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 7.7[les ]Re[les ]46.5 and 0.52[les ]ReSr[les ]12.55 in the spatially dependent mode and 12[les ]Re[les ]93 and 0.26[les ]ReSr[les ]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.