Concentration fluctuations according to fluctuating plume models in one and two dimensions

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 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.

Dispersion of a Passive Scalar Fluctuating Plume in a Turbulent Boundary Layer. Part I: Velocity and Concentration Measurements

“…13 and 14 provide excellent estimates of L vv and L ww assuming α v ≈ 0.4 and α w ≈ 0.6, respectively. Note that both values are significantly lower than those currently adopted in the literature, which vary between a minimum of 0.8 (Sawford and Stapountzis 1986) and a maximum of 1.8 (Postma et al 2011). The direct measurements of the Eulerian integral length scales can be further used to estimate the characteristic 'life time' of the larger scale flow structures as (Tennekes and Lumley 1972;Frisch 1995),…”

“…In the modelling of the mass and momentum transfer across the boundary layer, the scales L vv and L ww can be parametrized assuming the stationarity of the energy cascade as (Sawford and Stapountzis 1986),…”

Conditional concentration statistics for surface plumes in the atmospheric boundary layer

“…Now, in the meander-dominated near-field in homogeneous turbulence (Sawford and Stapountzis, 1986), the shape of the probability density function or frequency distribution is strongly dependent on the location of the receptor point and source geometry. Thus we consider only data from ground-level (or effectively ground-level) sources, since near-field dispersion from elevated sources in a boundary layer is similar to dispersion in homogeneous turbulence.…”

Effect of Vertical Wind Shear on Concentration Fluctuation Statistics in a Point Source Plume

“…Pseudo-meandering refers to a profile where the meander ratio M is calculated from the fluctuation intensity i and not evaluated directly from estimates of plume meander spread σ m . This equation was derived from the higher moment concentration relations developed by Sawford and Stapountzis (1986),…”

“…The shear history model we propose extends currently available dispersion models, such as the meandering plume model of Gifford (1959) and extended by Sawford and Stapountzis (1986), Sykes (1988) and Wilson (1995), that predict plume statistics in more homogeneous turbulence well above the ground. The algebraic shear history model we present here can be used with any dispersion model that predicts no-shear concentration fluctuation statistics to adjust for the effect of vertical wind shear on intensity i, intermittency factor γ and integral time scale T c of concentration fluctuations in a well-developed rough surface boundary layer.…”