The Rise of Moist, Buoyant Plumes

Abstract

The governing equations for a moist, buoyant plume in a cross wind are presented. A comparison of the energy equations for saturated and unsaturated plumes, the subject of some previous controversy, shows that the form of the two equations is identical only when the saturated plume is in a saturated atmosphere. In this case, the moist adiabatic lapse rate replaces the dry adiabatic lapse rate in the energy equation. Analytical results for the maximum plume rise zmm and the distance xmm to the maximum rise are obtained for a nearly horizontal, saturated plume in a stable, saturated atmosphere using the complete set of governing equations. Stable plume rise conditions exist for the saturated plume in a saturated atmosphere as long as the ambient temperature lapse rate dTo/dz is greater than ?Γm, a reference lapse rate. Γm is slightly greater than the moist adiabatic lapse rate. Comparisons are made between 1) zmm and the maximum dry plume rise of Fay et al., and 2) zmm and the moist plume rise calculations of Hanna.