The process that creates deep ocean currents is known as 1) Thermohaline Circulation.
Thermohaline circulation is driven by differences in temperature and salinity (hence "thermo" for temperature and "haline" for salinity) in ocean water, which affects its density. Cold, salty water sinks in polar regions, while warmer water rises in other areas, creating a global conveyor belt of ocean currents that circulate throughout the world's oceans.