The effect of temperature fluctuations on the spread of a buoyant plume

Abstract

Emissions from many natural and anthropogenic sources are hot compared with the surrounding ambient air. Such buoyancy effects cause the emitted plume to rise, increasing the effective source height and significantly decreasing the maximum ground level concentrations (in the vicinity of the source). A major aspect that distinguishes buoyant and passive dispersion is that buoyant fluid particles create their own turbulence and hence exchange processes between the plume and its environment need to be accounted for. The inclusion of plume rise in Lagrangian stochastic models (LSMs) of turbulent dispersion has been considered by many authors but the interaction of the buoyant plume with the environment (by means of entrainment) is difficult to model in a Lagrangian framework. Webster and Thomson [8] formulated a hybrid model in which the mean flow is calculated from a simple plume model and the fluctuations of velocity are calculated using an LSM. They model the effect of turbulence generated by the plume by an additional random increment to the position of a particle. Here, instead of including this extra term, we add a stochastic differential equation (SDE) for the temperature fluctuations suitably coupled with the SDE for the velocity fluctuations. The interaction of temperature and velocity fluctuations, directly related to the turbulence within the plume, determines the plume’s spread. The results of the model are compared with large-eddy simulation (LES) of buoyant plumes in a uniform crosswind and also with the plume generated by the explosion and fire at the Buncefield oil depot in 2005 using realistic profiles of the wind speed and direction and thermal stratification.