Movement of heavy particles in tornadoes

Abstract

The horizontal movement of inertial particles in the intensive vortices, where the centrifugal force can be substantially higher than the gravity, is studied analytically. A similar problem was studied earlier for small (Stokes) particles at low Reynolds number, which allow one to be limited to the linear resistance law. It is shown that the previous results to a great extent can be extrapolated to the case of considerably heavier particles (e.g., water droplets with a diameter up to 1 mm at Reynolds numbers up to 103). The nonlinear nature of the resistance, i.e., its dependence on the particle velocity relative to the medium, should be taken into account for such particles. Some general laws are established for particle dynamics. In particular, their tangential velocity is close to the velocity of the medium, while the radial velocity is substantially lower (it is close on the order of magnitude to the geometric mean of the particle tangential velocity and the difference between the latter and the tangential velocity of the medium). The limits of applicability of the results are found, i.e., the restrictions to the size and mass/density of particles.