It's a good question, EnumaElish... Uranus’ lower atmosphere (troposphere) consists of layered clouds: methane, ammonia, ammonium hydrosulfide, and water. They are stacked on top of each other because each chemical composition keeps them to a specific altitude.
I imaged them to looking similar to lenticular clouds on Earth where the ‘pancake stacking’ (nice analogy BTW) would emerge due to the slight convection currents in the planet’s interior... a sort of tumbling energy that would push up an array of lens’ shaped caps across the cloud decks... no doubt about it that it is ‘artistic license’ at its most severe but at least there are some loosely jumbled facts supporting the idea.
Really, very little is known about the interior of Uranian Atmosphere so for now it’s all educated visualization.
Might I digress... Uranus is my least favourite planet, and if it wasn’t for its awkward name, it would probably be the first planet we’d forget about. Frankly, it doesn’t have much going for it, sure it lies on its side but what else does it do? it’s a drearily coloured, featureless ball that is flanked by other gas giants that have much more obvious charisma.
So from an artist’s point of view, Uranus is definitely the last-on-the-list of planets to paint. Which begs the question, why do it? What started out as a casual challenge turned into a mission to alleviate Uranus of its identity crisis... at least from my perspective, but perhaps for others as well... at least enough anyway to have people stop and give it just a smidgeon more consideration. I think it worked.