Simple Models of Helical Baroclinic Vortices

Abstract

Two distinct asymptotic solutions of the inviscid Boussinesq equations for a steady helical baroclinic Rankine-like vortex with pre- scribed buoyancy forcing are considered and critically compared. In both cases the relative distribution of the velocity components is the same across the vortex at all altitudes (the similarity assumption). The first 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. The second vortex solution schematises the vortex core as an inverted cone of small angular aperture. These idealised vortices are then embedded in a convectively unstable boundary layer; the resulting approximate vortex solutions have been applied to determine the maximum rotational velocity in vortices. Both models predict essentially the same dependence of the model-inferred peak rotational velocity on the swirl number (the ratio of the maximum swirl velocity to the average vertical velocity in the main vortex updraft). The helicity budget of the vortex flow is analysed in detail, where applicable.