The space and time scales over which wind forcing can directly drive flows over regions of closed topographic contours are explored using an idealized numerical model and theory. It is shown that stratification limits the vertical scale of the mean flow but also results in an enhanced recirculation strength in shallow water by distorting the isopycnals in the bottom boundary layer. Time-dependent forcing can drive flows that extend deeper than the mean flow because the initial response is primarily barotropic. This response is limited at low frequencies by baroclinic Rossby wave propagation. It is expected that these wind-driven flows might be important in the vicinity of islands and over large-scale topographic features.