The effect of including swirling motion in a buoyant plume arising from a point source of heat is considered. One case in which the circulation tends to zero outside of the plume has been studied previously; a second case in which the circulation tends to a finite constant is considered and yields closed form solutions when the Prandtl number is equal to 1 and 2. The voricity distributions for the two cases are very different. Numerical solutions are presented for other values of the Prandtl number in the range 0.005 to 500.0.