Planetary Vorticity vs. Coriolis

[Michael Wilkinson]

I’m trying to understand how Coriolis is positive vorticity since it always acts to the right, which seems intuitively to me that a pull to the right would contribute to negative vorticity.

I know there’s a hole in my knowledge/understanding of this concept. If the answer is long and difficult, could someone perhaps suggest a link that would help?

Below is of list of aspects of this problem that I think are correct based on many different online resources I’ve read or listened to. Please point out any mistakes I’ve made. I’m having trouble understanding how everything in the list can be correct. (Example: I don’t understand how #1 can be correct if #2 and #3 are correct.

1. Planetary Vorticity is exactly equal to Coriolis.

2. Planetary Vorticity is a function of latitude.

3. Coriolis always acts to the right (Northern Hemisphere) not only when moving N/S or S/N, but also E/W or W/E since a move to the West necessarily requires an object to slow down relative to the Earth’s rotation and a move to the East necessarily requires an object to speed up relative to the Earth’s rotation. This slowing down or speeding up exerts an apparent force that pushes the object toward a latitude which is of a smaller circumference or larger circumference respectively.

4. Coriolis (acting to the right) always contributes to an increase in Positive Vorticity.

 

[Jeff Duda]

It would help to straighten out your terminology first. Don't use the term "Coriolis" with no additional factors/words. "Coriolis" refers to a force, so say "Coriolis force". "Planetary vorticity is exactly equal to coriolis" is a confusing statement and doesn't reflect anything accurate anyway.

Planetary vorticity is vorticity caused simply by the fact that Earth rotates about its own central axis (connecting the geographical north and south poles). The magnitude of this vorticity is f = 2*omega*sin(lat), where omega ~= 7.27e-5 s-1. I believe this same factor also happens to be the factor that is applied to the wind field to determine the Coriolis force, but the actual CF magnitude is f*u or f*v, which means the Coriolis force magnitude depends on wind speed.

I think what you're really missing here is that the Coriolis force never acts alone, which you seem to be assuming. The pressure gradient force (and momentum, really just Newton's First Law of motion) are also ALWAYS acting. And when they do, they result in a situation in which the Coriolis force can act in a way such that positive vorticity can exist.

You should look up some force-body diagrams for air near a center of low pressure.

 

[Michael Wilkinson]

It would help to straighten out your terminology first. Don't use the term "Coriolis" with no additional factors/words. "Coriolis" refers to a force, so say "Coriolis force". "Planetary vorticity is exactly equal to coriolis" is a confusing statement and doesn't reflect anything accurate anyway.

Planetary vorticity is vorticity caused simply by the fact that Earth rotates about its own central axis (connecting the geographical north and south poles). The magnitude of this vorticity is f = 2*omega*sin(lat), where omega ~= 7.27e-5 s-1. I believe this same factor also happens to be the factor that is applied to the wind field to determine the Coriolis force, but the actual CF magnitude is f*u or f*v, which means the Coriolis force magnitude depends on wind speed.

I think what you're really missing here is that the Coriolis force never acts alone, which you seem to be assuming. The pressure gradient force (and momentum, really just Newton's First Law of motion) are also ALWAYS acting. And when they do, they result in a situation in which the Coriolis force can act in a way such that positive vorticity can exist.

You should look up some force-body diagrams for air near a center of low pressure.

Thank you, Jeff. I’ll be looking for force-body diagrams for air near a center of low pressure and for videos or lectures explaining the diagrams. I appreciate you providing specific advice on what to search for.

I understand that all the forces are at work all the time. I’m just trying to straighten out in my mind what each force is contributing in each situation.

Thank you also for pointing out the statement that doesn’t reflect anything accurate. That helps to put me on the right path.

 

[Michael Wilkinson]

While researching this further, I’ve stumbled upon a few Coriolis force explanations and demonstrations that seem flawed.

A demonstration is done at about the one minute mark of this video

Is that really a demonstration of the Coriolis force? The pen does not start out stationary relative to the spinning disc. The pen has no angular momentum.

This video is very similar

 

[Jeff Duda]

I think there are subtle differences between the Coriolis "effect" and the Coriolis "force". One is related to inertia, whereas the other is about conservation of angular momentum. The demonstrations in the above post are more related to the former, which the experimenter does consistently refer to as the Coriolis "effect", not "force".

 

[Michael Wilkinson]

Thank you, Jeff. I did think that the Coriolis Effect and Coriolis Force could be used interchangeably. It’s time for another study session tonight.

 

[Michael Wilkinson]

I went down a rabbit hole learning about the Foucault pendulum. I was surprised that in Paris it takes a Foulcault pendulum 31.8 hours to make a complete circle. I would have guessed 24 hours. Researching why it’s not 24 hours led to an “A-ha” moment that made me feel very stupid; but now I think I understand planetary vorticity better and I understand why planetary vorticity changes with latitude.

Now, at the risk of embarrassment, I’ll throw out my newest understanding of this subject. I’ve been unable to confirm this with anyone that knows whether it’s correct or not. So, other newbies, ignore this until someone responds with corrections: I think that I was confusing planetary vorticity and the Coriolis force because the factor applied to determine the magnitude of planetary vorticity is the same as the factor applied to the wind field to determine the Coriolis force. This factor is not indicating that “planetary vorticity” is the “Coriolis force”. Rather the factor is what it is, and is applied in both calculations because it is factoring in the Earth’s different rotational velocities at different latitudes. The factor must be used in both independent calculations since a part of the Coriolis force is determined by Earth’s rotational velocity, and also a part of the magnitude of planetary vorticity is determined by Earth’s rotational velocity.