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 Cc, 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,, 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 < m2/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 < s2/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.