# Does upper atmosphere rotate with earth?

Basic question that I should know the answer to but sadly don't.

The lower atmosphere must rotate with the earth because of friction---at least the very bottom of it.

But what about 30 miles up? There the effects of friction are well gone. Does the upper atmosphere rotate with the earth? If so, does it trail behind (so that if on the ground we move 360 deg/day, the upper atmosphere would move 50 deg/day instead, say)?

This may be the dumbest question I've asked all year, but I frankly never thought about the upper atmosphere before, much less its dynamics.

Thanks if you can clarify!!

• Related question for Jupiter: astronomy.stackexchange.com/questions/39752/… Commented Jan 9, 2021 at 4:19
• Different question, but somewhat related: Rocket drag and lift based on flight direction - in which frame of reference? and What forces a spacecraft, returning from Earth orbit, to synchronize with Earth spin?
– uhoh
Commented Jan 9, 2021 at 4:34
• 1) Why would "the effects of friction (be) well gone... 30 miles up?" What is it exactly that's holding that part of the atmosphere up there and keeping it from falling to Earth? 2) What (if anything) might it be above it that could slow it down?
– uhoh
Commented Jan 9, 2021 at 4:38
• You should think about the very long time the Earth and its atmosphere is rotating. So not only the lower atmosphere rotates with the earth, the upper does the same. There is not only friction between the Earth surface and the atmosphere, there is also friction between different layers of the atmosphere.
– Uwe
Commented Jan 9, 2021 at 17:29
• another way to ask this question: there are particles of various forms in space. At what distance from Earth do they stop rotating with Earth? If I found an atom of oxygen near Mars it is pretty much unaffected by Earth's rotation. If I found an atom of oxygen 1000 miles above ground is it likely to be rotating with Earth? Commented Jan 17, 2021 at 19:09

Certainly a reasonable question.

A possibly useful mental model is to spin a bucket of water in some form. Initially only the surface layers will spin but each layer transfers motion to the next layer in and eventually the entity of the mass is spinning in a steady state.

Similarly with the atmosphere over geologic time scales the atmosphere is spinning with the earth in a steady state. The human time scales the details are far more complex and interesting but are not particularly impactful for spacecraft launches in terms of changing required delta V.

There certainly are impacts to design and trajectory due to the fact the rocket is traveling through moving air shifting the flight path,and a rocket can cross moving air masses quickly enough to produce non trivial side loads.

The lower atmosphere must rotate with the earth because of friction---at least the very bottom of it.

That is true, but only at the very, very bottom of the Earth's atmosphere, perhaps the last few millimeters. There are winds, after all. The trade winds and the prevailing westerlies (along with the discovery of how to beat against the wind) resulted in the 300 to 400 year long "age of sail". Higher up, the discovery of the jet streams enabled Japan to loft balloons that would later drop bombs on the western parts of the United States during the Second World War.

What can be said is that the lower part of the Earth's atmosphere more or less rotates with the Earth as the velocities with respect to the surface of the trade winds, the prevailing westerlies, and even the jet streams, are small compared to the rotation rate of the Earth's surface with respect to inertial. The stratosphere and mesosphere also have winds relative to the surface, but these winds are small compared to the winds in the troposphere.

But what about the uppermost parts atmosphere? Studies in the 1960s suggested that the thermosphere super-rotates compared to the surface of the Earth. More recent studies indicate that this may not be the case; modeling upper atmospheric winds is difficult. What is known is that there are significant vertical winds in the upper atmosphere. The upper atmosphere swells as it faces the Sun during daytime, and retracts as it faces the darkness of space at nighttime.

The atmosphere would rotate with the Earth surface but there are 2 major factors that affect it:

## Coriolis effect

If you calculate what speeds each bit of the atmosphere would be moving at you'll find the largest speed at the equator and near 0 speed at the poles. In these situations fluid dynamics says the air will start rotating, creating vortices. This leads to hurricanes on Earth and the big stable vortex on Jupiter.

## Sun heating effects, Westerlies

I'll just cite wikipedia here because it does a good job explaining it:

If the Earth were tidally locked to the Sun, solar heating would cause winds across the mid-latitudes to blow in a poleward direction, away from the subtropical ridge. However, the Coriolis effect caused by the rotation of Earth tends to deflect poleward winds eastward from north (to the right) in the Northern Hemisphere and eastward from south (to the left) in the Southern Hemisphere.[3] This is why winds across the Northern Hemisphere tend to blow from the southwest, but they tend to be from the northwest in the Southern Hemisphere.[4] When pressures are lower over the poles, the strength of the westerlies increases, which has the effect of warming the mid-latitudes. This occurs when the Arctic oscillation is positive, and during winter low pressure near the poles is stronger than it would be during the summer. When it is negative and pressures are higher over the poles, the flow is more meridional, blowing from the direction of the pole towards the Equator, which brings cold air into the mid-latitudes.[5]

It is a reasonable question, one that finds its answer in the concept of the planetary boundary layer.

The rotating Earth, through its various irregularities on the surface and in topography, drags the atmosphere along. This vertical momentum transfer becomes weaker and weaker as one goes up in the vertical coordinate, until at a height of about ~1km the atmosphere does not 'feel' the ground anymore and one reaches the free-streaming atmosphere.

The exact thickness of the boundary layer will be modified when mountains are present, which can easily be higher than 1km. Furthermore, turbulent motions and convection tend to mix layers of different momentum and thusly act to drag the atmosphere along. A vigorously convecting atmosphere will have a thicker boundary layer. While this involves turbulent momentum transfer, which is in general an unsolved problem in physics, progress has been made in understanding the height of this layer through semi-analytic means, such as the law of the wall.

In the lower free-streaming atmosphere, the motion is governed by geostrophic balance modulo mass, momentum and heat injected by the Hadley-circulations. Higher up, where the free-streaming atmosphere is stably stratified, the atmosphere behaves like the gas mass of any gaseous body with no bottom, such as gas giants.

• Thanks! Super interesting. I'd never heard of the law of the wall! How recent a development is this? Did my education fail me :/
– user36480
Commented Jan 13, 2021 at 9:43
• @Alex: Wiki says "This law of the wall was first published by [...] Theodore von Kármán, in 1930." The dimensional argument he used, retains validity today, but I guess various better estimations and measurements for the stress parameter are available by now. Commented Jan 13, 2021 at 10:19
• So much for education then ;-)
– user36480
Commented Jan 13, 2021 at 11:00
• If the atmospheric boundary layer is 1 km thick, what can we say about the atmosphere above this height? Does air at the equator move more or less at the 450 m/s relative to the ground imparted by earth's rotation (adjusting for other wind factors like temperature, etc)? Given that planes routinely fly 6-12 km above ground at cruise altitude and that they do not experience winds roughly as fast as the planes themselves, this seems unlikely.
– user36480
Commented Jan 22, 2021 at 17:32
• @a1ex: Not sure where you get the 450m/s from. The thing we can say about the free-streaming atmosphere is that its streaming solution can be found locally, i.e. independently of the properties of the boundary. The free-streaming atmosphere doesn't feel the boundary, but it's still stratified, obeys force balances and forcings etc. Commented Jan 23, 2021 at 10:27

In a world with a perfectly still atmosphere it would rotate with the earth. However in the real world, rising air heated by the sun drifts westward because the required orbit speed to stay in same position relative to the ground increases as it gains height. The Coriolis effect is caused by the same phenomenon when moving north or south