The predominantly low-chlorophyll conditions of the Southern Ocean are punctuated by regions of elevated phytoplankton biomass, including a bloom in the Antarctic Circumpolar Current (ACC) that extends for 1000 km downstream of the Kerguelen-Heard islands. Summer-time studies have demonstrated that iron from the islands and intervening shallow plateau (300–600 m) fuels localized production. Whether this supply, or alternatively iron brought to the surface by enhanced mixing in ACC eddies, drives the more extensive downstream bloom has not been addressed. We show that the extent and shape of the downstream bloom can be reproduced by simulating the winter-time spread of a slowly-decaying tracer (iron) from the islands and plateau using a satellite-altimetry based advection scheme. This suggests that mesoscale activity in the ACC plays a minor role in generating the enhanced biomass and emphasizes the importance of shallow bathymetry, large-scale advection, and winter-time observations in understanding the productivity of the Southern Ocean.