warm currents tend to be shallow, narrow curents going in any direction. Cold currents tend to be big, slow, deep currents that follow more of a path. Basically, there are more warm because they are smaller (think of a stram/brook) compared to the cold currents (like a river). Thy both move the same amount of water, but each river moves more than a brook or a stram
Well, at least on the surface. This question does not seem to consider the deep ocean cold counter currents.
However the major currents we see such as the Gulf stream are driven by the heating of water in the regions either side of the equator. As they heat they expand and the density goes down so they spread out. That looks like a flow of warm water out of a source on the surface for example in a region North of the equator. If an observer is North of this region, the source flow would be coming at the observer if the earth did not rotate. However the earth surface moves from west to east slower and slower as the flow moves north because it gets closer to the axis of rotation of earth. Therefore the flow that was North when it started relative to the earth there, is moving northeast by the time it gets to the observer because its east speed remained high while the earth surface slowed down. Similarly the flow toward the South out of the region ends up going more West. (This is the Coriolis effect) The net effect is a clockwise rotation of the warm water flow in the Northern Hemisphere.
This is a tremendous simplification but might give you an idea of what is going on. Deep down under where the water is colder and denser, the effect is different but I think this question is about the big currents we see like the Gulf Stream.
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