A General Description of Entrainment in Buoyant Cloudy Plumes Including the Effects of Mixing-Induced Evaporation

In this work, the steady-state one-dimensional axisymmetric plume theory is revisited and generalized to include the effects of nonhomogeneous updraft velocity and buoyancy profiles across the plume, environmental shear, and, more importantly, evaporative cooling resulting from the mixing between cloudy air and the dry environment. Based on an energy consistency argument, a method is proposed to derive a relationship for the fractional lateral mixing rate (which may here be positive or negative) from the plume’s integral equations, as well as a set of equations for the equivalent plume properties, both of which maintain a high degree of generality by incorporating effects of environmental shear and inhomogeneous radial distributions. In the absence of wind shear, a simpler entrainment-rate closure is proposed, which is then further constrained by systematically varying the plume and environmental conditions and allowing evaporative cooling to occur. The fractional mixing rate is shown to be strongly correlated with the plume buoyancy and, to a lesser extent, to the critical mixing fraction (i.e., the fraction of dry air that needs to be mixed with cloudy air to make the mixture neutrally buoyant). Quantitative estimates of this dependency are given to facilitate implementations of the new model in convection parameterizations. Analyzing the proposed closure suggests that it could capture features observed in recent high-resolution simulations and that it is consistent with the buoyancy-sorting concept. The results therefore support recent findings concerning the parameterization of entrainment for moist atmospheric convection.