# Is the movement of winds due to coriolis or centripetal force?

1. Aug 21, 2011

### Order

Is the movement of winds due to coriolis or centripetal force? Or is there no way to tell, like for example for tidal forces, there is no way to tell wether they are caused by centripetal forces or gravity. (At least that is how I have understood the problem.)

Earth is like a huge turntable with the difference that there are no centripetal forces if you are standing still (and the earth is rotating), because earth is slightly flattened towards the equator. So the gravitational forces balance out the centripetal forces, if you are standing still.

But when wind is moving east there is an extra movement in the rotational direction, so there is a force towards the equator. Now, looking from an inertial frame the force is $$F_{r}=\frac{mv^{2}}{r}=\frac{mv_{earth}^{2}}{r} + \frac{mv_{wind}^{2}}{r}+\frac{2mv_{earth}v_{wind}}{r}$$ The first term cancels to gravity. The second term is the centripetal force and the third term $2mv_{wind}\omega$ is the coriolis force. My problem is: if the coriolis force is constant and the centripetal force obviously is not constant, since the wind's speed in the east west direction changes. How comes winds are moving in circles and not in elipses?

2. Aug 21, 2011

### MrNerd

I always thought winds resulted from pressure differences in the atmosphere resulting from differences in temperature.

In spot A, the temperature is higher. In spot B, the temperature is lower. Therefore, there is a difference in temperature. A difference in temperature will also result in differences in pressure. The difference in pressure causes a flow of air from high pressure to low pressure. Thus, wind.

As a disclaimer, I don't think I've ever had any formal education in this, but I do start community college this week with meteorology(oddly enough, it's in the geography or geology class group, I don't remember which) as a class.

3. Aug 21, 2011

### BruceW

the coriolis effect is the same thing as the centrifugal force.

Low pressure systems in the north hemisphere rotate anticlockwise and low pressure systems rotate clockwise in the southern hemisphere due to the coriolis effect.

In general, the weather is explained by temperature, pressure and the rotation of the earth.

4. Aug 21, 2011

### A.T.

No, it's not. While the centrifugal force also affects objects at rest in the rotating frame of reference, the Coriolis force affects only objects that are already moving in the rotating frame. So you need something to make the air move in the first place. Coriolis force alone cannot create any wind.

5. Aug 21, 2011

### Order

Thanks for answers and good luck MN with your new class. I would like more proofs of what you are saying instead of just claims, though.

I was looking at my equation above (which is not completely correct I can tell, but still good enough for reasoning about the issue) and I can see in this equation that the coriolis term is much larger than the centripetal term, since the velocity of the wind is much smaller than the rotational speed of the earth. Is this right? If this is right, it would explain a lot.

I can see also that much of the difficulty here arises from dealing with pseudo forces. Therefore the answer to my questions might be, kind of, frame dependent. No wonder I am so confused!

6. Aug 21, 2011

### BruceW

Oh I see now. Thanks for pointing that out A.T. I got it wrong because I thought Coriolis force and Centrifugal force both meant the total fictitious force. But actually the total fictitious force equals the sum of the Centrifugal force, Coriolis force and Euler force.

In the case of the earth, the Euler force is practically zero. and the Coriolis force is:
$$-2m \Omega \times v$$
And the Centrifugal force is:
$$-m \Omega \times ( \Omega \times x)$$

where omega is the vector angular frequency of the earth, and the velocity and position are of some object with respect to the rotating reference frame.
So if we consider an air parcel which is stationary with respect to the rotating earth, then the Coriolis force on it is equal to zero, as A.T. said.

7. Aug 21, 2011

### rcgldr

8. Aug 21, 2011

### RedX

I'm pretty confused by the post - I think you might have a lot of misconceptions.

First, tidal forces have nothing to do with centripetal acceleration. Tidal forces are due to gravity.

Second, if you're standing still on the earth, unless you're at the poles, there is a centripetal force on you.

Third, the reason your equation says the wind moves in circles is because you wrote it that way: at the very beginning you said assume the wind blows from the west to the east, so of course you'll get that they move in circles from west to east. I'm also not sure how you can say that the Coriolis force is obviously constant and the centripetal force is not.

Here is a picture of global surface winds, taken from the reference frame of a stationary observer fixed to the earth:

http://www.colorado.edu/geography/blanken/GEOG 6181 Fall 2003/noble/images/06_tradewind_1.jpg

The earth is hotter at the equator, causing warm air to rise high in the air where it's at greater pressure than colder air at the same height, so the warm air moves north and south of the equator where it cools down and sinks at 30 degrees latitude. The air here is now high pressure at the surface, so winds flow back towards the equator on the surface of the earth but due to the Coriolis force (which pushes things right in the Northern hemisphere and left in the Southern hemisphere) it gets bent westward. These are the trade winds. Similarly, above 30 degrees you have the Westerlies until you reach the polar front (when the cold air drops at 30 degrees, it can flow north or south, so if it flows north in the northern hemisphere the coriolis force pushes it east).

9. Aug 22, 2011

### chrisbaird

I simplified way of thinking about it is that in general local winds are caused by temperature/pressure differences and global winds are caused by the Coriolis force. I don't think the centrifugal force has much effect on winds since it applies equally outwards at all points and essentially just weakens the effect of gravity.

10. Aug 22, 2011

### chrisbaird

By the way, you have to be careful to define what frame you are in. If your frame is a stationary spot in space, watching the earth spin, then there is no coriolis force or centrifugal force. The global winds are described directly by the rotation of the earth. There is only gravity which is a centripetal force holding everything in orbit and your inertia. If your frame of reference is fixed to the surface of earth, so that you are rotating with the earth, but from your frame you do not appear to be rotating. The rotational effects are then treated as fictitious forces: The coriolis force and the centrifugal force. So, to use "coriolis force" and "centripetal force" in the same sentence is to confuse together the two different frames.

11. Aug 22, 2011

### A.T.

Really? What does "outwards" mean?

12. Aug 22, 2011

### Staff: Mentor

No, that is not correct. As said previously, temperature and density/pressure variations cause the winds to blow. The coriolis force only affects the direction in which they blow.

13. Aug 22, 2011

### olivermsun

But of course motions (the winds) are caused by forces (pressure gradients)!

I wonder if the OP is asking in a sense if and how the winds as we know them are governed by the Coriolis force.

14. Aug 22, 2011

### K^2

Earth surface is a (nearly) equipotential surface. Since centrifugal effect merely adds to effective potential, it makes no contribution to the weather.

The two forces that give you weather are the pressure gradients and Coriolis force.

15. Aug 22, 2011

### Order

Yes, that is enlightening. Good explanation.

Thinking about it, I think I really meant centrifugal force (rotation of the earth) and not centripetal force (gravity).

16. Aug 22, 2011

### Order

Thanks for a good post.
Sure I have a lot of misconceptions since I have never studied this seriously.
Maybe I should start a new post just about this then.
Oh, I thought this was exactly balanced by gravity. I better watch out when I am going outside then; I might fall down to the equator. Right? Or all the air might go from where I live and down to Africa. Then it will be really hard to breath. Right? I am just surprised, that’s all.
But look at the equations that Bruce posted. To begin with the coriolis effect is given by $$-2m \Omega \times v$$ Here $\Omega$ is perpendicular to v no matter how v moves so it is always constant. Now look at the equation for centrifugal force $$-m \Omega \times ( \Omega \times x)$$ Here $\Omega$ will be larger when something is moving in east west direction than if it is moving in north south direction. The north south components of the equation cancels out effectively as far as I can see.
Obviously it is a lot more complicated than I thought. Unfortunately I dont have time to study meteorology in depth. But it is good to know a little bit about it. Good thing you posted me this.

17. Aug 22, 2011

### Order

Obviously the Coriolis force does not make the wind move from rest. But just to be clear, my original question was due to the fact that in popular explanations of the global winds one says that centrifugal forces causes wind to bend, which confused me a lot. The consensus on this forum seems to be that this is wrong and that the coriolis effect alone is the cause.

18. Aug 22, 2011

### olivermsun

I guess the way it's being discussed is kind of funny anyhow. If you look at the equations of motion in the rotating (earth) frame, there aren't special terms which distinguish between Coriolis and centrifugal forces. As one earlier posted pointed out, the earth is close to an equipotential surface, so our "up" which is perpendicular to the ground happens to point the opposite way from the sum gravity + centrifugal (which is outward from the axis of rotation, not the center of the earth!). Therefore, winds which blow along "horizontal" (equipotential surfaces) aren't affected by centrifugal forces, and only Coriolis is left.

But this sounds like a bit of a definitional trick, right? I mean, suppose the wind starts blowing "poleward" from the equator. It pretty much has to bend to stay with the curve of the earth, right? And that curve is essentially defined by gravity + centrifugal...

But yes, if you are talking about "horizontal" cyclonic motions around around an axis sticking straight out of the earth (wherever you happen to be), then that's Coriolis.

19. Aug 22, 2011

### MrNerd

Alright, I've got my book here now, Essentials of Meteorology, 5th edition. It says, and I quote:

"An object will always accelerate in the direction of the total force acting on it. Therefore, to determine in which direction the wind will blow, we must identify and examine all of the forces that affect the horizontal movement of air. These forces include:
1. pressure gradient force
2. Coriolis force
3. centripetal force(not centrifugal, which is technically imaginary and outward. Centripetal means inward, thus causing the rotation. The outward illusion results from the tendency of you to keep forward, but the object accelerating you directionwise is pushing in on you, thus you push out, thus the illusion of an outward force)
4. friction"
the centrifugal/petal thing was me, not the book, by the way.
Pressuse gradient force is given by (difference in pressure)/distance(essentially the second law of thermodynamics, high to low)
The Coriolis Force/Effect results from the Earth's rotation, also only affecting direction, never speed.
The centripetal force is involved in spinning winds, such as tornadoes and hurricanes.
Friction is self-explanatory(I assume), it slows down the winds(presumably).

20. Aug 22, 2011

### RedX

For some information on tides, here's a website:

http://www.lhup.edu/~dsimanek/scenario/tides.htm

For some mathematical detail (just algebra):

http://mb-soft.com/public/tides.html

You only need gravity to explain the tides.

Omega is a constant, equal to the angular velocity of the earth. In those two equations, you plug in different x and v to calculate the centrifugal and coriolis force, but omega is fixed at the angular velocity of the earth.

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