Solutions for turbulent buoyant plumes rising from circular sources

Abstract

Analytical solutions are developed for turbulent plumes rising from circular sources of positive buoyancy in a quiescent environment of uniform density. From governing equations written in a form which encompasses both the Boussinesq and non-Boussinesq cases, we derive analytical expressions for all plume variables (radius, velocity, and density deficit) in terms of a single quantity Γ, called the plume function. For given source conditions, we then show that Γ (and, subsequently, all plume variables) can be evaluated at any height from two integral functions which are defined for lazy and forced plumes. For a practical use, these integral functions are given in tables. Moreover, exact values and locations of the maximum velocity and the plume neck are determined.