Analytical and numerical solutions of hydrometeor momentum equations

Momentum equations of hydrometeors and air variously forced by gravity and frictional dissipation are considered. Limiting cases are shown to reveal important behavior. The case of hydrometeors accelerating to the velocity of a constant horizontal wind reveals extremely long equilibration times due to friction alone. Velocity traces for the case of accelerating hydrometeors falling through air and the case of accelerating hydrometeors and air under the influence of gravity are found. They reveal that acceleration occurs for about twice as long as naive scaling would suggest. When the laden system can accelerate both horizontally and vertically, the solution to the momentum equations is complicated by the unique vector nature of the problem. Numerical solutions illustrate how drops act as a damper on the motion of air. A particular focus throughout is on the modification of terminal hydrometeor fall speeds due to multiple effects. Among these are enervation due to accounting for hydrometeor momentum, invigoration from viscous effects for the very smallest drops, and enervation from relative horizontal motion of particles during settling.