A mixed spectral finite-difference model for pollutant concentrations over a hill

Given incident logarithmic profiles of wind and pollutant concentration above a rough, absorbing surface, the three-dimensional distribution of pollutant concentration over a hill of gentle slope is determined from a linearized model. The model is applied in neutrally stratified flow, without chemistry, and is integrated using spectral methods in the horizontal and a finite-difference scheme in the vertical. This approach allows for flexibility in choosing a closure scheme and a variety of surface boundary conditions. This was not possible in the analytic approach of Padro (1987) who added pollutant concentration and flux to the MS3DJH/1 model of Walmsley et al. (1980). The present model requires as input the turbulent kinetic energy, E, dissipation, , and the perturbation vertical velocity, w, from the three-dimensional boundary-layer flow model of Beljaars et al. (1987), hereinafter referred to as MSFD, The latter model also supplies wind velocity perturbations at the upper boundary, as input to upper boundary conditions on the pollutant flux perturbations.The present study describes applications of the model to idealized terrain features: isolated two- and three-dimensional hills and ridges and an infinite series of ridges. (Application to real terrain, however, presents no difficulties.) Comparisons were made with different (though uniform) surface roughnesses. Tests were performed to examine the effect of upstream terrain features in the periodic domain and to illustrate the importance of the vertical resolution of the output for interpreting results from the sinusoidal terrain case.     

Measurements of the upstream turbulent flow during wind tunnel simulations of agricultural field burning

Mean streamwise and vertical velocities as well as streamwise and vertical turbulence intensities were measured in a combustion wind tunnel used to collect pollutant emission data for agricultural field burning. Objectives were to compare the flow field upstream of a fire to that without a fire present and to compare the wind tunnel flow upstream of a fire to field conditions. Vertical centerline traverses with an anemometer were conducted for 32 separate wind tunnel operating configurations (wind speed, position in the tunnel, with or without fire, ceiling position, and floor condition) with one replication for each configuration (total of 64 traverses). Certain configurational changes in the wind tunnel had substantial effects on the flow field. Turbulence intensities and velocity profiles (as modeled by the log law-of-the-wall to determinez ₀ andu _* values) in the wind tunnel were comparable to those in the field as reported in the literature. Velocities and turbulence intensities were generally higher, however, with a fire present in the tunnel and all other conditions constant.     

Velocity and Surface Shear Stress Distributions Behind a Rough-to-Smooth Surface Transition: A Simple New Model

A simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The wind velocity is estimated as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary-layer height, corresponds to the upwind velocity profile; the second log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z ₀₁)/ln(δ _i /z ₀₁), where z, δ _i and z ₀₁ are the elevation of the prediction location, the internal boundary-layer height at that downwind distance, and the upwind surface roughness, respectively. Unlike other simple analytical models, the new model does not rely on the assumption of a constant or linear distribution for the turbulent shear stress within the internal boundary layer. The performance of the new model is tested with wind-tunnel measurements and also with the field data of Bradley. Compared with other existing analytical models, the proposed model shows improved predictions of both surface shear stress and velocity distributions at different positions downwind of the transition.     

Wind tunnel wake measurements of heavier-than-air gas dispersion near a two-dimensional obstacle

The dispersion of a uniform two-dimensional flow of carbon dioxide gas in air over a square two-dimensional obstacle was studied experimentally in an atmospheric boundary-layer wind tunnel. The obstacle Reynolds number was about 6000 based upon the undisturbed velocity at the height of the obstacle, and the Froude number was about 1.75. Carbon dioxide was injected vertically upward from the surface at a rate of 10% of the freestream velocity. The injection surface area began one obstacle length upstream and extended upstream one and one-half obstacle lengths. A gas concentration measurement system for carbon dioxide and air mixtures was developed for use in an atmospheric wind tunnel. Centerline steady-state concentration profiles were measured for various locations downstream of the leading edge of the obstacle. The maximum concentrations of carbon dioxide occurred atop the obstacle in the thin recirculation zone above the obstacle. Immediately behind the obstacle within the larger downstream recirculation zone, concentration levels significantly decreased. Further downstream, the concentration levels continued to diminish.Experimental results were compared with the numerical solutions of Sutton et al. (1986). The experimental measurements of concentration were lower than the predicted results of the numerical solutions, which may be attributed to the higher value of the Froude number present in the experimental measurements.Associate Professor.     

A simple model of neutrally stratified boundary-layer flow over real terrain incorporating wavenumber-dependent scaling

Our experience in applying earlier versions of a model of boundary-layer flow over low hills to real terrain (see Walmsley et al., 1982) has led to the development of a new version which we designate MS3DJH/3. The main improvements are the use of terrain-dependent length and velocity scales and the blending of inner and outer layer results into a single universally valid solution for the velocity perturbation field. MS3DJH/3 was carefully calibrated against alternative computations of flow over idealized two-dimensional terrain features using more detailed models prior to its application to real, three-dimensional terrain. It still provides high spatial resolution with low computing cost and is applicable to flow over terrain features with horizontal scales from 10 m to 10 km.Contractor: 24 Heslop Drive, Toronto.     

Turbulent Helicity in the Atmospheric Boundary Layer

We consider the assumption postulated by Deusebio and Lindborg (J Fluid Mech 755:654–671, 2014) that the helicity injected into the Ekman boundary layer undergoes a cascade, with preservation of its sign (right- or alternatively left-handedness), which is a signature of the system rotation, from large to small scales, down to the Kolmogorov microscale of turbulence. At the same time, recent direct field measurements of turbulent helicity in the steppe region of southern Russia near Tsimlyansk Reservoir show the opposite sign of helicity from that expected. A possible explanation for this phenomenon may be the joint action of different scales of atmospheric flows within the boundary layer, including the sea-breeze circulation over the test site. In this regard, we consider a superposition of the classic Ekman spiral solution and Prandtl’s jet-like slope-wind profile to describe the planetary boundary-layer wind structure. The latter solution mimics a hydrostatic shallow breeze circulation over a non-uniformly heated surface. A 180°-wide sector on the hodograph plane exists, within which the relative orientation of the Ekman and Prandtl velocity profiles favours the left rotation with height of the resulting wind velocity vector in the lowermost part of the boundary layer. This explains the negative (left-handed) helicity cascade toward small-scale turbulent motions, which agrees with the direct field measurements of turbulent helicity in Tsimlyansk. A simple turbulent relaxation model is proposed that explains the measured positive values of the relatively minor contribution to turbulent helicity from the vertical components of velocity and vorticity.     

An Improved Ekman Layer Approximation for Smooth Eddy Diffusivity Profiles

The Ekman boundary-layer model is extended analytically for a gradually varying eddy diffusivity K(z) ≥ 0, z ≥ 0. A solution for the Ekman layer is provided having similar structure to the constant-K case; that is, exponentially decaying sine functions for the two horizontal wind components. The analytical asymptotic solution compares well with its numerical counterpart for various K(z). The result can be useful in theoretical studies such as Ekman pumping, for efficient estimation of the Ekman layer profiles in various analyses with near-neutral stratifications, or for a rapid initialization of mesoscale models.     

The Ekman boundary layer over orography: An analysis of vertical motion

A model of the planetary boundary layer is used to determine the field of vertical motion over large-scale orography. This model represents Ekman boundary-layer dynamics modified by the inclusion of accelerations of the geostrophic wind under the geostrophic momentum approximation. The orography is represented by a circular mountain. The inviscid solution is provided by the sum of a constant translation and a steady, uniform potential vorticity, anticyclonic vortex. The boundary-layer solution vanishes on the mountain, but is matched to the inviscid solution as the top of the boundary layer is approached. The vertical velocity field at the top of the boundary layer is determined by integration of the continuity equation. The field of motion is largely determined by descent from above into the anticyclonic circulation, as in the classical Ekman model. Contributions that arise from the inclusion of accelerations are associated with boundary-layer advection and ageostrophic divergence that produce vorticity tendencies. Finally, the boundary-layer vertical motion is shown to be comparable in magnitude to the vertical motion forced by inviscid flow over the orography, although the distributions of each are significantly different. Effects of mountain asymmetry and a changing pressure field, that can be treated more fully by numerical model simulations, are not considered in the present study.On leave at the University of Colorado, 1990.     

The influence of the geostrophic wind advection approximation on a well-mixed layer

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.     

Aerodynamic boundary-layer adjustment over a crop in neutral stability

An experimental study of the modification of the neutral wind profile as air flows to a rougher surface is presented. The analysis is based on wind profiles measured at four locations extending about 100 m downwind from the leading edge of a mature wheat crop. The form of the modified wind profile, and the rate of internal boundary-layer growth are analyzed in terms of a non-dimensional wind velocity. Friction velocities, based on wind-profile computations, are also examined at different points in the flow field. Boundary-layer growth was more rapid than expected, but could be approximated by a 4/5th power of the fetch if a roughness factor is included. It is suggested that simple height:fetch ratios, such as 1:100 be avoided, especially where large roughness-length changes are involved.     

Comparison Between Large-Eddy Simulation and Reynolds-Averaged Navier–Stokes Computations for the MUST Field Experiment. Part II: Effects of Incident Wind Angle Deviation on the Mean Flow and Plume Dispersion

Large-eddy simulations (LES) and Reynolds-averaged Navier–Stokes (RANS) computations of pollutant dispersion are reported for the Mock Urban Setting Test (MUST) field experiment flow. In particular we address the effects of incident wind angle deviation on the mean velocity and on the mean concentration fields. Both computational fluid dynamical methods are assessed by comparing the simulation results with experimental field data. The comparative analysis proposes to relate the plume deflection with the flow channelling effects. The results show that the plume deflection angle varies with the altitude. As the ground is approached the plume is shown to be almost aligned with the street canyon direction and independent of the incident wind directions considered. At higher altitudes well above the obstacles, the plume direction is aligned with the mean wind direction as in dispersion over flat terrain. The near-ground plume deflection is the consequence of a strong channelling effect in the region near the ground. The mean concentration profiles predicted by LES and RANS are both in good qualitative agreement with experimental data but exhibit discrepancies that can be partly explained by the influence of small incident wind angle deviation effects. Compared to RANS, LES predicts a higher channelling and thus a higher deflection of the plume. Results on the fluctuating intensity of the concentration obtained from LES show a satisfactory agreement with experiments. This information is not available from RANS for which only the mean concentration modelling is considered.     

The Baroclinic, Variable Eddy Viscosity Ekman Layer

The WKB method is used in conjunction with the variation of parameters technique to find an approximate analytical solution for Ekman layers with eddy viscosity and horizontal pressure gradient that are each variable with height from the surface. Behaviour of the solution is illustrated by comparing model output when several eddy viscosity and horizontal pressure gradient profiles are used. Cases where the pressure gradient decreases with height accentuate the super-geostrophic peak in the wind velocity profile, with decreasing eddy viscosity with height further enhancing this effect. Increasing pressure gradient with height reduces or eliminates the peak. The model output when using an eddy viscosity that has a low-level peak fits marine boundary-layer data taken during ASTEX better than the classic solution - the model giving greater low-level mixing which is seen in ASTEX data as well as in data from ERICA.     

A microscale model for air pollutant dispersion simulation in urban areas: Presentation of the model and performance over a single building

A microscale air pollutant dispersion model system is developed for emergency response purposes. The model includes a diagnostic wind field model to simulate the wind field and a random-walk air pollutant dispersion model to simulate the pollutant concentration through consideration of the influence of urban buildings. Numerical experiments are designed to evaluate the model's performance, using CEDVAL(Compilation of Experimental Data for Validation of Microscale Dispersion Models) wind tunnel experiment data, including wind fields and air pollutant dispersion around a single building. The results show that the wind model can reproduce the vortexes triggered by urban buildings and the dispersion model simulates the pollutant concentration around buildings well. Typically, the simulation errors come from the determination of the key zones around a building or building cluster. This model has the potential for multiple applications; for example, the prediction of air pollutant dispersion and the evaluation of environmental impacts in emergency situations; urban planning scenarios;and the assessment of microscale air quality in urban areas.     

Simulation of three-dimensional wind flow over complex terrain in the atmospheric boundary layer

A three-dimensional model for wind prediction over rough terrain has been developed for practical use. It is a compromise between hydrodynamic and objective wind models. The proposed model includes: (1) a statistical model to predict the wind velocity and potential temperature at anemometer height at observing stations, (2) the drainage wind model expressed by Prandtl's analytic solution for the slope wind, (3) the Businger-Dyer surface-layer formulation which considers the surface energy budget and (4) the model for three-dimensional boundary-layer solutions to the stationary flow. In this model, mass consistency is guaranteed by using flow fields that satisfy the continuity equation. Model predictions show good agreement with the observations.     

Mean circulations of boundary-layer rolls in lake-effect snow storms

An observational study of the roll-average flow fields of boundary-layer rolls is presented. Data used for this purpose were collected by dual-Doppler radar and aircraft measurements taken over southern Lake Michigan during the 1983/1984 field operations of Project Lake Snow. The roll circulations agreed well with findings of past observational, numerical and theoretical studies, with cross-roll components roughly 10% of the convective internal boundary layer (CIBL)-mean wind speeds and weaker vertical components. Along-roll winds were systematically stronger in the rollupdraft regions than in the roll-downdraft regions, probably due to distortion of the along-roll wind profile by the rolls. Comparison of observed wind profiles to those required by roll formation mechanisms found by past numerical and theoretical studies suggested that the observed rolls were formed by the along-roll wind shear (Asai, 1970) or wind shear curvature (Kuettner, 1971) in the lowest 0.2Z _i, whereZ _i is the height of the top of the CIBL.     

Large-eddy simulations of thermally forced circulations in the convective boundary layer. Part II: The effect of changes in wavelength and wind speed

This paper extends previous large-eddy simulations of the convective boundary layer over a surface with a spatially varying sensible heat flux. The heat flux variations are sinusoidal and one-dimensional. The wavelength is 1500 or 4500 m (corresponding to 1.3 and 3.8 times the boundary-layer depth, respectively) and the wind speed is 0, 1 or 2 m s^-1.In every case the heat flux variation drives a mean circulation. As expected, with zero wind there is ascent over the heat flux maxima. The strength of the circulation increases substantially with an increase in the wavelength of the perturbation. A light wind weakens the circulation drastically and moves it downwind. The circulation has a significant effect on the average concentration field from a simulated, elevated source.The heat flux variation modulates turbulence in the boundary layer. Turbulence is stronger (in several senses) above or downwind of the heat flux maxima than it is above or downwind of the heat flux minima. The effect remains significant even when the mean circulation is very weak. There are effects too on profiles of horizontal-average turbulence statistics. In most cases the effects would be undetectable in the atmosphere.We consider how the surface heat flux variations penetrate into the lower and middle boundary layer and propose that to a first approximation the process resembles passive scalar diffusion.The research reported in this paper was conducted while the first author was on study leave at Colorado State University.     

A study of wind speed modification and internal boundary-layer heights in a coastal region

Wind profile data within the first two kilometres of a coast have been used to study the wind field modification downstream of this surface discontinuity. The land area is generally very flat, having an overall roughness length of 0.04 m. A wind model, suitable for practical applications and inexpensive to run, has been tested against the data and was found to give satisfactory results. Knowing the climatological statistics of wind and stratification, e.g., at the coast, the model may thus be used to estimate, on a climatological basis, how the wind field is modified with distance inland, at least in areas with only minor topography. This type of information is of great importance when locating wind turbines. It is in these cases also important to know the statistics of the internal boundary-layer (IBL) height, as the turbulence intensity may be quite different in and above the IBL, which in turn may influence load and fatigue calculations. Using the wind profile data, the IBL height was clearly discernible in the majority of cases. Having very unstable stratification over land, the IBL height could, however, not be determined from the wind profiles, as the wind in these cases did not decrease inland. This result was also obtained using the wind model. A simple model of the type z _IBL = a · x ^b, was instead tested, and was shown to give reasonable results.     

Measurements of flow over an elongated ridge and its thermal stability dependence: The mean field

Measurements of mean wind flow and turbulence parameters have been made over Cooper's Ridge, a 115 m high elongated ridge with low surface roughness. This paper describes measurements of the streamwise and vertical variations in the mean field for a variety of atmospheric stability conditions. In near-neutral conditions, the normalised speedup over the ridge compares well with measurements from Askervein (Mickleet al., 1988). The near-neutral results are also compared to an analytical flow model based on that of Huntet al. (1988a). Measured streamwise variations show less deceleration at the foot of the hill and slightly more acceleration at the crest of the hill than does the model. In non-neutral conditions, the speedup over the ridge reduces slightly in unstable conditions and increases by up to a factor of two in stable conditions. The model is modified to allow boundary-layer stability to change the upwind wind profile and the depths of the inner and middle layers. Such a modification is shown to describe the observations of speedup well in unstable and weakly stable conditions but to overestimate the speedup in moderate to strongly stable conditions. This disagreement can be traced to the model's overestimation of the upstream scaling velocity at the height of the middle layer through its use of a stable wind profile form which has greater shear than that of the observed profiles, in possible combination with the three-dimensionality of the ridge which would allow enhanced flow around, rather than over, the feature in more stable conditions.     

Mass Transfer Velocity and Momentum Vertical Exchange in Simulated Deep Street Canyons

A box model to simulate mass transfer inside deep street canyons and with atmospheric flow above is introduced and discussed. Two ideal deep street canyons with aspect ratios of 3 and 5 (the aspect ratio being the ratio between building height and street width H/W) are considered. This range of aspect ratios, found in many densely populated historical centres in Mediterranean cities as well as in other cities around the world, potentially creates high air pollutant concentration levels. Our model is based on a combination of analytical solutions and computation fluid dynamics (CFD) simulations using carbon monoxide (CO) as a tracer pollutant. The analytical part of the model is based on mass transfer velocity concepts while CFD simulations are used both for a preliminary validation of the physical hypothesis underlying the model (steady-state simulations) and to evaluate the concentration pattern with time (transient or wash-out simulations). Wash-out simulation curves were fitted by model curves, and mass transfer velocities were evaluated through a best-fitting procedure. Upon introducing into the model the contribution of traffic-produced turbulence, the modelled CO concentration levels became comparable with those obtained in real-world monitoring campaigns. The mass transfer rate between the canyon and the above atmosphere was then expressed in terms of an overall mass transfer velocity, which directly allows the evaluation of the mass transfer rate between the bottom volume of the canyon (pedestrian level) with the above atmosphere. Overall mass transfer velocities are reported as a function of the operating conditions studied (H/W = 3–5 and wind speeds = 2–8 ms⁻¹). Finally, a simple expression is reported for determining pollutant concentrations at the pedestrian level based on the overall mass transfer velocity defined.