Flow characteristics above a very low and gently sloping hill

Tower measurements of wind and turbulence in near neutral conditions at the top of a very low and gently sloping hill (height ~ 20 m, with a length scale ~ 1000 m) are analysed in terms of current flow-over-hill theory. Measurements of wind maximum height and the change of the variances of the three wind components from the inner to the outer region are found to be in agreement with predictions from the theory. Spectra of the longitudinal and vertical wind components in the inner region, scaled according to Panofsky et al. (1982), come close to the corresponding Kansas curves in the high frequency range. They have higher energy in the low frequency region, probably a spectral lag effect caused by rougher upwind terrain. In the outer region, the spectra coincide with the corresponding Kansas curves if normalized by their respective variances and plotted against f/f _m.     

Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China

We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels.     

北京城区二氧化碳时空分布及湍流谱特征

利用北京325 m气象塔上安装的7层CO₂涡动相关系统在2014年12月到2015年11月的观测资料,分析了北京城区不同高度上CO₂浓度、通量时空分布及湍流谱的特征。结果表明:城市CO₂浓度日变化除了冬季都呈现双峰型,冬季由于人为碳源排放的大幅增加,双峰型不明显。每层的CO₂浓度、通量都有明显的季节变化:冬季最高,春末、夏季最低。CO₂浓度整体随高度的增加而降低。北京城区是CO₂源,CO₂通量的日变化不如CO₂浓度日变化规律明显。CO₂通量在47 m以下为负,47 m以上为正。通量在140 m以下随高度的增加而增加;140m以上随高度的增加而减少。根据对CO₂时空分布的分析可知:边界层CO₂浓度、通量强烈受到碳源、下垫面植被、大气稳定度、环境温度和天气过程等因素的影响。各变量谱与Kaimal等的研究结果接近:归一化速度谱和CO₂谱在惯性子区有－2/3的斜率,在低频区与稳定度参数（Z/L）有一定的关系。这说明复杂地形的城市下垫面的湍流谱结构与平坦地形相比没有太大的实质性差异。     

Effects of Topographical Slope Angle and Atmospheric Stratification on Surface-Layer Turbulence

The effect of topographical slope angle and atmospheric stratification on turbulence intensities in the unstably stratified surface layer have been parameterized using observations obtained from a three-dimensional sonic anemometer installed at 8 m height above the ground at the Seoul National University (SNU) campus site in Korea for the years 1999–2001. Winds obtained from the sonic anemometer are analyzed according to the mean wind direction, since the topographical slope angle changes significantly along the azimuthal direction. The effects of the topographical slope angle and atmospheric stratification on surface-layer turbulence intensity are examined with these data. It is found that both the friction velocity and the variance for each component of wind normalized by the mean wind speed decrease with increase of the topographical slope angle, having a maximum decreasing rate at very unstable stratification. The decreasing rate of the normalized friction velocity (u _* /U) is found to be much larger than that of the turbulence intensity of each wind component due to the reduction of wind shear with increase in slope angle under unstable stratification. The decreasing rate of the w component of turbulence intensity (σ _w /U) is the smallest over the downslope surface whereas that of the u component (σ _u /U) has a minimum over the upslope surface. Consequently, σ _w /u _* has a maximum increasing rate with increase in slope angle for the downslope wind, whereas σ _u /u _* has its maximum for the upslope wind. The sloping terrain is found to reduce both the friction velocity and turbulence intensity compared with those on a flat surface. However, the reduction of the friction velocity over the sloping terrain is larger than that of the turbulence intensity, thereby enhancing the turbulence intensity normalized by the friction velocity over sloping terrain compared with that over a flat surface.     

A test of isotropy and Taylor's hypothesis in the atmospheric boundary layer

This study attempts to determine the scales of turbulence in a high Reynolds number shear flow near which transition to isotropy occurs and the scales for which Taylor's hypothesis is applicable. The flow studied was the wind near height x ₃ = 2 m above a flat land surface. Four hot-wire anemometers were mounted in a three-dimensional array with equal separations between 1.8 m and 2 cm in three different directions. Theoretical cross-spectra were computed from the observed spectra of downwind velocity fluctuations assuming isotropy and Taylor's hypothesis. Comparison between these and the observed cross-spectra revealed that the turbulence in the flow studied was consistent with both assumptions provided k _1x3&> 20, where k ₁ is the radian wavenumber; this was the lower bound to which no departure from isotropy could be detected by the experiment. For 4 k _1x3 20, the observations are consistent with symmetry of the turbulence about the downstream direction. That part of Taylor's hypothesis relating observed frequency at a stationary sensor to the downstream wavenumber component appears to be justified within experimental error for k _1x3& > 3.     

Measurements of turbulence and fossil turbulence near ampere seamount

Measurements of temperature and velocity microstructure near and downstream of a shallow seamount are used to compare fossil turbulence versus non-fossil turbulence models for the evolution of turbulence microstructure patches in the stratified ocean. According to non-fossil oceanic turbulence models, all overturn length scales L_T of the microstructure grow and collapse in constant proportion to each other and to the turbulence energy (Oboukov) scale L_O and the inertial buoyancy (Ozmidov) scale of the patches; that is, with L_Trms ≈1.2L_R and viscous dissipation rate ≈ ₀^*. According to the Gibson fossil turbulence model, all microstructure originates from completely active turbulence with ₀ ≈ 3L_T²N³(≈ 28₀^*) and L_{T/√6 ≈ LTrms}, but this rapidly decays into a more persistent active-fossil state with _0F ≈ 30vN², where N is the buoyancy frequency and v is the kinematic viscosity and, without further energy supply, finally reaches a completely fossil turbulence hydrodynamic state of internal wave motions, with _F. The last turbulence eddies, with ≈ _F, vanish at a buoyant-inertial-viscous (fossil Kolmogorov) scale L_KF that is much smaller than the remnant overturn scales L_T for large ₀/_F ratios. These density, temperature, and salinity overturns with L_T ≈ 0.6 L_R0 0.6 L_R persist as turbulence fossils (by retaining the memory of _o) and collapse very slowly. In the near wake below the summit depth of Ampere seamount, a much larger proportion of completely active turbulence patches was found than is usually found in the ocean interior away from sources. Dissipation rates and turbulence activity coefficients of microstructure patches were found to decrease downstream, suggesting that the active turbulence indicated by the patches with A_T 1 was caused by the presence of the seamount as a turbulence source. Therefore, the turbulence and mixing processes of ocean layers far away from turbulence sources probably have been undersampled by microstructure data sets lacking any A_T 1 patches. This is because large fractions of the mixing and viscous dissipation of the patches occur in short-lived active turbulence regimes that are too brief to be detected. Consequently, large underestimates of the true space-time average turbulence fluxes and turbulence and scalar dissipation rates may result if non-fossil turbulence models are assumed in ocean microstructure data interpretation.     

Different Turbulent Regimes and Vertical Turbulence Structures of the Urban Nocturnal Stable Boundary Layer

Turbulence in the nocturnal boundary layer(NBL) is still not well characterized, especially over complex underlying surfaces. Herein, gradient tower data and eddy covariance data collected by the Beijing 325-m tower were used to better understand the differentiating characteristics of turbulence regimes and vertical turbulence structure of urban the NBL. As for heights above the urban canopy layer(UCL), the relationship between turbulence velocity scale(V_TKE) and wind speed(V) was con...     

Possibility of Solid Hydrometeor Growth Zone Identification Using Radar Spectrum Width

In this study, the correlation between simulated and measured radar velocity spectrum width(σ_v) is investigated. The results show that the dendrites growth zones(DGZs) and needles growth zones(NGZs) mostly contain dendrites(DN) and needles(NE), respectively.Clear σ_v zones(1.1 < σ_v(m s^–1) < 1.3 and 0.3 < σ_v(m s^–1) < 0.7 for the DGZ and NGZ, respectively) could be identified in the case studies(27 and 28 February 2016) n...     

Turbulent Flow at 190 m Height Above London During 2006–2008: A Climatology and the Applicability of Similarity Theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ _i /u _* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.     

Observations of the energy-containing oceanic Eddies,and theoretical models of waves and turbulence

Two of the best available observed frequency spectra of energy-containing oceanic motions are summarized. Without provoking any simple explanation, they affirm that an efficient, homogeneous cascade of energy to small scales isnot occurring. The way is left open for interpretation as a mixture of geostrophic turbulence and waves.Detailed models are given which yield plausible behavior of various parts of the wave-number and frequency spectra, and illustrate the workings of nonlinearity and wave dispersion: (i) simple dispersion of linear, wind-generated internal waves gives at depths an inertial peak and a steeply sloping high-frequency spectrum (the inertial peak at the very top of the ocean is a direct response of the mixed layer to the wind); (ii) at longer periods,two-dimensional turbulence subjected to the beta effect produces well-ordered motions from a chaotic initial state, with dominant length and time-scale independent of initial conditions. The turbulence evolves quickly and naturally into Rossby waves, leaving a peaky, quasi-stationary spectrum; (iii) inone dimension, the Korteweg de Vries equation again shows how waves may sharpen and fix the wave-number spectrum while dispersing the energy in physical space; (iv) possible application of the ideas tothree-dimensional turbulence and waves is discussed.The most general result is that the scale-dependent boundary, at which the wave steepness is about unity, often divides energy-frequency/wave-number space into regions in which the mobility of energy is vastly different; depending on the direction and speed of nonlinear migration within these regions, energy may pile up at this boundary. Thus, wave-restoring forces can concentrate spectra at certain wave numbers while dispersing the fields in physical space.Now at Woods Hole Oceanographic Institution.     

The scintillation method tested over a dry vineyard area

Measurements of a scintillometer device mounted at 4 m above a dry vineyard area in La Mancha, Spain, are used to obtain an average sensible heat flux densityH. Averaging is over a rectangular area determined by the distance between the scintillometer light source and receptor (875 m) and some upwind distance governed by the horizontal wind speed perpendicular to that line. Using similarity relations obtained from La Crau, a good correspondence betweenH measured with the scintillometer and an eddy-correlation device in the centre of a vineyard is obtained. The friction velocityu _* was either measured directly using a sonic anemometer or obtained indirectly from two wind speeds and known values of the roughness length z_o and displacementd. The free convection formulation underestimates the sensible heat flux by about 30%. This is due to a significant contribution of mechanically generated turbulence to the total turbulent transport, which was caused by relatively strong winds and rough terrain.     

Microscale ordered motions and atmospheric structure associated with thin echo layers in stably stratified zones

The interpretation of ultra-high resolution radar observations of thin clear-air echo strata is made with the aid of fine-scale aircraft measurements. The echo layer, generally comprising two sub-strata each 5 m thick and spaced 7–10 m apart, is found within a 10–20 m deep section of a strong inversion where the thermal stability and shear are maximized, and the Richardson number is close to 0.25. Mechanical turbulence is restricted entirely to this layer; the variance of the N-S velocity component, ³, is the strongest, consistent with the orientation of the shear vector in this stratum. Spectra and cospectra of a 9-s slant run through the echo stratum show remarkably ordered motions. A strong negative peak of <w> covariance at 80-m scale, accompanied by a zero of <uw> covariance and bulges in the longitudinal () and vertical (w) velocity spectra, is identified with breaking Kelvin-Helmholtz waves oriented in the N-S direction along the shear vector. A synthesis of the temperature and velocity structures from measurements along the flight path confirms the ordered motion deduced from the spectra and reveals a group of K-H waves of 80-m length and 10-m height at the height of the radar echo. Microscale K-H ripples of 3–4 m length are also deduced to be present in the 0.5 m thick interfacial region where the thermal gradient and shear are strongly enhanced by the larger shearing K-H wave.Two possible sources of the echoes are proposed: (1) scatter from fully developed turbulence within the interfacial zone in an inertial subrange falling entirely in sub-meter scales; and (2) the incoherent summation of specular reflections from properly oriented portions of the microscale K-H ripples. While the authors favor the first of these mechanisms, both require stringent conditions of the physical microstructure which are beyond the available observations. Fossil turbulence is precluded as an echo mechanism.This paper is based in part on the doctoral dissertation by the senior author.Present affiliation: Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A.     

Influence of chemistry on the flux-gradient relationships for the NO-O3-NO2 system

It is shown that K-theory has to be modified for chemical systems that react with time scales similar to the turbulence time scale. In such systems, the value of the exchange coefficient depends not only on the turbulence parameters, but also on the chemical reaction rates. As an example, the NO-O₃-NO₂ chemical system is studied. Using second-moment equations, new flux-gradient relationships for the neutral atmospheric surface layer are obtained which depend on the time scale ratios of turbulence ( _t ) and chemical reactions ( _ch), i.e., reactive K-theory. Within the framework of this reactive K-theory, the flux of a chemical species is both a function of the concentration gradients of the three chemical species involved and of the ratio of the time scale of turbulence to the time scale of chemistry. In the special case of slow chemistry ( _{t ch}) inert K-theory is applicable.The reactive exchange coefficients are implemented in a surface-layer model that calculates the flux and concentration profiles of the three chemical species. The results of the calculations of the effective exchange coefficients are different for reactive K-theory and inert K-theory; the differences are largest for nitric oxide, but smaller for ozone and nitrogen dioxide.     

Spectral Short-circuiting and Wake Production within the Canopy Trunk Space of an Alpine Hardwood Forest

Using synchronous multi-level high frequency velocity measurements, the turbulence spectra within the trunk space of an alpine hardwood forest were analysed. The spectral short-circuiting of the energy cascade for each velocity component was well reproduced by a simplified spectral model that retained return-to-isotropy and component-wise work done by turbulence against the drag and wake production. However, the use of an anisotropic drag coefficient was necessary to reproduce these measured component-wise spectra. The degree of anisotropy in the vertical drag was shown to vary with the element Reynolds number. The wake production frequency in the measured spectra was shown to be consistent with the vortex shedding frequency at constant Strouhal number given by f _vs = 0.21ū/d, where d can be related to the stem diameter at breast height (dbh) and ū is the local mean velocity. The energetic scales, determined from the inflection point instability at the canopy–atmosphere interface, appear to persist into the trunk space when , where C _du is the longitudinal drag coefficient, a _cr is the crown-layer leaf area density, h _c is the canopy height, and β is the dimensionless momentum absorption at the canopy top.     

On the initial streakness of a dispersing tracer in two- and three-dimensional turbulence

If a spot of tracer is released into a turbulent flow, the peak concentration at some subsequent time will initially be much greater than that implied by a solution for the ensemble average concentration at fixed points. For two-dimensional turbulence three areas may be defined: (1) an area A_d related to the ensemble average concentration field; (2) an area A_p defined in terms of the relative dispersion of particles seeded into the patch after a short initial diffusion time; and (3) the area A_t occupied by tracer. It is argued that A_d grows linearly with time, whereas A_p and A_t grow exponentially; A_p faster than A_t. Thus, the concentration field is significantly streaky, even within the particle domain, until A_t becomes comparable with A_d. The time taken for this to occur is estimated; after this time, fluctuations about the ensemble average concentration field should not be greater than those given by a simple mixing length argument. In three-dimensional turbulence the volume V_t of the tracer domain grows much more rapidly than the volume V_p of the particle domain if the merging of streaks is ignored. However, V_t cannot be greater than V_p so streaks must merge and V_p can be used to provide a rough estimate of peak concentration, or concentration variance.     

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.     

Swaying of trees in response to wind and thinning in a stand of Scots pine

Observations have been made of the windspeed, wind direction, and tree movement at the edge and 20 m within a stand of Scots pine (Pinus sylvestris L.) close to 11 m in height. The spectra of windspeed near canopy top, together with the output of accelerometers and video observations of tree movement at mid-crown, were compared in the same stand prior and two years after first thinning. Furthermore, the transfer of wind energy into tree movement was investigated by calculating the mechanical transfer function (H _m ² ) between the wind spectrum (S _uu) and the tree's response (S _yy), i.e. H _m ² = S_yy/S_uu. Trees were found to behave like damped harmonic oscillators. They reacted to sudden increases in windspeed, reached their greatest displacement during the first cycle, and then returned to their rest position under the influence of damping. The spectral peak frequencies in S _yy and in H _m ²coincided with the estimated natural sway frequency of trees. Response in the second mode was, however, also evident, especially within the unthinned stand. The periodogram plots showed a consistent trend of a marked decrease in the response of the tree to increase in frequency. Almost no difference in the wind energy transfer, i.e. peak frequencies and peak width, and damping of the system was found between Scot pine at 2700 and 1500 stems per hectare. However, along the stand edge tree movement was greater than within the stand indicating greater wind energy transfer and damping of the system along the stand edge than within the stand.     

Boundary-layer resistances of artificial leaves in turbulent air: I. Leaves parallel to the mean flow

Boundary-layer resistance to heat transfer from plates was studied in a wind tunnel which produced turbulence with streamwise intensity in the range 3.5 to 25% and a longitudinal integral scale of the streamwise turbulence component (L _u,x) in the range from 8 to 100 mm. It was found that heat transfer enhancement occurred due to the turbulence, and that at any given intensity, this enhancement was determined by the ratio of L _u,x to the characteristic dimension of the plate.     

Stability classification by acoustic remote sensing

Two different Doppler acoustic sounders have been operated at the Kernforschungszentrum Karlsruhe (KfK) since 1982. It has been investigated whether meteorological data from these sounders can be used for dispersion modeling and monitoring in the environment of pollutant-emitting plants. Data from the sounders and from a 200 m high meteorological tower have been sampled continuously for intercomparison.Two schemes of stability classification are presented. They are based on 30-min mean values of the following meteorological data measured by the acoustic sounders: (a) standard deviation σ_w of the vertical wind speed and horizontal wind speed u, at a height of 100 m; and (b) standard deviation σ_φ of the vertical wind direction at a height of 100 m and vertical profile of the backscattered amplitude A_w.The class limits applied in these schemes are determined by “statistical equivalence” with a standard classification scheme. This standard scheme is based on σ_φ, measured by a vector vane at the 100 m level of the tower. Statistical equivalence in this context means that the frequency distributions of the classes are approximately equal at the same site and during the same period.The reliability of these schemes is investigated and compared to the standard scheme by correlation analysis. Finally, the schemes are compared with other commonly applied classification methods.     

A generalized scaling for convective shear flows

During the last two decades, different scalings for convective boundary layer (CBL) turbulence have been proposed. For the shear-free regime, Deardorff (1970) introduced convective velocity and temperature scales based on the surface potential temperature flux,Q _s , the buoyancy parameter, , and the time-dependent boundary-layer depth,h. Wyngaard (1983) has proposed decomposition of turbulence into two components, bottom-up (b) and top-down (t), the former characterized byQ _s , the latter, by the potential temperature flux due to entrainment,Q _h . Sorbjan (1988) has devised height-dependent velocity and temperature scales for both b- and t-components of turbulence.Incorporating velocity shear, the well known similarity theory of Monin and Obukhov (1954) has been developed for the atmospheric surface layer. Zilitinkevich (1971, 1973) and Betchov and Yaglom (1971) have elaborated this theory with the aid of directional dimensional analysis for a particular case when different statistical moments of turbulence can be alternatively attributed as being of either convective or mechanical origin.In the present paper, we attempt to create a bridge between the two approaches pointed out above. A new scaling is proposed on the basis of, first, decomposition of statistical moments of turbulence into convective (c), mechanical (m) and covariance (c&m) contributions using directional dimensional analysis and, second, decomposition of these contributions into bottom-up and top-down components using height-dependent velocity and temperature scales. In addition to the statistical problem, the scaling suggests a new approach of determination of mean temperature and velocity profiles with the aid of the budget equations for the mean square fluctuations.Notation ATL alternative turbulence layer - CBL convective boundary layer - CML convective and mechanical layer - FCL free convection layer - MTL mechanical turbulence layer