Concentration fluctuations according to fluctuating plume models in one and two dimensions |
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Authors: | B L Sawford H Stapountzis |
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Institution: | (1) CSIRO Division of Atmospheric Research, Private Bag No. 1, 3195 Mordialloc, Vic., Australia;(2) Department of Engineering, University of Cambridge, CB2 1PZ Cambridge, U.K. |
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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.Present address: School of Mechanical Engineering, Aristotle University, Thessaloniki, 54006 Thessaloniki, Greece. |
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