Diapycnal mixing (across density surfaces) is an important process in the global ocean overturning circulation(1-3). Mixing in the interior of most of the ocean, however, is thought to have a magnitude just one-tenth of that required to close the global circulation by the downward mixing of less dense waters(4). Some of this deficit is made up by intense near-bottom mixing occurring in restricted 'hot-spots' associated with rough ocean-floor topography(5,6), but it is not clear whether the waters at mid-depth, 1,000 to 3,000 metres, are returned to the surface by cross-densitymixing or by along-density flows(7). Here we show that diapycnal mixing of mid-depth (similar to 1,500 metres) waters undergoes a sustained 20-fold increase as the Antarctic Circumpolar Current flows through the Drake Passage, between the southern tip of South America and Antarctica. Our results are based on an open-ocean tracer release of trifluoromethyl sulphur pentafluoride. We ascribe the increased mixing to turbulence generated by the deep-reaching Antarctic Circumpolar Current as it flows over rough bottom topography in the Drake Passage. Scaled to the entire circumpolar current, the mixing we observe is compatible with there being a southern component to the global overturning in which about 20 sverdrups (1 Sv = 10(6) m(3) s(-1)) upwell in the Southern Ocean, with cross-density mixing contributing a significant fraction (20 to 30 per cent) of this total, and the remainder upwelling along constant-density surfaces. The great majority of the diapycnal flux is the result of interaction with restricted regions of rough ocean-floor topography.