A Model for Temperature Fluctuations in a Buoyant Plume

We present a hybrid Lagrangian stochastic model for buoyant plume rise from an isolated source that includes the effects of temperature fluctuations. The model is based on that of Webster and Thomson (Atmos Environ 36:5031-5042, 2002) in that it is a coupling of a classical plume model in a crossflow with stochastic differential equations for the vertical velocity and temperature (which are themselves coupled). The novelty lies in the addition of the latter stochastic differential equation. Parametrizations of the plume turbulence are presented that are used as inputs to the model. The root-mean-square temperature is assumed to be proportional to the difference between the centreline temperature of the plume and the ambient temperature. The constant of proportionality is tuned by comparison with equivalent statistics from large-eddy simulations (LES) of buoyant plumes in a uniform crossflow and linear stratification. We compare plume trajectories for a wide range of crossflow velocities and find that the model generally compares well with the equivalent LES results particularly when added mass is included in the model. The exception occurs when the crossflow velocity component becomes very small. Comparison of the scalar concentration, both in terms of the height of the maximum concentration and its vertical spread, shows similar behaviour. The model is extended to allow for realistic profiles of ambient wind and temperature and the results are compared with LES of the plume that emanated from the explosion and fire at the Buncefield oil depot in 2005.