A simple model of dry convective helical vortices (with applications to the atmospheric dust devil)

An asymptotic solution of inviscid Boussinesq equations for a 'dry convective Rankine vortex' with prescribed buoyant forcing is given. The obtained vortex solution demonstrates monotonic growth with height of the vortex core radius, which becomes infinite at a certain critical altitude, and the corresponding attenuation of the vertical vorticity. This idealized vortex is then embedded in a convectively unstable boundary layer; the resulting approximate vortex solution has been applied to determine the maximum rotational wind speed and diameter of dry convective dust-devil-like vortices.