As an amateur trying to wrap my head around the fluid dynamics of the atmosphere. That the atmosphere is rotating with the earth is obvious as a general concept. But barring the localized effects like jet streams, is the atmosphere rotating at the same angular velocity as the ground directly below?

In that case, the higher up you go, the higher the velocity of air. And the farther you move from equator the slower the velocity. So it would seem that there is a lot of relative motion. Is there a modal or animation that shows a solid ball moving in a viscous fluid leading to this patter of fluid movement? Note that I am not questioning the rotation. Just trying to understand it’s exact mathematical and physical properties.