Earth's Rotation and Atmosphere

[Bystander]

the relative motion.

"Relative" to what? What is moving relative to what else?

 

[Bandersnatch]

The constant rotation of the Earth essentially provides the relative motion.

And you think this relative motion remains constant why exactly? Would you say there is no friction between molecules in the air?

@Bystander: the scenario is the atmosphere begins stationary over rotating Earth.

 

[Iseous]

The Earth is rotating at a constant speed, so the molecules outside of the boundary layer will be moving at the freestream velocity (speed of rotation) relative to the Earth. And I'm not saying there is no friction between the molecules. The viscous forces are causing the boundary layer.

 

[OmCheeto]

Ok. So what is the new question?

 

[Iseous]

Ok. So what is the new question?

Russ linked me to a page about boundary layers and I used those equations to get a very rough estimate of the size of that layer for Earth. Those equations weren't really for a sphere rotating, so I'm not sure if they really mean anything.

 

[Bandersnatch]

The Earth is rotating at a constant speed, so the molecules outside of the boundary layer will be moving at the freestream velocity (speed of rotation) relative to the Earth.

No they will not. All they have is inertia, and there is a constant force acting on them through their viscosity. Unless you provide another force to keep the freestream velocity constant with respect to the ground, the atmosphere will accelerate and eventually match the rotation as per the Newton's laws.

Perhaps approach this this way: I'm sure you do recognise that for every action there is a reaction. The lower layer of the atmosphere in contact with the ground will exert a force on the surface in the opposite direction to the drag the surface exerts on the atmosphere. This force will produce torque through the Earth's radius acting to slow down the rotation.
Under your understanding, the atmosphere will then eventually stop the rotation of the Earth, or any other planet, but the planet will somehow not manage to accelerate the atmosphere.

 

[Iseous]

So if you were to take a ball, put it in the center of a large enclosed room, and keep it spinning constantly, the layer of air being rotated by the ball would increase in size over time?

 

[russ_watters]

Your error is here:

This calculation will be done for the equator with the assumption that the distance is the circumference of the Earth. I'm not sure if that would really be accurate since these equations are for a flat plate.

The Earth has no beginning or end. If a bundle of air has been circling Earth for four billion years, the distance is the entire distance it has covered in that time.

 

[Iseous]

The Earth has no beginning or end. If a bundle of air has been circling Earth for four billion years, the distance is the entire distance it has covered in that time.

I started to think about that and I think that would be correct. However, that's assuming those equations would even apply to a rotating sphere. I found a paper about boundary layers of a rotating sphere in a still fluid, and I'll try to look into it more to see what it says when I get a chance. http://www2.leicester.ac.uk/departm...f-profiles/sjg50/Garrett - Peake 2002 JFM.pdf

However, there was an interesting tidbit in the introduction:
"When a sphere rotates in still fluid a flow is induced in which the fluid moves over the outer surface from the poles to the equator and is ejected radially from the equator." That's what I was saying in the beginning.

 

[Bystander]

When a sphere rotates in still fluid

What "still" fluid?

 

[Iseous]

In a fluid that was initially stationary, if that's what you mean.

 

[Bystander]

What are the boundaries of this stationary fluid volume/mass?

 

[PeterDonis]

"When a sphere rotates in still fluid a flow is induced in which the fluid moves over the outer surface from the poles to the equator and is ejected radially from the equator."

What happens if the sphere has enough gravity to keep the fluid from escaping when it rises radially at the equator?

 

[olivermsun]

What happens if the sphere has enough gravity to keep the fluid from escaping when it rises radially at the equator?

Presumably you develop some sort of closed circulation

 

[jim hardy]

Dad's 1940-ish meteorology textbook "Climate and Man" had a simplistic explanation that i kept in a crevice of my alleged mind:

Air near the equator gets heated by the sun because the ground is warm there.

It picks up a lot of moisture which lightens it further because molecular weight of water is only 18 compared to air's 29...
So it rises and is replaced by cooler air flowing generally toward equator over the surface.
As it rises above the "boundary layer" it carries aloft its eastbound momentum
so the atmosphere rotates because it's well stirred. Somebody mentioned teacup...

Warm equatorial air aloft travels away from equator to where Earth's surface velocity is lower,
so it has excess eastbound momentum compared to surface air at same latitude..
At around 30 deg it sinks again and some of it becomes the aforementioned equator-bound surface air,
some of it becomes poleward-bound surface air.
The sinking air that continued away from equator overtakes Earth's surface due to its excess eastbound momentum giving us the Westerlies .
Near the equator Earth rotates out from under the south equator-bound air giving us the Tradewinds. (edit - sorry , had to edit it to be hemisphere-neutral jh)
See picture below.

So the thought model is a rotating sphere covered with a viscous liquid that's unevenly heated.

Way more thorough explanation here:
http://nc-climate.ncsu.edu/edu/k12/.atmosphere_circulation

Some folks think of it as a Carnot engine moving heat from equator toward poles.

 

[PeterDonis]

Presumably you develop some sort of closed circulation

Yes. Which, as jim hardy's post points out, is exactly what happens in the Earth's atmosphere.

 

[OmCheeto]

In a fluid that was initially stationary, if that's what you mean.

I think Drakkith answered this in post #2

The atmosphere formed with the rest of the Earth and thus has been rotating with it from the very beginning.

I'm still not sure what we are discussing, so I'll reference back to some research I did back in March, and my commentary on why the atmosphere is so weird, that I can't begin to explain it.

I was diddling around with the http://earth.nullschool.net simulator yesterday, and things were no better.
From sea level to about 1500 meters, the atmosphere is consistently random, and very much traveling at the same speed as the Earth.
Above that elevation, things get very strange, and I suspect it is the tilt of the Earth which is causing it.
The northern and southern hemispheres, atmospherically, look like they are from two different worlds.

 

[olivermsun]

Yes. Which, as jim hardy's post points out, is exactly what happens in the Earth's atmosphere.

Keep in mind, though, as Jim Hardy's post also points out, the Earth system is being heated at the equator, so there's quite a different set of mechanisms causing the large-scale circulation that we actually observe.

 

[rootone]

It has to be said a well that the atmosphere always has been a part of the planet. just as the ocean is.
It' s overall angular momentum has been in synch with the rocky planetary body from the beggnning, it did not need to be accelerated to match the rocky stuff,
and there is nothing at the outer edge of the atmosphere which is applying a braking force to it.

 

[PeterDonis]

the Earth system is being heated at the equator, so there's quite a different set of mechanisms causing the large-scale circulation that we actually observe.

Yes, good point; what we should be doing is comparing the relative numbers for convection and the rotation effect.

 

[D H]

I started to think about that and I think that would be correct. However, that's assuming those equations would even apply to a rotating sphere. I found a paper about boundary layers of a rotating sphere in a still fluid, and I'll try to look into it more to see what it says when I get a chance. http://www2.leicester.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/sjg50/Garrett - Peake 2002 JFM.pdf

However, there was an interesting tidbit in the introduction:
"When a sphere rotates in still fluid a flow is induced in which the fluid moves over the outer surface from the poles to the equator and is ejected radially from the equator." That's what I was saying in the beginning.

That article is about flow of air around a small object in a large, uniform gas. It has nothing to do with the topic at hand. I suggest you read about general circulation models instead.

 

[Iseous]

That article is about flow of air around a small object in a large, uniform gas. It has nothing to do with the topic at hand. I suggest you read about general circulation models instead.

So a spherical Earth rotating with an initially still atmosphere is nothing like a sphere rotating in an initially still gas?

 

[rootone]

But it didn't have an initially still atmosphere, (and what exactly does 'still' mean here anyway?, still in relation to what?)
The whole planet including the atmosphere originally formed out of a condensing cloud of material including gases, and all of it had angular momentum.

 

[Iseous]

Still to an outside observer who is not rotating with Earth. Regardless, once the sphere in that experiment started rotating and getting the gas to rotate with it, then it is no longer "still" either. So whether it started off not rotating, or you looked at a point once the sphere and gas around it was already rotating (fast forward into the experiment), you would get the same steady state eventually unless there was an outside energy source influencing the gas. But if you're going to claim it all had angular momentum, then where did that come from? These clouds were the result of gravitational forces acting on one another. But how would gravity cause something to rotate on its own axis? It acts at the center of mass, which would not do that. That would require a force not acting on the center of mass (i.e. not gravity).

 

[PeterDonis]

But how would gravity cause something to rotate on its own axis? It acts at the center of mass, which would not do that.

You are taking an approximation (that the gravity of a spherically symmetric body can be viewed as being produced at its center of mass) and using it where it is not valid. The solar system formed from a diffuse cloud of gas and dust. That cloud was not exactly spherically symmetric; the forces between individual pieces of the cloud did not average out to a single "force of gravity" acting from the center of mass of the cloud.

The above is actually another way of saying that the cloud started out with angular momentum. Other clouds that formed other stars also started with angular momentum. In order to average everything out to get zero angular momentum and spherical symmetry (to a good approximation), you need to look at much larger distance scales, comparable to the entire observable universe. At that scale, the universe as a whole has (as far as we can tell) zero angular momentum. But much smaller regions of it, like stellar systems, do not.

 

[rootone]

The entire solar system formed with an initial angular momentum, so for that matter did the Milky way galaxy.
Smaller structures obtain their momentum from larger more massive structures.
There is no evidence to the contrary - (which would be that initially static objects form and later they somehow start to spin).

Edit:
As Peter said, on the very largest scales it looks as if the spin of galaxies is arbitrary and cancels out overall on the cosmic scale, although locally within the gravitationally bound systems, a very definite and coherant rotation exists from their beginning.
The same applies to Earth's atmosphere - It came into existence as a part of the early Earth and it always has been rotating along with the rest of the planet.

 

[Iseous]

Any object can be simplified to a center of mass for a gravitational force or sum of gravitational forces. That is why if you drop an object of any shape, it falls straight down (toward the center of mass of Earth) without any rotation about its own axis (because the gravity is acting at the center of mass of the object that dropped). Even though it is being pulled by many different masses, the net force acts essentially between their centers of mass. An object would only rotate if you apply another non-gravitational force to it away from its center of mass.

 

[rootone]

Yes correct, but in the case of the Earth's atmosphere it isn't needing to acquire any spin, it's a part of the planet and it always was.
It's not as if the revolving planet with no atmosphere ran into a huge motionless and very dense gas cloud which then stuck to it.

 

[Iseous]

If this was part of a giant gas cloud, then the gas would have just been pulled toward Earth from gravity just like all the other mass. So yes, the atmosphere did not necessarily have to have its own spin initially. But gravity would not explain the initial spin of the Earth or other bodies to then rotate the atmosphere in any way.

 

[rootone]

The initial spin of Earth, all of it including the atmosphere, arises because the initial cloud of material from which the Earth condensed was already rotating.
That cloud of material obtained it's rotation from the larger scale cloud of material which was the nebula which gave rise to the overall solar system.
This also was initially formed with some amount of spin, (which is why the planets have orbits and do not fall into the Sun)

 

[Iseous]

Okay, but that doesn't specify what forces actually caused that. You just keep going back further into the past and say that the thing before it had the spin already, but no explanation of the forces involved to actually do that. The big bang was basically an explosion outward, which would give an outward radial motion, not any spinning. So unless you just want to keep going back and say that everything already had a spin right from the start of the big bang...

 

[PeterDonis]

Any object can be simplified to a center of mass for a gravitational force or sum of gravitational forces.

This is not correct as you state it. Strictly speaking, only an object with zero angular momentum can be simplified in this way. In practice, objects that are small enough can be approximated this way even if they have angular momentum, for many purposes, but not for all. (For what "small enough" means, see below.)

That is why if you drop an object of any shape, if it isn't already spinning, it falls straight down (toward the center of mass of Earth) without any rotation about its own axis (because the gravity is acting at the center of mass of the object that dropped).

See my correction above. The object has zero angular momentum at the end because it has zero angular momentum at the start.

Also, suppose the object is a long ("long" meaning kilometers long), thin rod, oriented horizontally, with one end higher than the other. What will happen when you drop it? The Earth's gravity will pull the lower end a little more strongly than the upper end, so the lower end will fall faster. Which means...the object will start rotating (about a horizontal axis).

So your claim breaks down in two scenarios: one, objects that are already spinning; two, objects that are large enough for different parts to have different gravitational forces on them (i.e., large enough for tidal effects to be important), which can start them spinning.

 

[PeterDonis]

Yes correct

No, he's not correct. See my previous post.

 

[PeterDonis]

The big bang was basically an explosion outward, which would give an outward radial motion on average, not any spinning.

See my correction above. I've already posted about this here; the universe as a whole has zero angular momentum (as best we can tell), and has since the big bang, but that is just a large-scale average; it does not mean individual sub-regions of the universe cannot have angular momentum.

 

[rootone]

It's observationally true that objects on the scale of galaxies are spinning, and from that we can see why smaller systems within galaxies derive their rotations.
I agree with you that it isn't clear how the spinning on the largest scales got going, but it does seem that there is no preferred direction for spinning galaxies, it's apparently random.
So on the scale of the whole observable Universe the total spin is zero as far as we can tell.
However spin does exist at the scale of galaxies, as a matter of observation, it's not theory.

@Peter - OK. I'll check back the detail of that later, no time now,
What I was agreeing with, (forgetting spin for this purpose), was that if two massive objects exist within a cosmologically close distance they will be gravitationally bound and would attract each other.