Part of the driving force is probably their fast rotation. Both planets are about four times the diameter of Earth, but spin on their axis in 16 (Neptune) to 17 (Uranus) hours, which generates huge Coriolis forces along bands parallel to their equators. The winds on Neptune are the strongest in the Solar System, reaching up to 2,100 kilometres (1,305 miles) per hour, and those on Uranus are similarly fierce, but these are the two farthest planets from the Sun, and so receive the least heat to drive weather. In addition, Neptune seems to have some powerful internal energy source that helps power its winds – one idea is that this may come from liquid methane condensing to form diamonds around the planet’s core.
Answered by Giles Sparrow.