In the Southern Ocean, nutrient-rich North Atlantic Deep Water upwells to the surface, and the northward surface water sinks at mid-depth (as Subantarctic Mode Water and Antarctic Intermediate Water) and transports nutrients into the low-latitude thermocline. According to a recent article appeared in Science, climate model simulations under RCP 8.5 scenario project that the Antarctic sea-ice will completely disappear after 2100 increasing primary productivity in the Southern Ocean. As a result, nutrients will be trapped in the Southern Ocean, which will drive a global net transfer of nutrients to the deep ocean. This in turn drives steady declines in primary production outside the Southern Ocean.
Moore, J. K. et al. 2018: Sustained climate warming drives declining marine biological productivity. Science, 359, 1139-1143. doi:10.1126/science.aao6379.