Numerical modeling of buoyant plumes in a turbulent, stratified atmosphere

Abstract

A widely applicable computational model of buoyant, bent-over plumes in realistic atmospheres is constructed. To do this, the two-dimensional, time-dependent fluid mechanics equations are numerically integrated, while a number of important physical approximations serve to keep the approach at a tractable level. A three-dimensional picture of a steady state plume is constructed from a se- quence of time-dependent, two-dimensional plume cross sec- tions--each cross section of the sequence is spaced pro- gressively further downwind as it is advected for a pro- gressively longer time by the prevailing wind. The dyna- mics of the plume simulations are quite general. The buoyancy sources in the plume include the sensible heat in the plume, the latent heat absorbed or released in plume moisture processes, and the heating of the plume by a radioactive pollutant in the plume. The atmospheric state in the simulations is also quite general. Atmospheric variables are allowed to be functions of height, and the ambient atmospheric turbulence (also a function of height) is included in the simulations. A demonstration of the ability of the model to repro- duce the solutions to problems that are known is under- taken. Comparisons to buoyant line-thermal laboratory experiments show that the model calculates the dynamics of the fluid motions to an acceptable accuracy. Comparisons to atmospheric plume rise and dispersion experiments show that the model can simulate individual plumes more accur- ately than existing correlations because it calculates the effect of the atmospheric turbulence and stratification from first-principles. The comparisons also show that improvements to the model are likely to be made by more accurately describing the anisotropic nature of atmospheric turbulence, and the production of turbulence by the sources of buoyancy.