How does the rotation change the thermal convection? Let's make a simple experiment.
We will put water into a donut-shaped container, which will be the earth's atmosphere. We'll heat the outer edge of the container, and cool the inner edge, so the inner edge will be the poles, and the outer edge will be the equator.
Because warm water is light, and cold water is heavy, this difference makes
a pressure gradient between the inner and outer edges.
If the earth wasn't rotating, this pressure gradient pushes the cold water under the lighter warm water, causing a convective current.