We present a unified algorithm for the collisional interchange instabilities (Rayleigh-Taylor and gradient drift instabilities) occurring in the F and E regions of the equatorial ionosphere. The similar underlying mechanism of both instabilities enables us to derive the general two-dimensional continuity and potential equations. The equations are integrated numerically to study the nonlinear evolution of the polarization field (fringe field) associated with the generalized Rayleigh-Taylor instability. In particular, the effects of the fringe field into the equatorial E and transition (or valley) regions are investigated. The characteristics of the fringe field beneath the F region are investigated quantitatively for the first time. It is shown that the fringe field is capable of transporting plasma from the region where ions are highly magnetized (i.e., from the valley region). It is further shown that only under strongly driven but realistic conditions, the fringe field recognizes the part of the E region plasma where ions are marginally magnetized. The E region irregularities which are often located in such a region (near 120 km) during evening and nighttime can be effectively convected by the fringe field across the valley region and to the higher altitudes. On the other hand, because of the small ratio of ion-gyro-frequency to collision frequency below 120--115 km altitude the fringe field is unable to convect the E region irregularities lying below this region. These characteristics are important in the context of observed valley region echoes which are yet to be explained quantitatively.