Subsurface ocean currents continually circulate from warm waters near the equator to the colder waters in other parts of the world. what is the reason for this?

I believe that the main cause of these currents is the differences in density of ocean water. The subsurface currents are oceanic currents that runs beneath the surface currents. They are driven by differences in the density of sea water. The density of sea water deviates in the oceans due to variations in temperature and the salinity of the water. Near the surface the sea water starts its travel deep into the ocean in the North Atlantic. 

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