Abstract
Concentration probability density functions (pdfs) calculated according to fluctuating plume models in one- and two-dimensions, representing the limiting cases of one-dimensional dispersion from a line source or a point source in strongly anisotropic turbulence and of axisymmetric dispersion from a point source in isotropic turbulence, are discussed and analyzed in terms of the location of the sampling point within the mean plume and of the ratio, s/m, of the standard deviations for relative dispersion and meandering.
In both cases, the pdfs cover the finite concentration range from zero to C 0, the centreline concentration of the instantaneous plume. The main difference between them is that whereas the 2-D pdf is always unimodal, the 1-D pdf has a singularity at C 0 which under some circumstances results in a bimodal form. However, the probability associated with this singularity is not always significant. Differences of practical importance in the shape of the pdfs occur mainly for centreline or near-centreline sampling locations when meandering is not too much larger than relative dispersion (1 < m 2/s2 < 10) and for sampling locations a distance of order s from the centreline when relative dispersion is not too much larger than meandering (1 < s 2/m2 < 5).
Comparison against wind tunnel measurements not too far downstream of a line source in grid turbulence shows that the 1-D model reproduces the essential features and trends of the measurements. Under appropriate circumstances the measurements show the bimodal pdf predicted by the 1-D model (but not by the 2-D model) confirming that the effect of the anisotropy in the source distribution is observable.
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Present address: School of Mechanical Engineering, Aristotle University, Thessaloniki, 54006 Thessaloniki, Greece.
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Sawford, B.L., Stapountzis, H. Concentration fluctuations according to fluctuating plume models in one and two dimensions. Boundary-Layer Meteorol 37, 89–105 (1986). https://doi.org/10.1007/BF00122758
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DOI: https://doi.org/10.1007/BF00122758