The first thing to keep in mind is that ocean currents are very thin compared to the diameter of Earth. They’re only about four kilometers (13,000 feet) deep at most, and surface currents can be just a few hundred meters thick. As with gas and vapor currents on other planets, they tend to move in an east-west direction.
These currents have trouble crossing the equator, but they can. The answer for why they usually don’t involves a concept that’s relatively new in the science world. It’s a principle called potential vorticity conservation. It’s related to a very well-known concept of angular momentum conservation.
It starts with the rotation of the earth. Think of the planet as a spinning top and think of the water as columns that are no taller than the ocean depth. Water at the North Pole spins along with the planet like an ice skater. But as one moves closer to the equator, the water is less and less aligned with the spin of the planet. As one moves from the equator to the South Pole, the alignment returns, but now the spin is upside down. Thus surface currents in the Southern Hemisphere are predominantly counterclockwise and in the Northern Hemisphere they are clockwise, for the most part.
As an ocean current moves toward the equator, the angle of the water column relative to the earth's rotation changes. The water’s tendency is to compensate for that. That’s where conservation of potential vorticity comes in. The water develops vorticity or “spin.” That spin stifles north-south motion. The water that does make it to the equator often turns to flow along the equator. The part that does cross the equator trails off into swirls known as eddies.
When currents come up against boundaries, such as continents, they can overcome the forces that keep them otherwise bound to one hemisphere, but not for long. The North Brazil Current is a prominent example, where a western land boundary supports the current flowing northward from the South Atlantic to the equator. But soon after crossing the equator, it “eddies out” into gigantic swirls that are several hundred kilometers across. These rings move on northward towards the Caribbean.
– Lynne Talley, physical oceanographer, Climate, Atmospheric Sciences, and Physical Oceanography (CASPO) division