| A lumped parameter model of downdrafts driven by evaporative cooling in cloudy air is developed. Equations governing the state of a parcel of cloud air, that exchanges mass, momentum, and energy with its environment, are derived. Linear analysis yields familiar results on the local stability of parcel motion. The full system of equations is simplified by a singular perturbation technique that makes use of the large evaporation--condensation rate parameter. This simplified system represents an "outer" asymptotic solution.; A conservative property, the total energy of the parcel, is identified and shown to be the sum of the kinetic energy and the moist static energy. Energy methods are employed to determine the global nature of the motion of a saturated parcel. The usual method of computing parcel temperature, requiring the temperature to follow the wet adiabat, is found to be equivalent to neglecting the kinetic energy in the total energy balance. This neglect of the kinetic energy is found to be significant for high velocities, and in particular for microbursts. |
