A Theoretical and Experimental Investigation of Energy-Containing Scales in the Dynamic Sublayer of Boundary-Layer Flows

The existence of universal power laws at low wavenumbers (K) in the energy spectrum (E_u) of the turbulent longitudinal velocity (u) is examined theoretically and experimentally for the near-neutral atmospheric surface layer. Newly derived power-law solutions to Tchen's approximate integral spectral budget equation are tested for strong- and weak-interaction cases between the mean flow and turbulent vorticity fields. To verify whether these solutions reproduce the measured E_u at low wavenumbers, velocity measurements were collected in the dynamic sublayer of the atmosphere at three sites and in the inner region of a laboratory open channel. The atmospheric surface layer measurements were carried out using triaxial sonic anemometers over tall corn, short grass, and smooth desert-like sandy soil. The open channel measurements were performed using a two-dimensional boundary-layer probe above a smooth stainless steel bed. Comparisons between the proposed analytical solution for E_u, the dimensional analysis by Kader and Yaglom, and the measured Haar wavelet E_u spectra are presented. It is shown that when strong interaction between the mean flow and turbulent vorticity field occurs, wavelet spectra measurements, predictions by the analytical solution, and predictions by the dimensional analysis of Kader-Yaglom (KY) are all in good agreement and confirm the existence of a -1 power law in E_u(= C_uuu² _* K^-1, where C_uu is a constant and u_* is the friction velocity). The normalized upper wavenumber limit of the -1 power law (Kz = 1, where z is the height above the zero-plane displacement) is estimated using two separate approaches and compared to the open channel and atmospheric surface-layer measurements. It is demonstrated that the measured upper wavenumber limit is consistent with Tchen's budget but not with the KY assumptions. The constraints as to whether the mean flow and turbulent vorticity strongly interact are considered using a proposed analysis by Panchev. It is demonstrated that the arguments by Panchev cannot be consistent with surface-layer turbulence. Using dimensional analysis and Heisenberg's turbulent viscosity model, new constraints are proposed. The new constraints agree with the open channel and atmospheric surface-layer measurements, Townsend's inactive eddy motion hypothesis, and the Perry et al. analysis.     

Large-Scale Turbulence Structures and Their Contributions to the Momentum Flux and Turbulence in the Near-Neutral Atmospheric Boundary Layer Observed from a 213-m Tall Meteorological Tower

Large-scale turbulence structures in the near-neutral atmospheric boundary layer (ABL) are investigated on the basis of observations made from the 213-m tall meteorological tower at Tsukuba, Japan. Vertical profiles of wind speed and turbulent fluxes in the ABL were obtained with sonic anemometer-thermometers at six levels of the tower. From the archived data, 31 near-neutral cases are selected for the analysis of turbulence structures. For the typical case, event detection by the integral wavelet transform with a large time scale (180 s) from the streamwise velocity component (u) at the highest level (200 m) reveals a descending high-speed structure with a time scale of approximately 100 s (a spatial scale of 1 km at the 200-m height). By applying the wavelet transform to the u velocity component at each level, the intermittent appearance of large-scale high-speed structures extending also in the vertical is detected. These structures usually make a large contribution to the downward momentum transfer and induce the enhancement of turbulent kinetic energy. This behaviour is like that of “active” turbulent motions. From the analysis of the two-point space–time correlation of wavelet coefficients for the u velocity component, the vertical extent and the downward influence of large-scale structures are examined. Large fluctuations in the large-scale range (wavelet variance at the selected time scale) at the 200-m level tend to induce the large correlation between the higher and lower levels.     

南海台风边界层湍流小波分析

利用小波变换（WT）对香港天文台飞机观测台风“妮妲”（1604）资料进行分析,研究在不稳定、不均匀的台风边界层中湍流涡旋的垂直传输作用。在0.1~5 Hz惯性子区内横风和顺风分量功率谱密度能较好符合-5/3幂律。小波分析显示:横风的小波功率谱峰值集中在1 km之下,顺风分量的小波功率谱峰值集中在1~6 km之间;眼区动量通量的主要贡献尺度为2.3 km,眼区外主要贡献尺度在1~2 km,中低层为较小尺度（< 1.0 km）;湍流功能(TKE)的生成尺度主要集中在4 km之下。这项研究定量描述了南海北部台风边界层各个区域湍流结构的差异特征,讨论了对台风边界层通量参数化的可能影响。      

Turbulent Flux Measurements Above and Below the Overstory of a Boreal Aspen Forest

Turbulent flux measurements both above and beneath the canopy of a boreal aspen forest are described. Velocity skewness showed that, beneath the aspen canopy, turbulence was dominated by intermittent, downward penetrating gusts. Eulerian horizontal length scales calculated from integration of the autocorrelation function or spectral peaks were 9.0 and 1.4 times the mean aspen height of 21.5 m respectively. Above-canopy power spectral slopes for all velocity components followed the -2/3 power law, whereas beneath-canopy slopes were closer to -1 and showed a spectral short cut in the horizontal and vertical components. Cospectral patterns were similar both above and beneath the canopy. The Monin–Obukhov similarity function for the vertical wind velocity variance was a well-defined function of atmospheric stability, both above and beneath the canopy. Nocturnal flux underestimation and departures of this similarity function from that expected from Monin–Obukhov theory were a function of friction velocity. Energy balance closure greater than 80% was achieved at friction velocities greater than 0.30 and 0.10 m s-1, above and below the aspen canopy, respectively. Recalculating the latent heat flux using various averaging periods revealed a minimum of 15 min were required to capture 90% of the 30-min flux. Linear detrending reduced the flux at shorter averaging periods compared to block averaging. Lack of energy balance closure and erratic flux behaviour led to the recalculation of the latent and sensible heat fluxes using the ratio of net radiation to the sum of the energy balance terms.     

A grid nesting method for large-eddy simulation of planetary boundary-layer flows

A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models.Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.     

A spectral and lag-correlation analysis of turbulence in a deciduous forest canopy

The processes influencing turbulence in a deciduous forest and the relevant length and time scales are investigated with spectral and cross-correlation analysis. Wind velocity power spectra were computed from three-dimensional wind velocity measurements made at six levels inside the plant canopy and at one level above the canopy. Velocity spectra measured within the plant canopy differ from those measured in the surface boundary layer. Noted features associated with the within-canopy turbulence spectra are: (a) power spectra measured in the canopy crown peak at higher wavenumbers than do those measured in the subcanopy trunkspace and above the canopy; (b) peak spectral values collapse to a relatively universal value when scaled according to a non-dimensional frequency comprised of the product of the natural frequency and the Eulerian time scale for vertical velocity; (c) at wavenumbers exceeding the spectral peak, the slopes of the power spectra are more negative than those observed in the surface boundary layer; (d) Eulerian length scales decrease with depth into the canopy crown, then increase with further depth into the canopy; (e) turbulent events below crown closure are more correlated with turbulent events above the canopy than are those occurring in the canopy crown; and (f) Taylor's frozen eddy hypothesis is not valid in a plant canopy. Interactions between plant elements and the mean wind and turbulence alter the processes that produce, transport and remove turbulent kinetic energy and account for the noted observations.     

Characterisation and Simulation of the Multiscaling Properties of the Energy-Containing Scales of Horizontal Surface-Layer Winds

The multiscaling statistics of atmospheric surface-layer winds at low wavenumbers above farmland and in the lee of a mountain range were examined using a hot-wire and lightweight cup anemometer. It was found that the horizontal velocity spectra could be broken into high and low-wavenumber regimes according to the parameters given by this analysis. The low-wavenumber end of the spectrum possessed a spectral slope parameter that varied between values of 0.8 and 1.35 at the farmland site during the period of the experiment, and the high-wavenumber end – corresponding to the inertial range – possessed a spectral slope slightly greater than -5/3. The larger values for this parameter for the low-wavenumber end appeared to coincide with unstable conditions. In the lee of the mountain range, the low-wavenumber spectral slope parameter was larger still, at 1.45. The low-wavenumber signals over farmland were much less intermittent than inertial-range signals, but in the lee of the mountain range the intermittency increased. From this analysis, it was shown that the statistical properties of the recorded wind signal could be reproduced using a bounded random multiplicative cascade. The model was successfully used to simulate the wind velocity field directly, rather than simulating the energy dissipation field. Since the spectral slope parameter for low wavenumbers appeared to be a function of atmospheric stability, the method presented is a simple way of generating wind signals characteristic of a variety of atmospheric conditions.     

The characteristics of turbulent moisture on Huaihe river basin in China

Summary ?A lot of work on near surface turbulence characteristics has been done in the experimental study of atmospheric turbulence, but little work on fluctuating scalar field has been done, especially on some quantities such as moisture and pollution. In this paper, with the methods of statistical theory, Fourier transform, fractal geometry and wavelet transform, the turbulent moisture data obtained from Huaihe River Basin Experiment (HUBEX) are studied to explore the statistical, spectral, fractal and intermittent characteristics of turbulent moisture. The results show that: (1) In the high humid area such as Huaihe river basin, the moisture plays an important role in the surface energy balance, energy transportation and cycle. (2) The energy spectra and cospectra are in agreement with the “−2/3” and “−4/3” scaling power law correspondingly in inertial sub-range. (3) The fractal dimension of turbulent moisture in Huaihe river basin is clearly higher than that in other areas (such as Beijing). (4) The fluctuating moisture field has strong intermittency, and is not in accordance with the Kolmogorov theory. With the orthonormal wavelet transform, the dissipative events of the fluctuating moisture field contributing to inertial sub-range intermittency buildup have been identified. After the dissipative events have been suppressed by introducing a conditioning wavelet sampling scheme, the intermittency that affects the statistical structure of inertial sub-range is restrained. However the repressive effects of intermittency on turbulent moisture field are worse than those on turbulent velocity field. The reason may be either the intermittency of turbulent moisture is strong or some coherence structures exist in the turbulent moisture field. Received April 27, 2001; Revised January 23, 2002     

The perturbed structure of the neutral atmospheric boundary layer over irregular terrain

The first-order (linear) response of the planetary boundary layer is calculated for flow over periodic terrain, for variations in both surface roughness and terrain elevation. Calculations are made for horizontal wavenumbers varying from 10^–4m^–1 to 3 × 10^–3m^–1. A simple second-order closure model of the turbulence is used, and Coriolis and buoyancy forces are neglected. As expected, flow over a periodic terrain produces corresponding periodic structure in all meteorological fields above the surface. The periodic structure consists of two components. The first is very nearly evanescent with height, showing little vertical structure. It corresponds to the motion that would be observed were the atmosphere inviscid. The second component, introduced by turbulent viscosity, exhibits considerable vertical structure, with vertical wavelengths the order of 100 m, and thus could be responsible for the layering often seen on acoustic sounder observations of the atmospheric boundary layer.Wave Propagation Laboratory.Environmental Science Group.     

Neutral surface-layer flow over isolated roughness strips

Numerical simulations are used to study neutral surface-layer flow which passes over isolated or widely separated strips of modified roughness embedded in an otherwise homogeneous surface.Simple power laws are given for the maximum height and horizontal extent of turbulent momentum and horizontal mean velocity wakes with an assessment of the range of validity of this proposal. Furthermore, it is indicated, how vertical profiles of energy budget and horizontal mean velocity are distorted by a roughness strip.     

Rapid vertical sampling in stably stratified turbulent shear flows

A new method for obtaining instantaneous vertical profiles of two components of velocity and temperature in thermally stratified turbulent shear flows is presented. In this report, the design and construction of the traversing system will be discussed and results to date will be presented. The method is based on rapid vertical sampling whereby probe sensors are moved vertically at a high speed such that the measurement is approximately instantaneous. The system is designed to collect many measurements for the calculation of statistics such as vertical wave number spectra, mean square vertical gradients, and Thorpe scales. Results are presented for vertical profiles of temperature and compared to vertical profiles measured by single-point Eulerian time averages. The quality of the vertical profiles is found to be good over many profiles. Some comparisons are made between vertical measurements and standard single-point Eulerian measurements for three cases of stably stratified turbulent shear flow in which the initial microscale Reynolds number, Re_λ≈30. In case 1, the mean conditions are characterized by a gradient Richardson number, Ri_g=0.015, for which the flow is “unstable”, meaning the spatially evolving turbulent kinetic energy (E_k) grows. In case 2, Ri_g=0.095, for which the evolving turbulent kinetic energy is almost constant. In case 3, the flow is highly stable, where Ri_g=0.25 and E_k decays with spatial evolution. The measurements indicate anisotropy in the small scales for all cases. In particular, it is found that the ratio grows initially to a maximum and then decays with further evolution. Maximum Thorpe displacements are measured and compared to single-point measures of the vertical scales. It is found that vertical length scales derived from single-point measurements, such as the Ozmidov scale, L_O=(ε/N³)^1/2 and the overturn scale, L_t=θ′/(dT/dz), do not represent well the wide range of overturning scales which are actually present in the turbulence.     

On the Time Evolution of the Turbulent Kinetic Energy Spectrum for Decaying Turbulence in the Convective Boundary Layer

Our focus is the time evolution of the turbulent kinetic energy for decaying turbulence in the convective boundary layer. The theoretical model with buoyancy and inertial transfer terms has been extended by a source term due to mechanical energy and validated against large-eddy simulation data. The mechanical effects in a boundary layer of height z _i at a convective surface-layer height z = 0.05z _i are significant in the time evolution of the vertical component of the spectrum, i.e. they enhance the decay time scale by more than an order of magnitude. Our findings suggest that shear effects seem to feedback to eddies with smaller wavenumbers, preserving the original shape of the spectrum, and preventing the spectrum from shifting towards shorter wavelengths. This occurs in the case where thermal effects only are considered.     

Characterization of Coherent structures in the Atmospheric Surface Layer

The ramplike coherent structures, observed in the temporal series of temperature and humidity in the atmospheric surface layer, are analyzed using the intermittency function and the wavelet transforms, with Haar, D4 and Mexican Hat functions as mother wavelets, in order to find the most efficient conditional sampling technique. It was found that the intermittency function and the wavelet transform, using Mexican Hat as mother wavelet, are the only ones that sample structures that fulfill the ramplike coherent structures definition of a slow rise followed by a sudden drop in the temporal series. The conditionally averaged structures detected by both techniques were similar for temperature, humidity, and vertical velocity at heights of 3, 5, and 9.4 m. Significant discrepancies were found among the conditional averaged structures detected by both techniques for zonal and meridional components of the wind at 11.5 m. Considering both techniques, it was observed that the averagedcoherent-structure duration ranged from 23.7 ± 0.5 s to 37.8 ± 3.0 s. Furthermore, the averaged number of events per 20-minute period ranged from 20.0 ± 1.0 to 28.5 ± 1.1, and the averaged intermittency factor from 45.0 ± 0.4% to 59.1 ± 1.3%. It was also observed that the averaged duration of the ramplike coherent structures increases with height, while their intensity, number, and intermittency factor decrease. Despite the good matching obtained for temperature and humidity, the coherent-structure properties did not show the expected variation with wind speed, stability parameter, and friction velocity. The Kolmogorov–Smirnov test indicated that the intermittent function and the wavelet transform did not detect coherent structures belonging to the same population.     

Turbulence above Lake Ontario: Velocity and scalar statistics

Measurements of the fluctuations of wind, temperature and humidity were made with an instrumented aircraft at altitudes from 30 to 300m above Lake Ontario. The variations of the standard deviations of these fluctuations are examined. By applying Monin-Obukhov similarity theory based on local fluxes, it is shown that the vertical velocity, temperature and humidity fluctuations scale with the local Monin-Obukhov length. In the limit of free convection, 1/3 and –1/3 power laws are approached with constants of 1.2, 1.2, and 0.8 for vertical velocity, temperature and humidity, respectively. The von Karman scale lengths increase with height but were much larger than those found by Taylor et al. (1970).     

An Analytical Footprint Model For Non-Neutral Stratification

We propose an analytical model for the so-called footprint of scalar fluxes in the atmospheric boundary layer. It is the generalization of formulations already given in the literature, which allows to account for thermal stability. Our model is only marginally more complicated than these, and it is therefore simple enough to be applicable for a routine footprint analysis within long-term measurements. The mathematical framework of our model is a stationary gradient diffusion formulation with height-independent crosswind dispersion. It uses the solution of the resulting two-dimensional advection – diffusion equation for power law profiles of the mean wind velocity and the eddy diffusivity. To find the adjoint Monin–Obukhov similarity profile, we propose two different approaches, a purely analytical one and a simplenumerical error minimalization.     

The detection and measurement of turbulent structures in the atmospheric surface layer

Turbulence data from the planetary boundary layer (PBL) indicate the presence of deterministic turbulent structures. These structures often show up as asymmetric ramp patterns in measurements of the turbulent fluctuations of a scalar quantity in the atmospheric surface layer (ASL). The sign of the slope of the sharp upstream edge of such a triangular pattern depends on the thermal stability conditions of the ASL.The turbulent structures in the ASL have been tracked by a detection method which searches for rapid and strong fluctuations in a signal — the VITA (variable interval time averaging) technique. This detection method has previously been employed in laboratory boundary layers. The VITA detection method performs well in the ASL and reveals the presence of vertically coherent turbulent structures, which look similar to those in laboratory shear flows. At the moment that a sharp temperature interface appears, the horizontal alongwind velocity shows a sharp increase, along with a sudden decrease of vertical velocity, independent of the thermal stability conditions of the ASL. The fluctuating static pressure reveals a maximum at that moment. The vertical turbulent transports show a twin-peak character around the time that the sharp jumps in the temperature and the velocity signals appear.     

On equilibrium profiles of suspended particles

A power law is often used to represent the vertical profile of uniform suspended particles above a horizontally homogeneous surface. It serves as an analytical solution representing an equilibrium between vertical turbulent diffusion and gravitational settling, andcan be used to extract settling velocity information from observed particle number density profiles. In this note, we analyse this situation and use a numerical model to investigate the temporal change of particle number density and of the net vertical flux due to turbulent diffusion and gravitational settling. The results show that the net flux approaches zero very slowly for small particles (w_s/ u_* < 1), and show that the power law does not hold for small particles. If the power law is used to extract settling velocities from observed vertical distributions of particle number density in these cases, the estimated settling velocity may be unrealistically large.     

Edge Flow and Canopy Structure: A Large-Eddy Simulation Study

Sharp heterogeneities in forest structure, such as edges, are often responsible for wind damage. In order to better understand the behaviour of turbulent flow through canopy edges, large-eddy simulations (LES) have been performed at very fine scale (2 m) within and above heterogeneous vegetation canopies. A modified version of the Advanced Regional Prediction System (ARPS), previously validated in homogeneous conditions against field and wind-tunnel measurements, has been used for this purpose. Here it is validated in a simple forest-clearing-forest configuration. The model is shown to be able to reproduce accurately the main features observed in turbulent edge flow, especially the “enhanced gust zone” (EGZ) present around the canopy top at a few canopy heights downwind from the edge, and the turbulent region that develops further downstream. The EGZ is characterized by a peak in streamwise velocity skewness, which reflects the presence of intense intermittent wind gusts. A sensitivity study of the edge flow to the forest morphology shows that with increasing canopy density the flow adjusts faster and turbulent features such as the EGZ become more marked. When the canopy is characterized by a sparse trunk space the length of the adjustment region increases significantly due to the formation of a sub-canopy wind jet from the leading edge. It is shown that the position and magnitude of the EGZ are related to the mean upward motion formed around canopy top behind the leading edge, caused by the deceleration in the sub-canopy. Indeed, this mean upward motion advects low turbulence levels from the bottom of the canopy; this emphasises the passage of sudden strong wind gusts from the clearing, thereby increasing the skewness in streamwise velocity as compared with locations further downstream where ambient turbulence is stronger.     

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.     

黄土高原复杂地形受中尺度运动影响的稳定边界层湍流特征

利用兰州大学半干旱气候与环境观测站(Semi-Arid Climate and Environment Observatory of Lanzhou University,简称SACOL)2008年12月观测资料,研究了稳定边界层湍流特征.使用涡动相关资料研究湍流通量时,定义湍流的平均时间τ内的中尺度运动是造成湍流统计量变化范围大的主要原因,稳定情形? τ取几十秒至几分钟.对梯度理查森数大于0.3的强稳定情形的湍流尺度分解(MRD)谱分析表明,感热通量在112.4～449.9 s存在谱隙,尺度大于谱隙的中尺度运动造成了通量观测资料离散性大,甚至有支配性影响.动量通量的谱隙在112.4～224.9 s之间.弱风时,中尺度运动的影响更大,垂直风速标准差以0.1的比率随中尺度风速变化;垂直风速标准差同广义风速表现出很好的相关性,并随着广义风速消失而消失.三维风速标准差与摩擦速度呈很好的线性关系,垂直、水平、横风风速的无量纲标准差分别为1.35、2.54、2.21.对湍流动能的研究发现,在梯度理查森数大于0.3的条件下,仍然存在连续的湍流.以湍动能为依据,分析了湍流的平稳时间长度,其长度随稳定度变化而变化,2008年12月7～11日从133.5 s变化到856.2 s,湍流平稳时间长度反映了中尺度运动的发生频率.