The Gulf of Mexico has surface and deep currents. The surface currents are considered to be shallower than 500 meters. At 200 meters or less, the wind is considered to be the cause. Deeper, the relationship between the water and the Earth's rotation is involved. This is called the geostraphic or "earth turned" effect.
The deep water currents are new territory. It is known that the deep water of the Gulf of Mexico comes from the Carribean, not from the Atlantic ocean, since the Carribean islands create a barrier that has more shallow gaps than deep ones. But exploration and study is just beginning and it is intensive.
The Gulf of Mexico has a type of geostraphic current that is called the Loop Current. This current comes in at the straits of Yucatan and exits the gulf at the straits of Florida. This unique current begins with the basic clockwise flow of water in the gulf. Then there are the Yucatan and Florida currents which join in the clockwise flow to create the Loop Current. The Loop Current is a variable current that can also be called the Cuban Vortex under certain extreme conditions.
The Loop Current is an important circulatory link between the North Atlantic and South Atlantic oceans in this way: The Caribbean Current, Guiana Current and North Equatorial Currents feed the Yucatan current, then the Loop Current draws water from the Yucatan Current and is affected by the Florida current.
It is a challenge to predict or to figure out the movements and configurations of the Loop Current. It may go extreme, with some influence from changes in the Yucatan current. It may go to the North and directly to the Florida current where it develops its clockwise pattern and becoms the Cuban current. It may go as far North as the Mississippi delta or the continental shelf off of Florida.
This animated videoshows the current as it would exit through the strait of Florida. It was for an oil spill prediction, but it is an excellent example of the ways in which modeling is used to produce animated imagery of predictions that are based on a host of complex factors. Another link has an LSU animated videoof the loop current.