William H. Snyder

Similarity criteria for the application of fluid models to the study of air pollution meteorology

Similarity criteria for modeling atmospheric flows in air and water are reviewed. It is shown that five nondimensional parameters plus a set of nondimensional boundary conditions must be matched in model and prototype. The neglect of the Rossby number can lead to serious errors in modeling of diffusion in a prototype with a length scale greater than about five kilometers. The Reynolds number, the Peclet number and the Reynolds-Schmidt product criteria may be neglected if the model flow is of sufficiently high Reynolds number. The Froude number criterion appears to be the most important. The complete specification of boundary conditions is found to be nebulous, but is discussed in some detail. Over-roughening of the model surface may be necessary to satisfy a roughness Reynolds number criterion. Both air and water appear to be suitable fluids to use as modeling media.

The structure of strongly stratified flow over hills: dividing-streamline concept

In stably stratified flow over a three-dimensional hill, we can define a dividing streamline that separates those streamlines that pass around the hill from those that pass over the hill. The height Hs of this dividing streamline can be estimated by Sheppards simple energy argument; fluid parcels originating far upstream of a hill at an elevation above Hs have sufficient kinetic energy to rise over the top, whereas those below Hs must pass around the sides. This prediction provides the basis for analysing an extensive range of laboratory observations and measurements of stably stratified flow over a variety of shapes and orientations of hills and with different upwind density and velocity profiles. For symmetric hills and small upwind shear, Sheppards expression provides a good estimate for Hs. For highly asymmetric flow and/or in the presence of strong upwind shear, the expression provides a lower limit for Hs. As the hills become more nearly two-dimensional, these experiments become less well defined because steady-state conditions take progressively longer to be established. The results of new studies are presented here of the development of the unsteady flow upwind of two-dimensional hills in a finite-length towing tank. These measurements suggest that a very long tank would be required for steady-state conditions to be established upstream of long ridges with or without small gaps and cast doubt upon the validity of previous laboratory studies.

The effects of stable stratification on turbulent diffusion and the decay of grid turbulence

Experiments are described in which a grid is towed horizontally along a large tank filled first with water and then with a stably stratified saline solution. The decay rates of the r.m.s. turbulent velocity components ( w ’, v ’) perpendicular to the mean motion are measured by a ‘Taylor’ diffusion probe and are found to be unaffected by the stable stratification over distances measured from 5 to 47 mesh lengths ( M ) downstream, and over a range of Froude number U/NM of ∞ and 8·5 to 0·5, U being the velocity and N the buoyancy frequency. The Reynolds number Mw ’/ν of the turbulence was about 10 3 , where v is the kinematic viscosity. The vertical velocity fluctuations produced near the grid were reduced by the stratification by up to 30% when U / MN ≈ 0·5. Large-scale internal wave motion was not evident from the observations within about 50 mesh lengths of the grid. The turbulent diffusion from a point source located 4·7 mesh lengths downstream was studied. σ y , σ z , the horizontal and vertical plume widths, were measured by a rake of probes. σ y was found to be largely unaffected by the stratification and grew like t ½ , while σ z was found in all cases to reach an asymptotic limit σ z ∞ where 0·5 [les ] σ z ∞ N / w ’ s [les ] 2, w ’ s being the r.m.s. velocity fluctuations at the source; the time taken for σ z to reach its maximum was about 2 N −1 . These results are largely in agreement with the theoretical models of Csanady (1964) and Pearson, Puttock & Hunt (1983).

Stratified flow over three-dimensional ridges

An experimental study of the stratified flow over triangular-shaped ridges of various aspect ratios is described. The flows were produced by towing inverted bodies through saline-water solutions with stable (linear) density gradients. Flow-visualization techniques were used extensively to obtain measurements of the lee-wave structure and its interaction with the near-wake recirculating region and to determine the height of the upstream dividing streamline (below which all fluid moved around, rather than over the body). The Froude number F (= U/Nh ) and Reynolds number ( Uh /ν), where U is the towing speed, N is the Brunt–Vaisala frequency, h is the body height, and ν is the kinematic viscosity, were in the nominal ranges 0.2–1.6 (and ∞) and 2000–16000 respectively. The study demonstrates that the wave amplitude can be maximized by ‘tuning’ the body shape to the lee-wave field, that in certain circumstances steady wave breaking can occur or multiple recirculation regions (rotors) can exist downstream of the body, that vortex shedding in horizontal planes is possible even at F = 0.3, and that the ratio of the cross-stream width of the body to its height has a negligible effect on the dividing streamline height. The results of the study are compared with those of previous theoretical and experimental studies where appropriate.

Wind tunnel investigation of the effects of a rectangular-shaped building on dispersion of effluents from short adjacent stacks

Abstract In a wind tunnel study, the influence of the highly turbulent region found in the lee of a model building upon plumes emitted from short stacks was examined through smoke visualization and tracer gas concentration mappings. A thick, simulated atmospheric boundary layer was used to provide background dispersion. A rectangular-shaped building with its length equal to twice its height and width was oriented with the long side perpendicular to the approaching wind. The stack was placed midway along the lee side of the building. In all phases of the study, each smoke or tracer release from the stack was repeated with the building removed. This allowed for a simple demonstration of the building wake effects. A simple mathematical model was developed that provided good estimates of concentrations in the building wake. The building influence was found to be reduced with increases in the effective source height. Application of the “2.5 times rule”, i.e. an effective source height at 2.5 times the height of the building, resulted in maximum ground-level concentration in the wake being approximately 20 per cent higher than found in the absence of the building. A stack 1.5 times the height of the building resulted in maximum ground-level concentrations in the wake being 250 per cent higher, a far more significant effect.

A wind tunnel study of dispersion from sources downwind of three-dimensional hills

Abstract The nature of the separated flow fields downwind of moderately steep hills of varying crosswind aspect ratios (spanwise breadth/height) has been examined using models placed in a simulated adiabatic atmospheric boundary layer in a meteorological wind tunnel. The hills ranged from an axisymmetric cone to a two-dimensional ridge. Concentration patterns resulting from sources placed at numerous heights and distances downwind of these hills were examined. Effective stack heights and amplification factors (i.e. ratios of maximum ground-level concentrations in the presence of the hills to those in the absence of the hills) were used to characterize the effects of the hills on plume transport and diffusion. Amplification factors were generally found to increase as the aspect ratio increased and as the source height approached the reattachment streamline (such that the plume was adverted toward the ground). The largest amplification factor (A = 11) was observed when the source was placed halfway from the hill center to the re-attachment point at a height of 1 1 4 hill heights downwind of the two-dimensional ridge.

Turbulent diffusion from a point source in stratified and neutral flows around a three-dimensional hill—part I. Diffusion equation analysis

Abstract In stable stratified flow around three dimensional hills vertical motion and vertical diffusion is negligible. Consequently turbulent diffusion from a point source can be modelled by considering horizontal flow and horizontal diffusion. Using an eddy diffusivity the advective diffusive equation around a three dimensional hill which is axisymmetric about a vertical axis is solved to show how source positions on and off the centre line affect the trajectories and splitting of impinging plumes and the value and position of the maximum surface concentration on the hill. In the second part of the paper we analyse a plume in a neutrally stable potential flow around an axisymmetric obstacle such as a hemisphere, also using the diffusion equation. The solutions show how, because streamlines approach the surface of a 3-dimensional hill much more closely than the surface of a 2-dimensional hill, the maximum surface concentrations on the hill can become very much greater than in the absence of the hill. But this only occurs for a limited range of source heights.

Dense gas vertical diffusion over rough surfaces: results of wind-tunnel studies

Abstract A cooperative program of measurements of vertical diffusion of continuous, dense gas plumes over rough surfaces in neutral boundary layers has been carried out in three wind tunnels in the USA and the UK. The three environmental boundary layer tunnels were at the Chemical Hazards Research Center (CHRC) at the University of Arkansas, the Fluid Modeling Facility (FMF) of the US Environmental Protection Agency in North Carolina, and the Environmental Flow Research Centre (EnFlo) at the University of Surrey. A simple and consistent set of definitions was adopted for the plume variables like plume depth, mean plume transport speed, vertical entrainment velocity, we, and plume Richardson number Ri ∗ , where Ri 1/2 ∗ is a ratio of buoyancy-induced flow velocities to u ∗ , the upstream-of-source ambient friction velocity. The present experiments focus on how Ri ∗ affects the ratio w e /u ∗ . In order to maintain nearly constant Ri ∗ in distance and time, continuous line sources of dense gas, primarily CO2, were employed. Good agreement was found among the three tunnels. The results also agree with the classic Prairie grass field experiment for the “passive limit” ( Ri ∗ =0): w e /u ∗ =0.6–0.7. For Ri ∗ up to 20, the results fit the equation w e /u ∗ =0.65/(1+0.2 Ri ∗ ). For Ri ∗ >20, molecular diffusion and viscosity effects were apparently quite strong because we was observed to collapse to values nearly commensurate with molecular diffusion alone.

Flow and dispersion of pollutants within two-dimensional valleys

Abstract Wind tunnel experiments and a theoretical model concerning the flow structure and pollutant diffusion over two-dimensional valleys of varying aspect ratio are described and compared. Three model valleys were used, having small, medium, and steep slopes. Measurements of mean and turbulent velocity fields were made upstream, within and downwind of each of these valleys. Concentration distributions were measured downwind of tracer sources placed at an array of locations within each of the valleys. The data are displayed as maps of terrain amplification factors, defined as the ratios of maximum ground-level concentrations in the presence of the valleys to the maxima observed from sources of the same height located in flat terrain. Maps are also provided showing the distance to locations of the maximum ground-level concentrations. The concentration patterns are interpreted in terms of the detailed flow structure measured in the valleys. These data were also compared with results of a mathematical model for treating flow and dispersion over two-dimensional complex terrain. This model used the wind tunnel measurements to generate mean flow fields and eddy diffusivities, and these were applied in the numerical solution of the diffusion equation. Measured concentration fields were predicted reasonably well by this model for the valley of small slope and somewhat less well for the valley of medium slope. Because flow separation was observed within the steepest valley, the model was not applied in this case.

A wind tunnel study of the flow structure and dispersion from sources upwind of three-dimensional hills

The flow fields around moderately steep hills of triangular cross section and varying crosswind aspect ratio and around a bell-shaped hill were examined by using models immersed in a simulated neutral atmospheric boundary layer in a meteorological wind tunnel. The triangular hills ranged from an axisymmetric cone to a two-dimensional ridge. Concentration patterns resulting from sources of three heights placed upwind of each of these hills were examined to determine plume deformations and terrain amplification factors. The separated flow fields, increasing in size with increasing aspect ratio, appeared to have dominating influences on the entire flow structure; changes in several flow parameters were plausibly explained in terms of the notion that the effective hill shape was the hill-plus-recirculation region rather than the actual hill shape. The concentration measurements showed strong distortions of plume shapes effected by the hills, with convergence in vertical planes and divergence in horizontal planes. Plumes from elevated sources approached the hill surfaces much more closely the smaller the aspect ratio; streamline displacements were generally within the limits suggested by potential flow theory. The terrain amplification factor A, defined as the ratio of the maximum surface concentration in the presence of the hill to the maximum in flat terrain, was found to decrease with increasing aspect ratio. For the half-hill-height sources, values of A ranged from 4 for the bell-shaped hill down to 1.5 for the two-dimensional ridge; for the hill-height source, from 1.8 for the cone down to 0.6 for the two-dimensional ridge. The latter value is suspect, however, because larger concentrations are expected downwind of the reattachment point, a region not probed in the current study.