Abstract

Two distinct asymptotic solutions of inviscid Boussinesq equations for a steady helical baroclinic Rankine-like vortex with prescribed buoyant 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 schematizes the vortex core as an inverted cone of small angular aperture. These idealized 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 local swirl ratio (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 analyzed in detail, where applicable.