If the Earth's atmopsphere spins with the earth due to friction, why is there no horizontal spiralling drag?

Imagine a bucket of paint with a spinning ball in it. The paint would form a spiral and would not all move in synchronous movement with the ball. To clairfy - In order for the Earth's atmosphere to appear to us to be still (as on a windless day) the upper atmosphere must be moving faster than the lower atmosphere - as it the case with any rotating spehere - the outer layers are moving faster than the inner layers. What force is causing the upper atmosphere to move faster than the lower atmosphere? If the atmosphere is being rotated soley by friction, then at best the upper layers would move at the same speed as the lower layers, thereby causing a spiralling effect. We do not see this effect. Why?

I'm not entirely clear on what you mean exactly, but I have a feeling you are unclear on the idea of a rotational and irrotational vortex.

Using your paint bucket analogy, there are two effects that create a rotational vortex. The spinning ball will drag fluid along with it. But because there is an outer wall to the bucket, viscosity requires that velocity to be zero. In a 2D sense, you are looking at a cylinder rotating within another. This is known as Taylor Couette flow. Also, notice that the TC flow sets up cellular structures due to the rotation -- this is the same kind of effect you see in my answer to your other question about bands forming in the atmosphere.

Essentially, because the outer boundary does not rotate at all (or if it did rotate but at a different angular velocity), you get that spiral effect because the tangential velocity is inversely related to radius.

If your bucket were free to spin with the ball inside (so imagine your paint bucket is suspended in the air with a paddle in the middle attached to a motor so it spins), the outer wall of the bucket will begin to accelerate. During this acceleration, you have a rotational flow between the inner paddle and the outer wall. Eventually, over a long time, the outer edge of the bucket would spin at the same speed as the paddle and you wouldn't see any spiral pattern. The flow becomes irrotational -- it is a rigid body rotation. Here, the tangential velocity is directly proportional to the radius.

Now back to the Earth. First, the Earth doesn't have an outer "bucket" edge to create viscous drag and cause a rotational flow. Secondly, the Earth has been spinning for awhile. Long enough that the viscous effects have made the atmosphere "drag along" with the body all the way through to the outer edge. Obviously there are way, way more complicated effects that make the atmosphere have variable speeds at different times. But for the most part, you don't see a lagging behind in the upper atmosphere like you would see in your paint bucket analogy. And you wouldn't see that lagging in your paint bucket if the entire bucket were allowed to spin and enough time elapsed for the viscous forces to do their work.

You can see good examples in these lecture notes and the associated video on YouTube dealing with rotational flows. And there are better examples of rotational and irrotational vortices in the lecture notes and video on YouTube for vorticity.

Also, you should take some time to go through all of the National Committee for Fluid Mechanics films and lecture notes. They do a great job of explaining and demonstrating the physics.

• You have stated that the outer edge of the bucket would eventually go the same speed as the inner paddle, therefore you must be agreeing that a spiralling effect would occur. In order for the outer edge of the bucket to remain at all times parrallel with the inner circle it would have to move faster! (in fact each layer would have to move at different speeds in order for it to appear still). What explaination is there for the outer atmosphere moving faster than the lower atmosphere? Mar 18 '15 at 9:24

If i interpreted your question correctly and based on my knowledge (i don't know how good it is). This is because there is nothing to apply frictional force on the outer edge of the earth's atmosphere, whereas in case of bucket the water rubs against the boundaries of the bucket which slows down the outer part of the spinning water (dont look at it for long you will be hypnotized)

• This does not answer the question Mar 21 '15 at 10:43
• how .. can you explain a bit Mar 28 '15 at 13:46

The same happens with the air around the earth, this phenomenon is called the Coriolis effect, and it affects our atmosphere. You also have to keep in mind that there are a lot of other variables to take into account when talking about atmosphere, like the angle of our axis towards the sun, etc...