Changes in Horizontal Plume Distributions at Larger Turbulence Intensities

Applications of Gaussian plume models often assume that the crosswind distribution of pollutant at a fixed downwind distance x is equivalent to its distribution at a fixed travel time x/U, where U is the mean wind speed. Additionally, plume models use rectangular coordinates to describe plume behavior, whereas tracer field studies frequently employ polar coordinates and place samplers on circular arcs at a radial distance r. Analyses of the field data normally assume that the tracer distribution as a function of arc length d in polar coordinates is equivalent to its distribution with crosswind distance y in rectangular coordinates. This presentation uses Lagrangian particle simulations to show that these basic assumptions about plume behavior are reasonably accurate as long as the horizontal turbulence intensity is less than about 0.2, equivalent to a standard deviation of the wind direction of around 11-12°. At larger intensities, the assumptions start breaking down.

A primary reason for the failure of these assumptions at larger turbulence intensities is that the travel times of pollutant parcels reaching a fixed downwind distance x actually have a positively skewed probability distribution rather than a symmetric distribution centered on the value x/U given by Taylor's hypothesis. As a result, the y plume distribution at fixed x increasingly deviates from a Gaussian shape at turbulence intensities above 0.2; it develops heavier tails that more resemble a Student's t distribution with a small number of degrees of freedom.

Standard Gaussian models are still commonly applied for turbulence intensities above 0.2, so the deviations in plume shape demonstrated by the Lagrangian particle simulations can affect the interpretation of both plume-model results and comparisons with tracer data. The lateral plume width σ_y at a fixed x in rectangular coordinates is always larger than the corresponding width at a travel time t equal to x/U. For turbulence intensities in the range of 0.2-0.3, the ratio of these two σ_y values can exceed a factor of 1.5. The particle simulations can also be used to compute the lateral plume width σ_d in polar coordinates for radial distance r and arc length d. Normally it is assumed in tracer studies that σ_d/σ_y = 1 for r = x, but this ratio can actually fall well below 0.75 for turbulence intensities between 0.2 and 0.3.