The equations of motion for moist atmospheric air

TL;DR

This paper clarifies the equations of motion for moist atmospheric air, resolving a controversy over the 'reactive motion' term by distinguishing assumptions for condensation and evaporation, and providing a revised equation.

Contribution

It offers a new, generally applicable equation for moist air motion, clarifying the role of phase transitions and correcting misconceptions about reactive motion.

Findings

Reactive motion does not occur during condensation.

The 'reactive motion' term applies only to evaporation, not condensation.

A revised equation for moist air motion is proposed.

Abstract

How phase transitions affect the motion of moist atmospheric air remains controversial. In the early 2000s two distinct differential equations of motion were proposed. Besides their contrasting formulations for the acceleration of condensate, the equations differ concerning the presence/absence of a term equal to the rate of phase transitions multiplied by the difference in velocity between condensate and air. This term was interpreted in the literature as the "reactive motion" associated with condensation. The reasoning behind this "reactive motion" was that when water vapor condenses and droplets begin to fall the remaining gas must move upwards to conserve momentum. Here we show that the two contrasting formulations imply distinct assumptions about how gaseous air and condensate particles interact. We show that these assumptions cannot be simultaneously applicable to condensation and evaporation. "Reactive motion" leading to an upward acceleration of air during condensation does not exist. The "reactive motion" term can be justified for evaporation only; it describes the downward acceleration of air. We emphasize the difference between the equations of motion (i.e., equations constraining velocity) and those constraining momentum (i.e., equations of motion and continuity combined). We show that, owing to the imprecise nature of the continuity equations, consideration of total momentum can be misleading and that this led to the "reactive motion" controversy. Finally, we provide a revised and generally applicable equation for the motion of moist air.