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Coriolis effect and base forces

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I wonder if anybody can point me to a good explication of the atmospheric Coriolis effect broken down into base forces. Most of the explanations I've seen are problematic, even flawed as far as I can tell, and they rarely talk about force vectors.

I've seen demonstrations, for instance a popular one is throwing a ball on a child's merry-go-round. I could be wrong, but I think this is absolutely an incorrect demonstration of the atmospheric Coriolis effect. It merely demonstrates differences in reference frames, which I believe is what the original mathematics of the Coriolis effect is about.

Why h20 aggregates and starts to rotate in the Earth's atmosphere is a very complex phenomenon as far as I can tell. There's a radial convection force for pushing hot air from the equator towards the colder polls, that definitely happens. Why it starts to rotate is another issue, I think.

I've read that rotating objects don't create rotating gravitational fields, so the idea that a rotating Earth could provide any force on air/water molecules seems dubious to me, but like I said I could be wrong. How does the Earth's rotation create any force at all on atmospheric molecules? Friction? Perhaps the curvature of the Earth plays a role?

Convection seems to be a very complex phenom. Can anybody point me to some good theory about predicting convection behavior?

I have this pet theory that warmer atmospheric temperatures make organized convection less probable, but when it does happen it becomes more violent. It would explain why we seem to have fewer, but more violent storms nowadays. Don't want to start a war about whether climate change is man made or not, just trying to understand Coriolis effect and atmospheric convection.

Thanks.

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