A three-dimensional, time-dependent, fluid model was used to investigate the velocity structure of the global ionosphere--polar wind system. Each simulation involved following a large number of high-latitude flux tubes (over 1000) as they moved under the influence of convection and corotational electric fields. A flux tube typically traversed various high-latitude regions during the course of a simulation, including the subauroral ionosphere, dayside and nightside auroral ovals, and polar cap. Heating due to auroral electron precipitation was included in the simulations, but nonclassical heating mechanisms at high altitudes, such as wave-particle interactions, were not. The model results show the variation of H+ and O+ drift velocities with respect to magnetic latitude and longitude over the northern polar region, as well as variations with altitude and universal time (UT). A simulated geomagnetic storm of moderate intensity was introduced at a particular UT, and the effect of variable geomagnetic activity levels on the two major ion species was studied. Equivalent simulations were performed for four geophysical cases, corresponding to summer and winter solstices at both solar maximum and minimum. These simulations reveal the seasonal and solar cycle dependence of the ion velocities for both quiet and geomagnetically active times. The H+ and O+ populations responded to the varying geophysical conditions in dramatically different ways. These responses provide insight into the role played by the polar wind in the larger and inclusive system of fields and plasmas referred to as the Sun-Earth connection. The self-consistent high-resolution results obtained here reveal structure in the polar wind that cannot be resolved by simpler studies using velocity profiles based on averaged experimental data. The results of this investigation were compared with those of relevant observational studies.