What direction do gyres flow in the northern and southern hemispheres?
In the Northern Hemisphere, to the right. In the Southern Hemisphere to the left.
So gyres are mainly caused by global wind patterns, and with the Coriolis effect, those winds that affect the water are shifted 45º to form the gyres. In the Northern hemisphere the right, or clockwise, and in the Southern Hemisphere, to the left or counterclockwise. The difference in direction is mainly due to the different wind patterns. So, you should look up a map of the global wind patterns and one of the ocean gyres to see the relationship.