The behavior of the geomagnetic field during polarity transitions has been studied by modelling Parker-Levy cyclonic convection cells with radial dipole sources located at the core/mantle boundary. The polarity transitions are generated by inverting the dipoles in an ever-increasing spherical cap. Initial results for observation sites at northern mid-latitudes demonstrate the dependence of the observed behavior of the geomagnetic field on the location of the center of the spherical cap. Although the modelling reproduces certain features of earlier models, it also accounts for observed phenomena not predicted by the other models. By initiating the reversal at 70¿S, 30¿W, we obtain a good fit to the available data for the Brunhes-Matuyama transition as observed at northern-latitude sites.