Changes in Horizontal Plume Distributions at Larger Turbulence Intensities
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 σy 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 σy values can exceed a factor of 1.5. The particle simulations can also be used to compute the lateral plume width σd in polar coordinates for radial distance r and arc length d. Normally it is assumed in tracer studies that σd/σy = 1 for r = x, but this ratio can actually fall well below 0.75 for turbulence intensities between 0.2 and 0.3.