Abstract
An idealized precipitation process in a 3-dimensional unsteady mesoscale flow with a Boussinesq approximation is considered. The process is assumed as follows: Immediately after precipitation particles are generated, they attain such an equilibrium that they fall with a constant terminal vertical velocity relative to the flow, and their horizontal velocity is equal to that of the flow. The ground is in general not flat, and other forcings (e. g., thermal) may be included in order to induce the vertical flow velocity.
Based on these assumptions, a simple formula describing the concentration of trajectories of precipitation particles at the ground is derived. In particular, in the case of a steady flow, the concentration (scattering) of trajectories occurs when w0 is positive (negative). Here w0 is the vertical flow velocity at the generation point of particles. In the case of an unsteady flow, the unsteadiness may suppress or enhance the concentration (scattering) of trajectories.
