Recent observations by the Dynamics Explorer 1 satellite over the dayside polar cap magnetosphere have indicated downward flows of heavy ions (O+, O++, N+, N++) with flow velocities of the order 1 km/s (Lockwood et al., 1985b). These downward flows were interpreted as the result of ''parabolic'' flow of these heavy ionospheric ions from a source region associated with the polar cleft topside ionosphere. Here we utilize a two-dimensional kinetic model to elicit features of the transport of very low energy O+ ions from the cleft ionosphere. Bulk parameter (density, flux, thermal energies, etc.) distributions in the noon-midnight meridian plane illustrate the effects of varying convection electric fields and source energies. The results illustrate that particularly under conditions of weak convection electric fields and weak ion heating in the cleft region, much of the intermediate altitude polar cap magnetosphere may be populated by downward flowing heavy ions. It is further shown how two-dimensional transport effects may alter the characteristic vertical profiles of densities and fluxes from ordinary profiles computed in one-dimensional steady state models.