Hi,
I have often wondered why a flat belt will stay on a convex pulley, and don’t remember ever seeing a reason why. I once was asked why by a visitor to a steam engine museum, who thought I looked knowledgeable!
Thinking about it, I wonder if it is because the linear speed (feet per minute) is slightly higher at the crown of the pulley, and this creates friction between belt and pulley in a direction towards the faster movement. As this happens on both sides of the belt towards the centre, it will tend to stay at the crown of the pulley.
This happens in fluids at the junction between two bodies of fluid, where a stream joins a river, for instance. The faster or more massive body drags the smaller along with it, creating turbulence. In a belt drive this will warm up the belt and pulley slightly, as well as will the overall friction between belt and pulley, as there isn’t 100% power transfer.
Alternatively, see film of the Great Red Spot on Jupiter and how it is affected by the adjacent bands of cloud.
Regards
Geoff