Mean‐square values of concentration in a contaminant cloud

Abstract

SUMMARYA simple and relatively general analytic expression for the distributed second central moments of scalar concentration is derived. The 'fluctuations' or mean-square values are given in terms of the mean concentration field and apply in either an inertial or cloud centre-of-mass reference frame. Clouds in homogeneous grid turbulence, in the neutral atmospheric boundary layer, and in the inertial sub-range are used as illustrative examples.

The Relationship between Skewness and Kurtosis of A Diffusing Scalar

“…The lower-ordered moments in (12)-(14) depend on the mean concentration Cðx; tÞ, a and b (which are functions of downstream distance), as well as additional functions k i for each higher moment (these are functions of time in the case of a cloud). Remarkably, as few as the first four of these moments can be inverted to yield a reliable estimate of the PDF of concentration C. The equations that describe the evolution of these functions are relatively straightforward and invite the use of simple closure schemes for their solution (see Labropulu and Sullivan, 1995;Mole and Clarke, 1995;Sullivan, 2004). A satisfactory solution scheme for the mean concentration for both clouds and continuous elevated sources in the atmospheric boundary layer has been given in Sullivan and Yip (1991).…”

“…A satisfactory solution scheme for the mean concentration for both clouds and continuous elevated sources in the atmospheric boundary layer has been given in Sullivan and Yip (1991). The important event of the sudden release of contaminant into the atmospheric boundary layer, as may result from and accidental spill, has been investigated in Labropulu and Sullivan (1995); there, the functions aðtÞ and bðtÞ were used to calculate the second central moment using (12). In principle, this scheme can be employed to calculate k 3 and k 4 , which would enable an approximation of the PDF via a four-moment inversion scheme.…”

Scalar concentration reduction in a contaminant cloud

“…The functions α(t) and β(t) have been predicted by taking advantage of the simplicity of (7) and using physical approximations for the fine-scale structure of the concentration field to effect closure (Labropulu andSullivan 1995, Clarke and. In principle, the r n (t) required for the higher moments could also be attempted with this solution procedure.…”

The α‐β model for concentration moments in turbulent flows

“…Experiments (Sawford and Sullivan 1995;Warhaft 1984;Stapountzis et al 1986;Karnik and Tavoularis 1989) show that the peaks of variance merge into a centreline peak, but that a bimodal distribution of variance may eventually return. These observations can be explained by the modelled evolution of a in Figure 3 (Moseley 1991) and in Clarke and Mole (1995) and Labropulu and Sullivan (1995).…”

“…Moseley (1991) showed that the results are consistent with experimental observations (although appropriate data are presently in short supply, especially for instantaneous releases). Discussion of further simplifications and developments of the model (making use of the asymptotic results given above and modifications of the closure scheme (13)) can be found in Clarke and Mole (1995) and Labropulu and Sullivan (1995).…”