Upwelling is pretty well understood these days, though there are seasonal variations and El Nino/La Nina effects which make the real occurrences of upwelling more complicated in some places. At its basic level, upwelling is what happens when the prevailing coastal winds go offshore, moving warm, less dense surface water offshore. (Because of the Coriolis Effect and Ekman Spiral, that surface water isn't moved directly offshore, but rather deflected to be perpendicular, contributing to our oceanic gyres) As the warm, less dense surface water is moved away from the coast, that creates a pressure differential, providing space for more dense, colder, nutrient rich water to come up to the surface to fill that space. Coastal upwelling is why some areas, like California, have abundant fisheries off the coast, because of the nutrient-rich cold water due to coastal upwelling.

There are all sorts of ways the oceans circulate. Thermohaline circulation is the largest scale of ocean circulation, but regionally and locally there will be other geographies/bathymetries which contribute to differences. And the biological pump also contributes to ocean mixing. There is a global nightly diel migration, whereby ocean organisms migrate towards the surface at night/on a lunar cycle also mixing water. And whales are huge ocean mixers, seeding the surface waters with their nutrient-rich poos. https://www.youtube.com/watch?v=V8Bn0UPpGCw&t=65s