On the Formation of Particle Sheaths in Columnar Vortices

Abstract

Geophysical columnar vortices such as tornadoes, waterspouts and dust devils are frequently observed to have one or more cylindrical sheaths of dust concentric with the axis of symmetry. The mechanisms by which such sheaths form have previously been investigated by assuming a balance between inward drag force (due to inward radial motion of the fluid) and outward centrifugal form (due to rotation of the particles around the vortex). However, the strong radial inflow required to establish this balance is confined to the surface inflow layer. In the upper two thirds of the vortex core, where the sheaths are most frequently observed, the radial component of fluid motion is very weak and may be outward. In this study, an alternative approach is presented wherein the drag forces arising from radial motion of the fluid are assumed negligible. The particles are thus continuously centrifuged out of the core. It is shown for four representative profiles of the tangential velocity component of the fluid that a particle sheath will form. The time required for its formation, the location of the sheath, and its evolution in time are in agreement with the available field evidence. Also, a two-celled vortex flow field is shown to produce a two-sheath structure. However, the inner sheath is a transient feature, so it is argued that the observed patterns of multiple concentric sheaths are probably due to the combined effects of the lifting of puffs of particles aloft by the vertical motion field while at the same time the particles are centrifuged out of the core.