Coriolis effect and base forces

[Jamal26]

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.

 

[dauto]

Turns out that the difference in reference frames as illustrated by child's merry-go-round that you dismissed off hand is the correct explanation.

 

[Jamal26]

I didn't dismiss anything. Maybe you can explain a little more. For instance what are the 2 frames, and how do they contribute to actual physical aggregation & rotation of atmospheric molecules?

 

[D H]

You don't care. The coriolis effect is an essential part of the dynamics when you use a rotating frame of reference. If you want to describe the dynamics of a planetary atmosphere from the perspective of an inertial (non-rotating) frame where there is no coriolis effect, good luck. Conceptually, there's no problem with this. In practice, it is so ridiculously impractical that nobody does this.

 

[dauto]

I didn't dismiss anything. Maybe you can explain a little more. For instance what are the 2 frames, and how do they contribute to actual physical aggregation & rotation of atmospheric molecules?

The Earth is the merry-go-round. If you're outside of the Earth looking at it spin, than there is no Coriolis. But if you're spinning along with the Earth than the Coriolis must be included because you're using a non-inertial (accelerated) reference frame.

 

[Jamal26]

Thanks for all of your replies. I have some things to say about them, but I want to generate some diagrams that will take a bit of time first.

I want to raise an issue on the question of computational impracticability that D H brings up. There are a lot of references to the concept of the Navier-Stokes equation being "chaotic," i.e. that solutions to it are extremely sensitive to initial conditions. Does anybody have any links to this being demonstrated mathematically?

Steven Wolfram discusses the issue a bit here where he talks about where randomness comes from in modeling mathematical systems.

http://www.wolframscience.com/reference/notes/997b

I really don't know enough about what Wolfram means by "intrinsic randomness" to know what he's talking about. Does he mean the equations generate randomness that can't be explained by initial conditions? Or does he mean that there is natural, perhaps quantum mechanical, randomness generation that can't be modeled?

 

[D H]

I didn't dismiss anything. Maybe you can explain a little more. For instance what are the 2 frames, and how do they contribute to actual physical aggregation & rotation of atmospheric molecules?

You are thinking that the fictitious forces represent something real, something that can be attributed to one of the four fundamental interactions (gravitation, electromagnetism, the weak interaction, or the strong interaction). They don't. They are fictitious, hence the name. You have two choices when you look at physics from the perspective of a non-inertial frame: (1) don't do that, or (2) use fictitious forces.

Option #1 says that strictly speaking, Newtonian mechanics is only valid in an inertial frame of reference. An object that isn't subject to any external forces does not remain stationary or move along a straight line when observed from the perspective of an accelerating or rotating frame of reference. If you want to use F=ma you should be describing behavior from the perspective of an inertial frame of reference.

Option #2 says that option #1 is a non-starter. There are a number of applications where describing behavior from the perspective of an inertial frame doesn't make sense from a practical point of view. The mathematics behind those fictitious forces is perfectly valid. With them, one can indeed describe behavior from the perspective of an accelerating and/or rotating frame of reference.

You seem to be thinking that those fictitious forces have to be traceable to something real (your opening post). They aren't. They're traceable to the fact that we have intentionally decided to model behaviors such as weather from the perspective of a non-inertial frame.