On the Dynamics of Convective Atmospheric Vortices

Abstract

A system of simplified yet sufficiently accurate equations adequate for atmospheric convection problems is derived by expanding the flow variables in powers of two small parameters, χ and α, defined, respectively, by the percentual variance of the equivalent potential temperature and density. These equations are applied to the investigation of the dynamics of convective atmospheric vortices through the introduction of a simple model, with unstable stratification and a basic vorticity as its two essential elements; the former works as the energy source while the latter acts as an organizing agent to determine their effective radius and momentum supply. Two buoyancy-driven similarity solutions of these equations are presented, the first of which is of a two-cell type, with descending motion in the center and ascending motion in the outer part, while the second is of a one-cell type. These solutions show that the vertical velocity is proportional to the square root of the equivalent potential temperature lapse rate and increases linearly with height, while the tangential velocity is proportional to the quartic root of the lapse rate and to the momentum supply, and is nearly irrotational outside the core. When appropriate values are assigned to the physical parameters, we find good resemblance between the two-cell solution and observed distributions of flow variables in tornadoes. The influence of the lower boundary has also been analyzed. It is shown that it has a profound effect on the velocity distributions near the ground if the vortex extends to this surface.