The characteristics of turbulent velocity components in the surface layer under convective conditions

It is proposed that the ratios of the standard deviations of the horizontal velocity components to the friction velocity in the surface layer under convective conditions depend only onz _i /L wherez _i is the height of the lowest inversion andL is the Monin-Obukhov length. This hypothesis is tested by using observations from several data sets over uniform surfaces and appears to fit the data well. Empirical curves are fitted to the observations which have the property that at largez _i /-L, the standard deviations become proportional tow _*, the convective scaling velocity.Fluctuations of vertical velocity obtained from the same experiments scale withz/L, wherez is the height above the surface, in good agreement with Monin-Obukhov theory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Local similarity relationships in a horizontally inhomogeneous boundary layer

Local similarity theory, an analogy to the Monin-Obukhov similarity theory, is successfully applied to airborne observations in a coastal area of South Australia. The boundary layer over this highly non-uniform surface is characterized by extensive variations in its thermal stratification and turbulence characteristics. However, the behaviour of some statistical parameters of second- and higher moments seems to be determined mainly by local forcing, while horizontal advection plays a less important role. For these parameters, local scaling is effective. It is shown that the dimensionless variances of vertical velocity and potential temperature are functions of z/ only, where is the local Monin-Obukhov length and z is the height above ground. The dimensionless variance of horizontal velocity components is found to depend on h/, where h is the height of the oundary layer. Similarity relationships for some triple correlations are also discussed. The empirically determined local similarity relationships are found to agree with those obtained from surface-layer similarity. Finally, to illustrate the complexity of the local forcing, distributions of vertical energy and momentum fluxes, from which the local scaling parameters are derived, are shown.     

Intermittent wind close to the ground within a grass canopy

Wind speed was measured at a height of 1 cm above the ground and at several other heights in and above a canopy of tall fescue grass (Festuca arundinacea) using single hot-wire and triple hot-film anemometers. The plant area density in the canopy was concentrated close to the ground, with 75% of the plant area standing belowz=15 cm, wherez is height above the ground. The frequency distributions of horizontal wind speeds,s, were sharply skewed towards positive values at all measurement heights, but were most highly skewed near the ground where the coefficient of skewness ranged from 1.6 to 2.9. Above mid-canopy height, the frequency distribution ofs was described reasonably well by a Gumbel extreme value distribution. Average wind speed,S, decreased exponentially with depth into the canopy with an exponential scale length of abouth/2.8, whereh is the height of the canopy. Atz=1 cm, the value ofS was about 11% of the surface-layeru _*. The standard deviation of the fluctuations of the vertical and horizontal components of the wind speed also decreased exponentially with depth inside the canopy with a scale length of abouth/2.5.Inside the canopy, the Eulerian integral time scales for the vertical ( _w ) and horizontal ( _u ) components of wind speed were about 0.1 s and 1.0 s, respectively, and were approximately constant with height. Above the canopy, these time scales increased sharply and, atz=2.25h, _w and _u were approximately 1.0 and 3.0s, respectively. Turbulence length scales in the vertical and downwind directions, _u and _w ·U, respectively, were approximately 1 cm for heights between 1 to 10 cm above the ground inside the canopy, while atz=2.25h, they were about 55 cm and 277 cm. Relatively quiescent periods (lulls) in the air close to the ground were interrupted frequently by gusts. The frequency of occurrence of gusts appears to be correlated with the value of the local shear near the top of the canopy.     

边界层局地相似理论在草原下垫面的适用性检验

利用锡林浩特草原平坦下垫面塔层湍流资料,对常值通量层的高度进行了估计,检验了局地相似理论在均匀草原下垫面的适用性,对Monin-Obukhov相似理论和局地相似理论在常值通量层以上的大气边界层的适用性进行了比较。结果表明:(1)对于锡林浩特草原来说,常值通量层厚度在50m左右;(2)通过分析无量纲风速和温度梯度、无量纲风速方差、无量纲标量(温度T、水汽q、CO2浓度C)方差与稳定度z/L之间的关系,验证了局地相似理论在均匀草原下垫面70m以下大气边界层的适用性;(3)感热通量尺度与浮力长度尺度之间存在线性关系;(4)从经典Monin-Obukhov长度、局地Monin-Obukhov尺度和浮力长度尺度的对比分析来看,局地尺度更适用于50m以上的大气边界层,而浮力长度尺度不适用于50m以上的大气边界层。     

The impact of soil moisture on dispersion-related characteristics

This study investigates the impact of soil moisture availability on dispersion-related characteristics: surface fric-tion velocity (u*), characteristic scales of temperature and humidity (T* and q*), the planetary boundary layer height (h) and atmospheric stability classified by Monin-Obukhov length (L), Kazanski-Monin parameter (μ) and convective velocity scale (w*) during daytime convective condition using a one-dimensional primitive equation with a refined soil model.     

A note on finite-difference schemes for the surface and planetary boundary layers

The solution of the planetary boundary-layer equations by finite-difference methods has recently become very popular. Among recent papers using such methods, several use somewhat arbitrary finite-difference meshes and some do not make use of a constant flux or wall layer near the ground. It is shown that the use of finite differences right down to the ground can be a very inaccurate procedure when used in conjunction with an eddy viscosity or mixing length proportional to (z +z ₀) orz near the ground. Such an approach can lead to results that are highly dependent on the finite-difference scheme used and virtually independent of the roughness length,z ₀. A scheme using an expanding grid, based on the form chosen for mixing length or eddy viscosity, is proposed which gives good results with or without a surface layer in the case of a neutrally stratified atmosphere.     

On the extension of the wind profile over homogeneous terrain beyond the surface boundary layer

Analysis of profiles of meteorological measurements from a 160 m high mast at the National Test Site for wind turbines at Høvsøre (Denmark) and at a 250 m high TV tower at Hamburg (Germany) shows that the wind profile based on surface-layer theory and Monin-Obukhov scaling is valid up to a height of 50–80 m. At higher levels deviations from the measurements progressively occur. For applied use an extension to the wind profile in the surface layer is formulated for the entire boundary layer, with emphasis on the lowest 200–300 m and considering only wind speeds above 3 m s^?1 at 10 m height. The friction velocity is taken to decrease linearly through the boundary layer. The wind profile length scale is composed of three component length scales. In the surface layer the first length scale is taken to increase linearly with height with a stability correction following Monin-Obukhov similarity. Above the surface layer the second length scale (L _MBL ) becomes independent of height but not of stability, and at the top of the boundary layer the third length scale is assumed to be negligible. A simple model for the combined length scale that controls the wind profile and its stability dependence is formulated by inverse summation. Based on these assumptions the wind profile for the entire boundary layer is derived. A parameterization of L _MBL is formulated using the geostrophic drag law, which relates friction velocity and geostrophic wind. The empirical parameterization of the resistance law functions A and B in the geostrophic drag law is uncertain, making it impractical. Therefore an expression for the length scale, L _MBL , for applied use is suggested, based on measurements from the two sites.     

Scaling Properties of Temperature Spectra and Heat-Flux Cospectra in the Surface Friction Layer Beneath an Unstable Outer Layer

Temperature variance and temperature power spectra in the unstable surface layer have always presented a problem to the standard Monin-Obukhov similarity model. Recently that problem has intensified with the demonstration by Smedman et al. (2007, Q J Roy Meteorol Soc 133: 37–51) that temperature spectra and heat-flux cospectra can have two distinct peaks in slightly unstable conditions, and by McNaughton et al. (2007, Nonlinear Process Geophys 14: 257–271) who showed that the wavenumber of the peak of temperature spectra in a convective boundary layer (CBL), closely above the surface friction layer (SFL), can be sensitive to the CBL depth, z _i. Neither the two-peak form at slight instability nor the dependence of peak position on z _i at large instability is compatible with the Monin-Obukhov model. Here we examine the properties of temperature spectra and heat-flux cospectra from between these extremes, i.e. from within the unstable SFL, in two experiments. The analysis is based on McNaughton’s model of the turbulence structure in the SFL. According to this model, heat is transported through most of the SFL by sheet plumes, created by the action of impinging outer eddies. The smallest and most effective of these outer eddies have sizes that scale on SFL depth, z _s. The z _s-scale eddies and plumes are organised within the overall convection pattern in the CBL, and in turn they organise the motion of smaller eddies within the SFL, whose sizes scale on height, z. The main experimental results are: (1) the peak amplitudes of the temperature spectra in the SFL are collapsed with a scaling factor (z_sz)^1/3e_o^2/3{(z_{\rm s}z)^{1/3}\varepsilon_{\rm o}^{2/3}} divided by the square of the surface temperature flux, where e_o{\varepsilon_{\rm o}} is the dissipation rate of turbulent energy in the outer CBL (above the SFL); (2) the peak wavenumbers of the temperature spectra are collapsed with the mixed length scale (z _i z _s)^1/2; (3) the peak wavenumbers of the heat-flux cospectra are collapsed with the doubly-mixed length scale (z _i z _s)^1/4 z ^1/2; (4) for z/z _s < 0.03, the peak in the cospectrum is replaced by another peak at a wavenumber about a magnitude larger. This peak’s position scales on z; (5) all these findings are consistent with the observations of Smedman et al.     

Relating Urban Surface-layer Structure to Upwind Terrain for the Salford Experiment (Salfex)

Profiles of wind and turbulence over an urban area evolve with fetch in response to surface characteristics. Sodar measurements, taken on 22 April 2002 during the Salford Experiment in the UK (Salfex), are here related to upstream terrain. A logarithmic layer up to z = 65m was observed in all half-hour averaged profiles. Above this height the profile showed a different vertical gradient, suggesting a change in surface cover upstream. The drag coefficient varied by a factor of two over only a 20° direction change. Turbulence intensity (σ _x ) for each wind component (x) decreased with height, but the ratio suggested an underestimate of σ _u compared to previous results. Mean urban and suburban cover fraction within the source area for each height decreased sharply between z = 20 and 50m, increasing slightly above. The near-convergence of cover fractions thus occured for source areas of minimum length ≈ 2,200 m. In comparison, the mean length scale of heterogeneity L _P was calculated from surface cover data to be 1,284 m, and the corresponding mean blending height h _b was 175 m. Finally, the mean streamline angle, α, was negative and the magnitude decreased with height. An exponential fit to α for z ≤ 65m gave an e-folding height scale of 159 m. A simple relationship between this height scale and L _P was assumed, giving L _P ≈ 1,080 m, which is in reasonable agreement with the estimate from surface cover type. The results suggest that more emphasis is required on modelling and measuring surface-layer flow over heterogeneous urban canopies.     

Regional roughness of the landes forest and surface shear stress under neutral conditions

Mean wind velocity profiles were measured by means of radio-windsondes over the Landes region in southwestern France, which consists primarily of pine forests with scattered villages and clearings with various crops. Analysis of neutral profiles indicated the existence of a logarithmic layer between approximately z – d ₀ = 67(±18)z ₀ and 128(+-32)z ₀ (z is the height above the ground, z ₀ the surface roughness and d ₀ the displacement height). The upper limit can also be given as z – d ₀ = 0.33 (±0.18)h, where h is the height of the bottom of the inversion. The profiles showed that the surface roughness of this terrain is around 1.2 m and the displacement height 6.0 m. Shear stresses derived from the profiles were in good agreement with those obtained just above the forest canopy at a nearby location with the eddy correlation method by a team from the Institute of Hydrology (Wallingford, England).     

Incorporation of a high-roughness lower boundary into a mesoscale model for studies of dry deposition over complex terrain

For flow over natural surfaces, there exists a roughness sublayer within the atmospheric surface layer near the boundary. In this sublayer (typically 50z ₀ deep in unstable conditions), the Monin-Obukhov (M-O) flux profile relations for homogeneous surfaces cannot be applied. We have incorporated a modified form of the M-O stability functions (Garratt, 1978, 1980, 1983) in a mesoscale model to take account of this roughness sublayer and examined the diurnal variation of the boundary-layer wind and temperature profiles with and without these modifications. We have also investigated the effect of the modified M-O functions on the aerodynamic and laminar-sublayer resistances associated with the transfer of trace gases to vegetation. Our results show that when an observation height or the lowest level in a model is within the roughness sublayer, neglect of the flux-profile modifications leads to an underestimate of resistances by 7% at the most.     

On the role of roughness lengths in flux parameterizations of boundary-layer models

Flux-profile relationships based on surface-layer similarity theory are used to derive relationships between the Monin-Obukhov stability parameter = z/L and the bulk Richardson number Ri _b . In contrast to previous studies, the roughness length for heat, z _0h ,is assumed unequal to the roughness length for momentum, z _0m .For the stable case, an analytic expression of in terms of Ri _b can be derived and in the unstable case, the solution is obtained through a simple iterative process.Errors introduced from the simplification of z _0h = z _0m are evaluated and are shown to be very significant in most cases. Thus, this error in many practical applications may invalidate the intended solution.     

Wind profile constants in a neutral atmospheric boundary layer over complex terrain

The roughness height z ₀ and the zero-plane displacement height d ₀ were determined for a region of complex terrain in the Pre-Alps of Switzerland. This region is characterized by hills of the order of 100 m above the valley elevations, and by distances between ridges of the order of 1 km; it lies about 20 to 30 km north from the Alps. The experimental data were obtained from radiosonde observations under near neutral conditions. The analysis was based on the assumption of a logarithmic profile for the mean horizontal wind existing over one half of the boundary layer. The resulting (z ₀/h) and (d ₀/h) (where h is the mean height of the obstacles) were found to be in reasonable agreement with available relationships in terms of placement density and shape factor of the obstacles, which were obtained in previous experiments with h-scales 2 to 4 orders of magnitude smaller than the present ones.     

Turbulence Structure of the Unstable Atmospheric Surface Layer and Transition to the Outer Layer

We present a new model of the structure of turbulence in the unstable atmospheric surface layer, and of the structural transition between this and the outer layer. The archetypal element of wall-bounded shear turbulence is the Theodorsen ejection amplifier (TEA) structure, in which an initial ejection of air from near the ground into an ideal laminar and logarithmic flow induces vortical motion about a hairpin-shaped core, which then creates a second ejection that is similar to, but larger than, the first. A series of TEA structures form a TEA cascade. In real turbulent flows TEA structures occur in distorted forms as TEA-like (TEAL) structures. Distortion terminates many TEAL cascades and only the best-formed TEAL structures initiate new cycles. In an extended log layer the resulting shear turbulence is a complex, self-organizing, dissipative system exhibiting self-similar behaviour under inner scaling. Spectral results show that this structure is insensitive to instability. This is contrary to the fundamental hypothesis of Monin--Obukhov similarity theory. All TEAL cascades terminate at the top of the surface layer where they encounter, and are severely distorted by, powerful eddies of similar size from the outer layer. These eddies are products of the breakdown of the large eddies produced by buoyancy in the outer layer. When the outer layer is much deeper than the surface layer the interacting eddies are from the inertial subrange of the outer Richardson cascade. The scale height of the surface layer, z _s, is then found by matching the powers delivered to the creation of emerging TEAL structures to the power passing down the Richardson cascade in the outer layer. It is z _s = u _* ³ /k_s, where u _* is friction velocity, k is the von Kármán constant and _s is the rate of dissipation of turbulence kinetic energy in the outer layer immediately above the surface layer. This height is comparable to the Obukhov length in the fully convective boundary layer. Aircraft and tower observations confirm a strong qualitative change in the structure of the turbulence at about that height. The tallest eddies within the surface layer have height z _s, so z _s is a new basis parameter for similarity models of the surface layer.     

Fluctuations of the horizontal wind under unstable conditions

The similarity relations for _u/u_* proposed by Panofskyet al. (1977) and Højstrup (1982) have been verified using eddy-correlation data collected during the EFEDA-experiment, conducted over the extensive plain of La Mancha (Spain), where vine plants form a primary crop. Also, the standard Monin-Obukhov relation is considered. It is found that the expressions by Panofskyet al. and Højstrup both yield almost identical results, and are better than the Monin-Obukhov expression. Also, _u measured with a cup anemometer obeys the similarity expressions well, provided that the effect of the variation of wind direction on propellor wind speed is accounted for. The relationship of Panofskyet al. works rather well even when the boundary-layer height scaleh is replaced by a fixed height,h _c. Best results were obtained forh _c=1800 m. This height scale is possibly associated with the horizontal variability in the surface sensible heat flux pattern.     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

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.     

Effect of thermal stratification on the growth of the internal boundary layer

The growth of a two-dimensional internal boundary layer (IBL), which develops when a neutral or unstably stratified flow over a uniform terrain encounters a step-change in surface roughness, is numerically investigated by a higher-order turbulence closure theory. It is found that the thickness of the IBL increases as ~ x ⁿ, where x is the downstream distance from the roughness-transition line. For a given set of upstream conditions, the value of the exponent n depends only on the Monin-Obukhov length L, and it is approximately independent of the roughness-change parameter M = In (z01/z02). At large fetches, increases markedly with increasing instability.NRC-NAS Resident Research Associate at AFCRL, 1973–74     

Effect of the plume rise and wind speed on extreme value of air pollutant concentration

Summary Extreme values of the ground level concentration of air pollutants were evaluated as a function of plume rise Δh, and wind speed in two cases. Firstly, when a plume rise depends on the downwind distance x, and secondly, with a constant plume rise (i.e., independent on x). Also, the extreme values for the effective stack height were evaluated for different stability classes. The maximum value of the ground level concentration was obtained in unstable stability when plume rise depends on x and in the neutral stability when plume rise independent on x. Also, in stable case, the extreme values of the ground level concentration of air pollutants showed similar values in the two cases when plume rise depends on x, and with constant plume rise. Finally, it was found that the extreme value of the ground level concentration occurred near the stack and after that it was decreases in all stabilities.