Local Log-Law-of-the-Wall in Neutrally-Stratified Boundary-Layer Flows

It is well known that in a neutrally-stratified turbulent flow in a deep constant-stress layer above a flat surface,the horizontal mean velocity varies logarithmically with height (the so-called `log-law-of-the-wall').More recently, the same logarithmic law has also been foundin the presence of non-flat surfaces, where it governs thedynamics of the areally-averagedvelocity and involves renormalized effective parameters.Here, we analyze wind profiles over two-dimensional sinusoidal hillsobtained both from numerical simulations performed with a primitiveequation model and from wind-tunnel measurements. We showthat also the local velocity profiles behave to a verygood approximation logarithmically, for a distance from the surface of the order of the maximum hill height almost to the top of the boundary layer. Such alocal log-law-of-the-wall involves effective parameters smoothly depending on theposition along the underlying topography.This dependence looks very similar to the topography itself.     

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.     

Richardson's Law in Large-Eddy Simulations of Boundary-Layer Flows

Relative dispersion in a neutrally stratified planetary boundary layer (PBL) is investigated by means of large-eddy simulations (LES). Despite the small extension of the inertial range of scales in the simulated PBL, our Lagrangian statistics turn out to be compatible with the Richardson t³ law for the average of square particle separation, where t is time. This emerges from the application of non-standard methods of analysis through which a precise measure of the Richardson constant was also possible. Its value is estimated as C₂ 0.5, in close agreement with recent experiments and three-dimensional direct numerical simulations.     

Estimation of the Friction Velocity in Stably Stratified Boundary-Layer Flows Over Hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.     

A Wind-Tunnel Investigation of Wind-Turbine Wakes: Boundary-Layer Turbulence Effects

Wind-tunnel experiments were performed to study turbulence in the wake of a model wind turbine placed in a boundary layer developed over rough and smooth surfaces. Hot-wire anemometry was used to characterize the cross-sectional distribution of mean velocity, turbulence intensity and kinematic shear stress at different locations downwind of the turbine for both surface roughness cases. Special emphasis was placed on the spatial distribution of the velocity deficit and the turbulence intensity, which are important factors affecting turbine power generation and fatigue loads in wind energy parks. Non-axisymmetric behaviour of the wake is observed over both roughness types in response to the non-uniform incoming boundary-layer flow and the effect of the surface. Nonetheless, the velocity deficit with respect to the incoming velocity profile is nearly axisymmetric, except near the ground in the far wake where the wake interacts with the surface. It is found that the wind turbine induces a large enhancement of turbulence levels (positive added turbulence intensity) in the upper part of the wake. This is due to the effect of relatively large velocity fluctuations associated with helicoidal tip vortices near the wake edge, where the mean shear is strong. In the lower part of the wake, the mean shear and turbulence intensity are reduced with respect to the incoming flow. The non-axisymmetry of the turbulence intensity distribution of the wake is found to be stronger over the rough surface, where the incoming flow is less uniform at the turbine level. In the far wake the added turbulent intensity, its positive and negative contributions and its local maximum decay as a power law of downwind distance (with an exponent ranging from −0.3 to −0.5 for the rough surface, and with a wider variation for the smooth surface). Nevertheless, the effect of the turbine on the velocity defect and added turbulence intensity is not negligible even in the very far wake, at a distance of fifteen times the rotor diameter.     

On the Structure and Adjustment of Inversion-Capped Neutral Atmospheric Boundary-Layer Flows: Large-Eddy Simulation Study

A range of large-eddy simulations, with differing free atmosphere stratification and zero or slightly positive surface heat flux, is investigated to improve understanding of the neutral and near-neutral, inversion-capped, horizontally homogeneous, barotropic atmospheric boundary layer with emphasis on the upper region. We find that an adjustment time of at least 16 h is needed for the simulated flow to reach a quasi-steady state. The boundary layer continues to grow, but at a slow rate that changes little after 8 h of simulation time. A common feature of the neutral simulations is the development of a super-geostrophic jet near the top of the boundary layer. The analytical wind-shear models included do not account for such a jet, and the best agreement with simulated wind shear is seen in cases with weak stratification above the boundary layer. Increasing the surface heat flux decreases the magnitude and vertical extent of the jet and leads to better agreement between analytical and simulated wind-speed profiles. Over a range of different inversion strengths and surface heat fluxes, we also find good agreement between the performed simulations and models of the equilibrium boundary-layer height, and of the budget of turbulent kinetic energy integrated across the boundary layer.     

Scalar Concentration Profiles in the Canopy and Roughness Sublayer

The mean flow and scalar concentration profiles within and above a tall canopy are well known to violate the standard boundary-layer flux-gradient relationships. We present a theory for the scalar concentration profile that is comprised of a canopy exchange model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing-layer analogy for the flow at canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the profiles depend and a set of criteria that allows a reduction in the empiricism associated with earlier forms in the literature. Predictions of the mean scalar concentration profiles are shown to match observations over a wide range of diabatic stabilities for both potential temperature and water vapour.     

The Budget of Turbulent Kinetic Energy in the Urban Roughness Sublayer

Full-scale observations from two urban sites in Basel, Switzerland were analysed to identify the magnitude of different processes that create, relocate, and dissipate turbulent kinetic energy (TKE) in the urban atmosphere. Two towers equipped with a profile of six ultrasonic anemometers each sampled the flow in the urban roughness sublayer, i.e. from street canyon base up to roughly 2.5 times the mean building height. This observational study suggests a conceptual division of the urban roughness sublayer into three layers: (1) the layer above the highest roofs, where local buoyancy production and local shear production of TKE are counterbalanced by local viscous dissipation rate and scaled turbulence statistics are close to to surface-layer values; (2) the layer around mean building height with a distinct inflexional mean wind profile, a strong shear and wake production of TKE, a more efficient turbulent exchange of momentum, and a notable export of TKE by transport processes; (3) the lower street canyon with imported TKE by transport processes and negligible local production. Averaged integral velocity variances vary significantly with height in the urban roughness sublayer and reflect the driving processes that create or relocate TKE at a particular height. The observed profiles of the terms of the TKE budget and the velocity variances show many similarities to observations within and above vegetation canopies.     

The Validity of Similarity Theory in the Roughness Sublayer Above Forests

Flux-gradient relationships based upon similarity theory have been reported to severely underestimate scalar fluxes in the roughness sublayer above forests, as compared to independent flux estimates (for example, eddy covariance or energy balance measurements). This paper presents the results of a unique three-month investigation into the validity of similarity theory in the roughness sublayer above forests. Eddy covariance and flux-gradient measurements of carbon dioxide (CO²) exchange were compared above a mixed deciduous forest at Camp Borden, Ontario, both before and after leaf senescence. The eddy covariance measurements used a Li-Cor infrared gas analyzer, and the flux-gradient (similarity theory) measurements featured a tunable diode laser Trace Gas Analysis System (TGAS). The TGAS resolved the CO² concentration difference to 300 parts per trillion by volume (ppt) based upon a half-hour sampling period. The measured enhancement factor (the ratio of independent flux estimates, in this case eddy covariance, to similarity theory fluxes) was smaller and occurred closer to the canopy than in most previous investigations of similarity theory. Very good agreement between the eddy covariance and similarity theory fluxes was found between 1.9 and 2.2 canopy heights (h^c), and the mean enhancement factors measured before and after leaf senescence were 1.10 plusmn; 0.06 and 1.24 ± 0.07, respectively. Larger discrepancies were measured closer to the canopy (1.2 to 1.4 h^c), and mean enhancement factors of 1.60 ± 0.10 and 1.82 ± 0.11 were measured before and after leaf senescence, respectively. Overall, the Borden results suggest that similarity theory can be used within the roughness sublayer with a greater confidence than previously has been believed.     

A Lagrangian Study of the Three-Dimensional Transport of Boundary-Layer Tracers in an Idealised Baroclinic-Wave Life-Cycle

The role of baroclinic-wave driven chemical transport is examined using the framework of a Lagrangiantrajectory model.The Lagrangian motion of transported trace gases are closely monitored through labelledboundary-layer tracers binned accordingto their latitudinal locations.From a set of 14-day Lagrangian paths, the mechanistically liftedsubtropical boundary-layer tracers track along tilted poleward paths, whilethe subsiding high-latitude tracers track along tilted equator-ward paths.The most significantmovements of tracers occur between days 6 and8. The vertical and latitudinal displacements during this time interval are3 km and 15° latitude. During a baroclinic-wave life-cycle,boundary-layertracers can either ascend vertically from 1 km to 7 km or descend to thesurface, while they arelatitudinally transported from 37° to 73° and from 45° to near 15° during the poleward and equator-ward motions,respectively.Vertical mixing of tracers occurs vigorously at mid-latitudes, where more than50%, by day 7, and a maximum of 70%, between days 9 and 10, of the boundary layer tracers have beentransported intothe free troposphere during the baroclinic-wave life-cycle.A clear 3D picture emerges from a Lagrangian analysis.Each time the tracer travels equator-ward, it descends, whilewhen it travels poleward, it ascends.Almost all of the low latitude tracers show tilted upward and poleward paths,while high latitude tracersshows downward tilted and equator-ward path.The maximum vertical displacement between poleward andequator-ward tracers are shown in mid-latitudes.Two types of the tilted upward and poleward paths are generally seen in thelatitude-height projections:anti-clockwise and clockwise paths.Both types of path transport tracers upward, however, the anti-clockwise pathsdeliver tracersequator-ward, while the clockwise paths deliver tracers poleward.Hence, whenlow latitude warm air arrives at mid-latitude, it can pick up enhanced tracerconcentrationand carry them on either poleward or equator-ward.     

A Sensitivity Analysis of the Nocturnal Boundary-Layer Properties to Atmospheric Emissivity Formulations

A one-dimensional model for the mean potential temperature within the nocturnal boundary layer (NBL) was used to assess the sensitivity of three NBL properties (height, thermal stratification strength, and near-surface cooling) to three widely used atmospheric emissivity formulations. The calculations revealed that the NBL height is robust to the choice of the emissivity function, though this is not the case for NBL Richardson number and near-surface cooling rate. Rather than endorse one formulation, our analysis highlights the importance of atmospheric emissivity in modelling the radiative properties of the NBL especially for clear-sky conditions.     

Local and Global Similarity in Turbulent Transfer of Heat, Water Vapour, And CO 2 in the Dynamic Convective Sublayer Over a Suburban Area

We investigated the ‘local’ and ‘global’ similarity of vertical turbulent transfer of heat, water vapour, and CO₂ within an urban surface layer. The results were derived from field measurements in a residential area of Tokyo, Japan during midday on fair-weather days in July 2001. In this study, correlation coefficients and quadrant analysis were used for the evaluation of ‘global’ similarity and wavelet analysis was employed for investigating ‘local’ similarity. The correlation coefficients indicated that the transfer efficiencies of water vapour and CO₂ were generally smaller than that of heat. Using wavelet analysis, we found that heat is always efficiently transferred by thermal and organized motions. In contrast, water vapour and CO₂, which are passive quantities, were not transferred as efficiently as heat. The quadrant analyses showed that the heat transfer by ejection exceeded that by sweep, and the ratios of ejection to sweep for water vapour and CO₂ transfer were less than that for heat. This indicated that heat is more efficiently transferred by upward motions and supported the findings from wavelet analysis. The differences of turbulent transfer between heat and both CO₂ and water vapour were probably caused both by the active role of temperature and the heterogeneity in the source distribution of scalars     

复杂地形城市多尺度气流对大气污染影响的研究进展

复杂地形城市一般建立在山地、丘陵、沿海地带。复杂地形下的大气污染传输、扩散机制是一个复杂的问题。本文依据城市地形地貌将复杂地形归类为河谷地形、三面环山临海地形、盆地地形、马蹄型地形和峡口地形。结合国内外对这五类地形下城市污染物传输扩散及污染形成机制的研究成果,介绍了不同地理位置、不同复杂地形城市多尺度气流相互或交替作用的特点及其对污染传输扩散的影响,期望能够为其它复杂地形城市污染形成机制研究和大气污染防治提供一些借鉴。     

Characteristics of the Drag Coefficient in the Roughness Sublayer over a Complex Urban Surface

The statistics of momentum exchange in the urban roughness sublayer are investigated. The analysis focuses on the characteristics of the dimensionless friction velocity, \({u_{*}}/U\) , which is defined as the square root of the drag coefficient. The turbulence observations were made at a height of 47 m above the ground on the 325-m meteorological tower, which is located in a very inhomogeneous urban area in Beijing. Under neutral conditions, the dependence of the drag coefficient on wind speed varies with wind direction. When the airflow is from the area of densely built-up buildings, the drag coefficient does not vary with wind speed, while when the airflow is from the area covered by vegetation, the drag coefficient appears to decrease with increasing wind speed. Also, the drag coefficient does not vary monotonically with the atmospheric stability. Both increasing stability and increasing instability lead to the decrease of the drag coefficient, implying that the roughness length and zero-plane displacement may vary in urban areas.     

Impact of Eddy Characteristics on Turbulent Heat and Momentum Fluxes in the Urban Roughness Sublayer

Eddy-covariance observations above the densely built-up Centre of Nanjing were made from December 2011 to August 2012. Separate eddy-covariance systems installed at two levels on a 36-m tower located on a rooftop were operated simultaneously, and observations grouped into two sectors (A, B) according to the prevalent wind directions. For sector A, where the nearby buildings are all below the lower measurement level, the sensible heat and momentum fluxes are generally greater at the upper level. For sector B, where several high-rise buildings are located upwind, the sensible heat and momentum fluxes at the upper level are close to those at the lower level. The analysis shows that the turbulent eddy characteristics differ between the two wind sectors, leading to a different behaviour of turbulent exchange between the two levels. A hypothesis is proposed that addresses the vertical variation of turbulent fluxes in the urban roughness sublayer (RSL). For sector A, the buildings block the flow, change the trajectory of scalars, and distort the footprint of scalar fluxes; this ‘blocking effect’ is believed to lead to a smaller sensible heat flux above the canopy layer. Such an effect should decrease with height in the RSL, explaining the increase of the observed turbulent heat flux with height. In addition, the presence of non-uniform building heights adversely affects turbulence organization around the canopy top, and likely elevates the inflection point of the mean flow to a higher elevation close to the upper measurement level, where larger shear results in a larger momentum flux. For sector B, wake effects from the nearby high-rise buildings strongly reduce turbulence organization at higher elevations, leading to similar sensible heat and momentum fluxes at both measurement levels.