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Rotating planets, like the Earth, are not perfect spheres but are instead oblates. This affects both the crust and the atmosphere, creating a bulge in the equator 1.

I was wondering if there are motions or currents in the atmosphere that are directly caused by this bulge (in the sense that, even in the absence of any other elements affecting the atmosphere like heating from the sun or the nucleus, these motions would still be produced by the planet's rotation and equatorial bulge).

I found some papers that mention "polar motions" that are caused by this 2, 3, as the equatorial bulge extends some kind of torque. Is this correct? Are these motions some kind of wind currents? If not, are there any other atmospheric motions/currents caused by the equatorial bulge?

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  • $\begingroup$ Related post by OP: physics.stackexchange.com/q/772328/2451 $\endgroup$
    – Qmechanic
    Jul 17, 2023 at 16:08
  • $\begingroup$ I'll be interested in the answers, partly because of my astonishment at a remark, on p.47 in a 2011 book titled "The 4% Universe", by Richard Panek (winner of a Guggenheim fellowship), saying that "Scientists had known since the nineteenth century that if you rotated an initially spherical liquid drop it would become oblate, increasingly so, and eventually compress into a bar shape." As Panek's book was on cosmology, I'm guessing that the friction with subatomic particles would have to account for such changes, on some phenomenally long time span. $\endgroup$
    – Edouard
    Jul 17, 2023 at 16:47

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The solid Earth is in hydrostatic equilibrium. One of the properties of a state of equilibrium is that from that state it is impossible to initiate some new motion.

John Marshall and R. Alan Plumb maintain a website that accompanies their book 'Atmosphere, Ocean and Climate Dynamics' .

The University where they teach has a laboratory for various tabletop demonstrations. One of those demonstrations is titled 'Construction of a parabolic turntable'

There is a rotating platform, about a meter in diameter, the usual rotation rate is 10 rpm.

The platform has a rim, so that fluid can be poured out.

The idea is to pour a slow curing resin onto the platform, while it is rotating. The resin redistributes itself, similar to how it would redistribute itself when poured out over a floor (for the purpose of making the floor a level surface.) The fluid settles into a form with the surface sloping down towards the center of rotation. That settled down state is a state of hydrostatic equilibrium. The cross section of the surface is a parabola, hence the name 'parabolic turntable' .


After the resin has cured:
If you would pour water out over that surface, while the platform is still rotating at the same rpm as when the resin was poured then that water will flow out to a layer with even thickness and no part of the water in motion relative to the total body of water. That state is referred to as 'solid body rotation'.

The shape of the resin is tuned to the rotation rate at the time of pouring. Therefore as long as the platform is kept at that rotation rate the slope of the surface will not start motion of water relative to the total body of water.

As long as the platform is kept at that rotation rate the slope of the surface is providing the required centripetal force for the fluid resting on the surface to be co-rotating with the platform.

As long as the platform is kept at that rotation rate the match is exact, and then the slope will not do anything other than providing required centripetal force for co-rotating.


All of the above is equally applicable for the case of the Earth's equatorial bulge.

Over geologic timescale the solid Earth is ductile, the solid Earth is very close to hydrostatic equilibrium.

(Example of a small, local deviation from hydrostatic equilibrium: There are regions on the Earth where during the last Ice Age there was a layer of ice kilomters thick, pressing the Earth crust underneath it down. With that ice weight gone; some of those regions are still in the process of bouncing back.)



I was wondering if there are motions or currents in the atmosphere that are directly caused by this bulge

While the rotation dynamics of the rotating Earth will modify any form of flow once that flow has be initiated by something else, in and of itself the slope of the Earth's equatorial bulge cannot initiate; all of the effect of the slope is already spoken for; providing required centripetal force.

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