A coupled magnetospheric-ionospheric (M-I) MHD model has been used to simulate the formation of Sun-aligned polar cap arcs for a variety of interplanetary magnetic field (IMF) dependent polar cap convection fields. The formation process involves launching an Alfvén shear wave from the magnetosphere to the ionosphere where the ionospheric conductance can react self-consistently to changes in the upward currents. We assume that the initial Alfvén shear wave is the result of solar wind-magnetosphere interactions. The simulations show how the E region density is affected by the changes in the electron precipitation that are associated with the upward currents. These changes in conductance lead to both a modified Alfvén wave reflection at the ionosphere and the generation of secondary Alfvén waves in the ionosphere. The ensuing bouncing of the Alfvén waves between the ionosphere and magnetosphere is followed until an asymptotic solution is obtained. At the magnetosphere the Alfvén waves reflect at a fixed boundary. The coupled M-I Sun-aligned polar cap arc model of Zhu et al. (1993a) is used to carry out the simulations. This study focuses on the dependence of the polar cap arc formation on the background (global) convection pattern. Since the polar cap arcs occur for northward and strong By IMF conditions, a variety of background convection patterns can exist when the arcs are present. The study shows that polar cap arcs can be formed for all these convection patterns; however, the arc features are dramatically different for the different patterns. For weak sunward convection a relatively confined single pair of current sheets is associated with the imposed Alfvén shear wave structure. However, when the electric field exceeds a threshold, the arc structure intensifies, and the conductance increases as does the local Joule heating rate. These increases are faster than a linear dependence on the background electric field strength. Furthermore, above the threshold, the single current sheet pair splits into multiple current sheet pairs. For the fixed initial ionospheric and magnetospheric conditions used in this study, the separation distance between the current pairs was found to be almost independent of the background electric field strength. For either three-cell or distorted two-cell background convection patterns the arc formation favored the positive By case in the northern hemisphere.