The oceanic circulation around New Zealand is strongly controlled by the bottom topography. One consequence of this control is the influence of the circulation on the depth of the mixed layer, which results from the isopycnals tilting upwards over shallowing bottom topography. The influence is strongest on the winter depth of the mixed layer, which marks the top of the main thermocline. In some regions where the depth of the mixed layer exhibits considerable relief both alongshore and offshore, and the transit time of the water is short compared to that for the horizontal current shear to be cancelled by the vorticity input from the vertical current shear, conservation of vorticity arguments may be applied to the flow of the mixed layer. Where these criteria are met, both near East Cape and on the west coast continental shelf near the head of the Hokitika Canyon, vorticity arguments indicate that the mean current would be expected to increase shorewards.