Nonlinear interaction between two components of motion upon precipitation of a heavy particle in a shear flow

When heavy particles move in a shear flow, the drag depends on the Reynolds number and, hence, on the magnitude of the particle velocity relatively to the medium. This leads to a nonlinear interaction between various components of motion. For example, when a particle precipitates in a horizontal air flow with vertical shear, it also acquires horizontal motion relative to air in addition to vertical motion. These two components of motion contribute to the hydrodynamic drag coefficient by affecting the Reynolds number and thereby influence each other. Steady motion of a particle in a flow with constant vertical shear is analyzed. Dimensionless criterion of significance of the nonlinear effect under consideration is determined. It is demonstrated that this effect can be significant in the near-surface atmospheric layer in the case of storm wind.