I Conceptual question about the Coriolis force and the weather

[A.T.]

If the inertial observer sees those trajectories being deflected, could you spell out exactly why this is?

Even without any wind the trajectories are curved in the inertial frame, because the air masses rotate with the Earth.

Somehow I'm misidentifying "how the hurricane looks like" with "the particle trajectories upon which forces act", i.e. what "looks" exactly means.

The visible cloud formations do not align with the trajectories of the air in the inertial frame, because the rotation of the whole atmosphere is part of the motion in the inertial frame.

As I pointed out in post #12, "what stuff looks like to humans" is a different matter from what the trajectories actually are. You have to decide if you want to discuss physics or human perception of relative motions.

 

[jartsa]

1: A guy on roller blades jumps off a moving train, then rolls on the platform, there was no real force that pushed the guy to high speed relative to the platform.

2: A guy on roller blades is skating at high speed towards the front of an accelerating train, then he starts free-rolling, his speed relative to the train starts decreasing without any real force pushing him backwards.

Now 1 and 2 both at the same time: A guy on roller blades is skating at high speed towards a point near the center of an large spinning carousel, then he starts free-rolling, his speed towards the center is decreasing without any real force, and he starts gaining sideways speed without any real force pushing him.

Actually in the last scenario the guy should sit on a shopping cart, which some assistants push towards a point near the center of the carousel, because shopping carts move freely to all directions, unlike roller blades. Originally the cart moves with the point on the carousel floor that is below the cart.And the next step is that there are many shopping carts that are thrown towards one point on the carousel. And then the carts stick together. If the carousel is spinning, then originally the fleet of carts has angular momentum in all inertial frames. As there are no forces on the carts, the angular momentum stays constant, so the final heap of carts spins around.

If the carousel is ridiculously large, then it might happen that before being pushed together the people sitting in the carts are not aware of any spinning.(I don't know how angular momentum works in rotating frames... If an ice skater standing on the north pole with extended arms pulls his arms next to his body, he starts spinning. Oh yes, it was the Coriolis force that caused that. Then the skater spins around because of the angular momentum that the Coriolis force gave him. He must resist the Coriolis force that is trying to pull his hands away from his body.)

 

[LURCH]

I think the carousel analogy works pretty well; it only fails because the air in the hurricane is not being thrown clear across the carousel, but drawn toward a point part way between the edge and the center. If you make the Earth the carousel , and look at it from the top (the North Pole), you see that, on a very still day, the air near the pole is moving eastward very slowly, while air near the equator is rushing toward the Eastern horizon at about 1,000 mph.

Now, if a huge low pressure area forms right at the 45th parallel, air from the equator will rush northward, while air from the pole rushes south. As the air from the north keeps moving south, it has almost no eastward movement, and so it will miss the target (the center of the low pressure area) by being too far west. From your external perspective, you would see the low pressure area moving to the east at about 700 mph, while the air from the North only moves eastward very slowly.

If inertia were the only factor, the polar blast would miss the low pressure center by being too far west, and proceed toward the equator, like the ball on the carousel. But, the main force making the air move is the low pressure area, drawing that air toward itself. Each particle of air is like a guided missile, tracking that low pressure center. As the center moves off to the East, the air particle turns its nose and bends its course Eastward in a constant attempt to keep moving straight towards it.

Similarly, air from the south is moving eastward way too fast as it comes North, so it also goes into a hard left turn to try to get to that low pressure area.

 

[FactChecker]

If inertia were the only factor, the polar blast would miss the low pressure center by being too far west, and proceed toward the equator, like the ball on the carousel. But, the main force making the air move is the low-pressure area, drawing that air toward itself.

I think this addresses the main misconception of the OP. Whereas the Coriolus "force" provides the "acceleration" that would appear unaccelerated in an inertial frame, the attraction toward the low pressure (moving with the Earth's rotation) gives it the spin of a hurricane. The spin is clearly visible to an observer in an inertial frame.

(Also the interaction with the air drawn to the low pressure from the other direction turns the "accelerations" into a rotation on a completely different axis.)

 

[haushofer]

I think the carousel analogy works pretty well; it only fails because the air in the hurricane is not being thrown clear across the carousel, but drawn toward a point part way between the edge and the center. If you make the Earth the carousel , and look at it from the top (the North Pole), you see that, on a very still day, the air near the pole is moving eastward very slowly, while air near the equator is rushing toward the Eastern horizon at about 1,000 mph.

Now, if a huge low pressure area forms right at the 45th parallel, air from the equator will rush northward, while air from the pole rushes south. As the air from the north keeps moving south, it has almost no eastward movement, and so it will miss the target (the center of the low pressure area) by being too far west. From your external perspective, you would see the low pressure area moving to the east at about 700 mph, while the air from the North only moves eastward very slowly.

If inertia were the only factor, the polar blast would miss the low pressure center by being too far west, and proceed toward the equator, like the ball on the carousel. But, the main force making the air move is the low pressure area, drawing that air toward itself. Each particle of air is like a guided missile, tracking that low pressure center. As the center moves off to the East, the air particle turns its nose and bends its course Eastward in a constant attempt to keep moving straight towards it.

Similarly, air from the south is moving eastward way too fast as it comes North, so it also goes into a hard left turn to try to get to that low pressure area.

Yes, this makes sense. The ball at the carousel does not experience any force; once released, it has a fixed velocity (in magnitude and direction) as observed by the inertial observer. But pressure areas of course rotate along with the Earth due to gravity and friction, and hence your "guided missile effect". But then I'd say the rotation of these hurricanes is not mainly due to the Coriolis-effect, but due to the dragged-along pressure areas.

By the way, in my experience a lot of these videos and analogies of carousels also don't mention that they neglect the friction between the disc and ball, and that the centrifugal force outsizes the Coriolis force in realistic cases. So I guess I'm holding too much onto the analogy anyway :P

 

[haushofer]

Even without any wind the trajectories are curved in the inertial frame, because the air masses rotate with the Earth.

Yes, I'm being too sloppy here. I understand that these trajectories are curved because they follow Earth's surface. What I meant was curved with respect to Earth's surface, as one views sattelite photo's (to make it even more obvious, approximate the Earth's surface as being flat, i.e. with its tangent space). But I guess that doesn't really make sense, now I think about it.

As I pointed out in post #12, "what stuff looks like to humans" is a different matter from what the trajectories actually are. You have to decide if you want to discuss physics or human perception of relative motions.

Well, the latter one, but I guess the exact distinction between the two in this particular case is one of my misunderstandings.

 

[haushofer]

By the way, I've always had this kind of confusions, also in discussion about the precise relation between passive and active coordinate transformations in General Relativity, the exact meaning of Lie derivatives, etc. It's sort of my running confusion in my life as a physicist. Everytime I think I have it figured out in one case, I can't reconcile it with the other one. It's a kind of mental relativistic ping-pong :P

So whatever my understanding will be in the end, thanks a lot for all the replies, really appreciated. I'm glad there is a PhysicsForums where I can spit out my confusion without people become annoyed (visibly) ;)

 

[A.T.]

...What I meant was curved with respect to Earth's surface...

You were asking about the trajectories in the inertial frame. The Earth's surface is rotating.

, as one views sattelite photo's.

Static images do not show movement.

 

[A.T.]

Let's make a comparison to the Foucault pendulum

Compare it to an invisible pendulum, that leaves visible traces on the rotating ground below it.

In the inertial frame the invisible pendulum is not deflected, but an inertial human observer who sees only the curved traces on the rotating ground will have a hard time identifying the actual motion in the inertial frame. Especially if he just looks at a static picture, as you do with the satellite image of a hurricane.

See this video at the very end, when the pendulum is hidden:



This might be part of you confusion, the other part is that fluid dynamics is more complex than a pendulum and the air masses have more forces acting on them.

 

[haushofer]

Compare it to an invisible pendulum, that leaves visible traces on the rotating ground below it.

In the inertial frame the invisible pendulum is not deflected, but an inertial human observer who sees only the curved traces on the rotating ground will have a hard time identifying the actual motion in the inertial frame. Especially if he just looks at a static picture, as you do with the satellite image of a hurricane.

See this video at the very end, when the pendulum is hidden:



This might be part of you confusion, the other part is that fluid dynamics is more complex than a pendulum and the air masses have more forces acting on them.

I think that might be it, indeed. It will take some time for me to digest, but many thanks for your efforts.