By experiments and supporting computations we investigate two methods of transport enhancement in two-dimensional open cellular flows with inertia. First, we introduce a spatial dependence in the velocity field by periodic modulation of the shape of the wall driving the flow; this perturbs the steady-state streamlines in the direction perpendicular to the main flow. Second, we introduce a time dependence through transient acceleration–deceleration of a flat wall driving the flow; surprisingly, even though the streamline portrait changes very little during the transient, there is still significant transport enhancement. The range of Reynolds and Reynolds–Strouhal numbers studied is 7.7les Reles 46.5 and 0.52les ReSrles 12.55 in the spatially dependent mode and 12les Reles 93 and 0.26les ReSrles 5.02 in the time-dependent mode. The transport is described theoretically via lobe dynamics. For both modifications, a curve with one maximum characterizes the various transport enhancement measures when plotted as a function of the forcing frequency. A qualitative analysis suggests that the exchange first increases linearly with the forcing frequency and then decreases as 1/Sr for large frequencies.