large coherent structure of the motion.     

Comparison of Kansas Data with High-resolution Large-eddy Simulation Fields

The surface layer of an atmospheric boundary layer (ABL) is most accessible to field measurements and hence its ensemble-mean structure has been well established. The Kansas field measurements were the first detailed study of this layer, providing numerous benchmark statistical profiles for a wide range of stability states. Large-eddy simulation (LES), in contrast, is most suitable for studying the mixed layer of the ABL where the energy-containing range of the vertical velocity field is well resolved. In the surface layer, typical large-eddy simulations barely resolve the energy-containing vertical-velocity fields and hence do not provide sufficient data for a detailed analysis.We carried out a nested-mesh simulation of a moderately convective ABL (-z_i/L = 8) in which the lower 6% of the boundary layer had an effective grid resolution of 512³. We analyze the LES fields above the 6th vertical grid level (z = 23 m) where the vertical velocity field has a well formed inertial subrange, for a detailed comparison with the Kansas results. Various terms in the budgets of turbulent kinetic energy, temperature variance, Reynolds stress, temperature flux, and some higher order moments are compared. The agreement is generally quite good; however, we do observe certain discrepancies, particularly in the terms involving pressure fluctuations.     

广州市近地层大气的湍流微结构和谱特征

本文利用UVW脉动风速仪资料分析了广州市区近地层大气的湍流强度、相关系数、尺度和速度谱,并获得了不同稳定度条件下的速度谱模式.结果表明,城市近地层大气湍流在惯性副区接近局地各向同性、速度谱符合Kolmogorov相似理论;气流方向上下垫面粗糙度的增加,使沿海城市近地层大气湍流能量(特别是铅直方向)比平坦、均匀下垫面上的增加.     

Drag coefficients and turbulence spectra within three boreal forest canopies

Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C _d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C _d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.     

A Lagrangian Decorrelation Time Scale in the Convective Boundary Layer

A new method for deriving the Lagrangian decorrelation time scales for inhomogeneous turbulence is described. The expression for the time scales here derived for the convective boundary layer is compared to those estimated by Hanna during the Phoenix experiment. Then the values of C₀, the Lagrangian velocity structure function constant, and of B_i, the Lagrangian velocity spectrum constant, were evaluated from the Eulerian velocity spectra and from the Lagrangian time scales derived, under unstable conditions, from Taylor's statistical diffusion theory. The numerical coefficient of the lateral and vertical Lagrangian spectra in the inertial subrange was found equal to 0.21, in good agreement with previous experimental estimates.     

Surface layer turbulence spectra and dissipation rates during low winds in tropics

Spectral characteristics of surface layer turbulence in an urban atmosphere are investigated. The observations used for this purpose represent low wind conditions in the tropics. The normalized power spectral shapes exhibit the usual characteristics in the inertial subrange and obey Monin-Obukhov scaling. However, the low-frequency behaviours do not conform to the previous observed relations. For horizontal components, large energy is contained in the low frequencies in contrast to the vertical component where roll-off to zero frequency is faster.The turbulent kinetic energy dissipation rate estimated from the spectra using Kolmogorov's inertial subrange law is found to be isotropic unlike the velocity variances. The expressions for the dimensionless dissipation rate do not seem to work well in low winds in an urban atmosphere. For the data considered, the dissipation rate exhibits a power law relationship with the mean windspeed and the friction velocity.     

Estimation of the Lagrangian Velocity Structure Function Constant C0 by Large-Eddy Simulation

The inertial subrange Kolmogorov constant C ₀, which determines the effective turbulent diffusion in velocity space, plays an important role in the Lagrangian modelling of pollutants. A wide range of values of the constant are found in the literature, most of them determined at low Reynolds number and/or under different assumptions. Here we estimate the constant C ₀ by tracking an ensemble of Lagrangian particles in a planetary boundary layer simulated with a large-eddy simulation model and analysing the Lagrangian velocity structure function in the inertial subrange. The advantage of this technique is that it easily allows Reynolds numbers to be achieved typical of convective turbulent flows. Our estimates of C ₀ is C ₀=4.3±0.3 consistent with values found in the literature     

An Investigation into Ridge-Top Turbulence Characteristics During Neutral and Weakly Stable Conditions: Velocity Spectra and Isotropy

An investigation into high Reynolds number turbulent flow over a ridge top in New Zealand is described based on high-resolution in-situ measurements, using ultrasonic anemometers for two separate locations on the same ridge with differing upwind terrain complexity. Twelve 5-h periods during neutrally stratified and weakly stable atmospheric conditions with strong wind speeds were sampled at 20 Hz. Large (and small) turbulent length scales were recorded for both vertical and longitudinal velocity components in the range of 7–23 m (0.7–3.3 m) for the vertical direction and 628–1111 m (10.5–14.5 m) for the longitudinal direction. Large-scale eddy sizes scaled to the WRF (Weather Research and Forecasting) numerical model simulated boundary-layer thickness for both sites, while small-scale turbulent features were a function of the complexity of the upwind terrain. Evidence of a multi-scale turbulent structure was obtained at the more complex terrain site, while an assessment of the three-dimensional isotropy assumption in the inertial subrange of the spectrum showed anisotropic turbulence at the less complex site and evidence of isotropic turbulence at the more complex site, with a spectral ratio convergence deviating from the 4/3 or unity values suggested by previous theory and practice. Existing neutral spectral models can represent locations along the ridge top with simple upwind complexity, especially for the vertical wind spectra, but sites with more orographic complexity and strong vertical wind speeds are often poorly represented using these models. Measured spectra for the two sites exhibited no significant diurnal variation and very similar large-scale and small-scale turbulent length scales for each site, but the turbulence energy measured by the variances revealed a strong diurnal difference.     

一次降水性冷锋的边界层谱特征及尺度分析

本文使用１９９４年１月１５日至１９日南京北郊二台洞梯度观测站１９９５年气象塔的实测资料，南京小教场的地面和探空资料。对９４年１月份发生的一次伴有大量降水的强冷锋的湍流谱及多尺度时间、空间分布进行了计算分析。     

The local effect of intermittency on the inertial subrange energy spectrum of the atmospheric surface layer

Orthonormal wavelet expansions are applied to atmospheric surface layer velocity measurements. The effect of intermittent events on the energy spectrum of the inertial subrange is investigated through analysis of wavelet coefficients. The local nature of the orthonormal wavelet transform in physical space makes it possible to identify a relationship between the inertial subrange slope of the local wavelet spectrum and a simple indicator (i.e. the local variance of the signal) of local intermittency buildup. The slope of the local wavelet energy spectrum in the inertial subrange is shown to be sensitive to the presence of intermittent events. During well developed intermittent events (coherent structures), the slope of the energy spectrum is somewhat steeper than -5/3, while in less active regions the slope is found to be flatter than -5/3. When the slopes of local wavelet spectra are ensemble averaged, a slope of -5/3 is recovered for the inertial subrange.     

稳定条件下盆地上空大气边界层湍谱特征

本文利用100m~3系留气艇携带超声风温仪在复杂的盆地地形上空对1000m以下大气进行观测所获得的资料,研究小风稳定条件下大气边界层湍流结构特征。结果表明,在双对数坐标中,纵向速度u谱,垂直速度w谱,温度T谱在惯性区均遵循Kolmogorov的-2/3次律;横向速度V谱有其特殊的情形;协谱uw,wT及近地层的uT协谱在惯性区服从-4/3次律。和平坦、均一、开阔下垫面不同的是谱的峰值频率向高频移动,且没有发现近地层具有的谱峰随高度的明显变化关系。     

On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy

Particle image velocimetry (PIV) data obtained in a wind-tunnel model of a canopy boundary layer is used to examine the characteristics of mean flow and turbulence. The vector spacing varies between 1.7 and 2.5 times the Kolmogorov scales. Conditional sampling based on quadrants, i.e. based on the signs of velocity fluctuations, reveals fundamental differences in flow structure, especially between sweep and ejection events, which dominate the flow. During sweeps, the downward flow generates a narrow, highly turbulent, shear layer containing multiple small-scale vortices just below canopy height. During ejections, the upward flow expands this shear layer and the associated small-scale flow structures to a broad region located above the canopy. Consequently, during sweeps the turbulent kinetic energy (TKE), Reynolds stresses, as well as production and dissipation rates, have distinct narrow peaks just below canopy height, whereas during ejections these variables have broad maxima well above the canopy. Three methods to estimate the dissipation rate are compared, including spectral fits, measured subgrid-scale (SGS) energy fluxes at different scales, and direct measurements of slightly underresolved instantaneous velocity gradients. The SGS energy flux is 40–60% of the gradient-based (direct) estimates for filter sizes inside the inertial range, while decreasing with scale, as expected, within the dissipation range. The spectral fits are within 5–30% of the direct estimates. The spectral fits exceed the direct estimates near canopy height, but are lower well above and below canopy height. The dissipation rate below canopy height increases with velocity magnitude, i.e. it has the highest values during sweep and quadrant 1 events, and is significantly lower during ejection and quadrant 3 events. Well above the canopy, ejections are the most dissipative. Turbulent transport during sweep events acts as a source below the narrow shear layer within the canopy and as a sink above it. Transport during ejection events is a source only well above the canopy. The residual term in the TKE transport equation, representing mostly the effect of pressure–velocity correlations, is substantial only within the canopy, and is dominated by sweeps.     

Turbulence Spectra And Dissipation Rates Above And Within A Forest Canopy

Three velocity componentsand temperature were measured usingthree-dimensional sonic anemometers/thermometers attwo levels, above and within a forest canopy, in theChangbai Mountains of northeast China. Turbulencespectral structure, local isotropy anddissipation rates above and within the forest canopywere calculated using the eddy correlation method.Results show that the normalized turbulent spectralcurves have -2/3 slopes in the inertial subrange.While the shapes of the spectra are in good agreementwith the Kansas flat terrain results, the atmosphericturbulence is anisotropic above the forest canopy. Dueto breaking down of large eddies by the foliage,branches and trunks, the spectral peak frequencies forvelocity and temperature are higher withinthan above the forest canopy. Compared withmeasurements from previous studies over flat terrain,the velocity and temperature spectra above andinside the forest canopy appear to shift toward higherfrequencies. The turbulence is approximately isotropicin the inertial subrange within the forest canopy, and isanisotropic above the forest canopy. The turbulentkinetic energy and heat energy dissipation rates aboveand inside the forest canopy are much larger thanthose obtained by Kaimal and Hogstrom over grasslandand grazing land. The distinct features in the resultsof the present experiment may be attributed to thedynamic forcing caused by the rough surface of the forestcanopy.     

On the Temporal Distribution of Bursts and Events in the Stable Marine Atmospheric Surface Layer

A methodology for tracing the bursting phenomenon occurring in the turbulent boundary-layer is applied to stable marine atmospheric boundary-layer (MABL) data, collected within the framework of the Coupled Boundary Layer Air-Sea Transfer, Low wind component experiment at Nantucket Island, 2003, Massachusetts, USA. For the definition of the events contributing to the bursting phenomenon, the quadrant analysis of the momentum flux with varying threshold value is utilized. The present work aims at the better understanding of the time scales of the microstructures in the MABL, by providing the number of the events and the groups and their mean duration and the time difference of all quadrants of the quadrant analysis, for different thresholds and under different meteorological conditions. The interrelation of the different time scales as well as the correlation between the quadrants are investigated and discussed. Also, it is demonstrated that the procedure of grouping events leads to bursts with a mean duration that is independent of the threshold value, for the most important quadrants of the momentum transfer (2 and 4). It is found that the combination of near-neutral conditions with low wind speed permits the development of larger duration events within the stable MABL. Finally, it is shown that the groups of events maintain adequate time and flux coherence only for quadrants 2 and 4.     

Estimation Of The Lagrangian Structure Function Constant C0 From Surface-Layer Wind Data

Eulerian turbulence observations, madein the surface layer under unstable conditions (z/L > 0),by a sonic anemometer were used to estimatethe Lagrangian structure function constant _O. Twomethods were considered. The first one makes use of arelationship, widely used in the Lagrangian stochasticdispersion models, relating _O to the turbulent kineticenergy dissipation rate , wind velocity variance andLagrangian decorrelation time. The second one employsa novel equation, connecting _O to the constant of thesecond-order Eulerian structure function. Beforeestimating _O, the measurements were processed in orderto discard non-stationary cases at least to a firstapproximation and cases in which local isotropy couldnot be assumed. The dissipation was estimated eitherfrom the best fit of the energy spectrum in theinertial subrange or from the best fit of the third-orderlongitudinal Eulerian structure function. Thefirst method was preferred and applied to the subsequentpart of the analysis. Both methods predict thepartitioning of _O in different spatial components as aconsequence of the directional dependence of theEulerian correlation functions due to the isotropy.The _O values computed by both methods are presented anddiscussed. In conclusion, both methods providerealistic estimates of _O that compare well withprevious estimations reported in the literature, evenif a preference is to be attributed to the second method.