The ocean is a turbulent fluid that is driven by winds and by surface exchanges of heat and moisture. It is as important as the atmosphere in governing climate through heat distribution, but so little is known about the ocean that it remains a “final frontier” on the face of the Earth. Many ocean currents are truly global in extent, such as the Antarctic Circumpolar Current and the “conveyor belt” that connects the North Atlantic and North Pacific oceans by flows around the southern tips of Africa and South America. It has long been a dream of some oceanographers to supplement the very limited observational knowledge by reconstructing the currents of the world ocean from the first principles of physics on a computer. However, until very recently, the prospect of doing this was thwarted by the fact that fluctuating currents known as “mesoscale eddies” could not be explicitly included in the calculation.