What would currents look like if there were no continents? Explain.

If there were no continents, these surface currents would travel all the way around the Earth, parallel to the equator ... Since these currents come from the equator, they are warm water currents, bringing warm water to the higher latitudes and distributing heat throughout the ocean.

My current project doesn't have any land to break up the equator currents formed by the Coriolis effect. This creates a cool waterway for international travel and trade but I'm not sure what the effect on the rest of the ocean would be. If anyone has any theorizes and wants to explain, I would be greatly appreciative.