During southward By periods the open field line region in the ionosphere (polar cap) expands due to increased dayside merging. Ionospheric plasma flow patterns result which can be classified by the sign of the interplanetary magnetic field (IMF) By component. In this paper we construct a time-dependent ionospheric convection model to simulate these flows. The model consists of a spiral boundary with a gap in it. The sign of the IMF By component determines the geometry of the gap. A potential is applied across the gap and distributed around the boundary. A flow results which enters the polar cap through the gap and uniformly pushes the boundary outward. Results of the model show that By effects are greatest near the gap and virtually unnoticeable on the nightside of the polar cap. Adding a day-night ionospheric conductivity gradient concentrates the polar cap electric field toward dawn. The resulting flow curvature gives a sunward component that is independent of By. These patterns are shown to be consistent with published observations. ¿ American Geophysical Union 1987