Rivers that flow “uphill” due to Earth's rotation

One of the fun tidbits that gets bandied around in physics departments is that the Mississippi River actually flows away from the center of the Earth. Due to the Earth's oblateness, the source of the Mississippi is actually significantly closer to the Earth's center than the mouth is, and it's only because of the Earth's rotation (and the centrifugal force present in a reference frame rotating with the Earth) that the water in the Mississippi ends up in the Gulf of Mexico.

My questions are two:

1. Does this mean that the Mississippi would flow north if the rotation of the Earth stopped? I'm leery of just looking at the distance to the center of the Earth, since the oblateness of the Earth also causes a distortion of its gravity field (i.e., the equipotential surfaces are no longer perfect spheres), and this distortion would seem to be on the same order of magnitude as the small differences in elevation we're considering. In other words, if one uses the actual gravitational potential for a non-rotating oblate spheroid, is the Gulf of Mexico at a higher gravitational potential than Minnesota?

2. Are there any other rivers in the world for which this is true? Obviously these would need to be rivers that flow towards the equator with a very shallow gradient (elevations measured relative to "sea level", which would be one of the equipotentials measured above.)

EDIT: For clarity's sake, assume that the Earth would remain the same shape if it wasn't rotating. (In reality, hydrostatic forces would eventually pull a non-rotating Earth into sphericity, but for this question I'm interested in the difference between an oblate, rotating Earth and an oblate, non-rotating Earth.)

• There are maps of gravitational force, which as you suggest are not purely a function of radius but also of material density between the point and the center of the earth. – Carl Witthoft Sep 29 '15 at 17:55
• Comment to the question (v2): Should we account for the fact that if we remove the centrifugal force, we would upset the hydrostatic equilibrium of Earth, so that the shape of Earth would readjust itself? Or should we pretend that the shape is unaltered? A similar premise appears in this Phys.SE post. – Qmechanic Sep 29 '15 at 18:47
• @Qmechanic: pretend that the shape is unaltered. (I've edited the question to clarify this.) – Michael Seifert Sep 29 '15 at 20:46

1. Are there any other rivers in the world for which this is true?

The Mekong, at least after it has left the Tibetan plateau.

Location          Latitude       Elevation (m)  Radial distance (km)
Source            33° 42' 30"       5224             6376.8
Manwan Reservoir  24° 45' 15.5"      997             6375.4
Ruak River mouth  20° 21' 16"        336             6375.9
Mekong delta       9° 27' 30"          0             6377.6


While the Mekong does flow "downhill" (toward the center of the Earth) at the start thanks to that four kilometer drop in altitude across the Tibetan plateau, it's pretty much all uphill from the Manwan Reservoir on.

1. If one uses the actual gravitational potential for a non-rotating oblate spheroid, is the Gulf of Mexico at a higher gravitational potential than Minnesota?

There's a nice what-if scenario at esri, the Environmental Systems Research Institute, that asks and answers this question: If the Earth Stood Still: Modeling the absence of centrifugal force. The scenario investigates what would happen to the Earth's waters if the Earth somehow stopped rotating over the course of a few decades. That's a long enough span of time that the waters would have a chance to adjust, but far too short a span of time for isostasy to readjust the shape of the Earth.

Not only would the Mississippi stop flowing southward, the waters of the oceans would flow away from the equator. This would leave a globe-spanning equatorial bulge of land surrounded by two polar oceans. The end result:

• Your globe picture is awesome. I imagined it would be something like that, but the map is so much better. The lakes in the gulf of Mexico and around the Caribbean are nifty too. I hadn't considered that. – userLTK Sep 30 '15 at 3:27

I can give a brief answer, though if anyone wants to do a better, more detailed one, feel free.

Sea level at the Equator is 21.36 KM higher than at the poles. Source, and with a distance of about 10,000 KM pole to equator, that's a natural rise moving towards the equator of 2.1 meters per KM. That works out to 2.136 meters per km or a bit over 11 feet per mile, a 1 mile drop every 468 miles and I'm not sure earth's bulge spreads consistently, but a 1 mile drop over 468 miles is quite a bit and likely more than most longitudinal elevation drops. (I'm not sure longitudinal elevation drops is a proper term, but I like the way it sounds).

I'd wager that most equator bound rivers flow "up hill" compared to the center of the earth over most of their routes. I looked, but couldn't find any good lists for river elevation drops so I couldn't verify.

Does this mean that the Mississippi would flow north if the rotation of the Earth stopped?

Pretty much yes, but if the Earth stopped (and you ignore the other effects of stopping a 1,000 MPH rotation) then, not just the Mississippi but the Oceans and all water would flow North and not in small amounts. All of Alaska might be submerged and most of Canada and the equator, even around the oceans might lose all it's water and form a land bridge. A 21.36 mile bulge in sea level is a LOT and if that suddenly goes away. Wow. The effect would extend way way way way past the Mississippi. This effect, of-course, would only be temporary as the land too would correct itself from the Equatorial bulge too, just more slowly than the oceans and you might see a number of 11 or 12 or even 13 Richter scale earthquakes as the Earth made gravitational adjustments to undo it's rotational bulge. (I rather like what if scenarios like this one. Kind of fun to imagine what they would be like).

since the oblateness of the Earth also causes a distortion of its gravity field (i.e., the equipotential surfaces are no longer perfect spheres), and this distortion would seem to be on the same order of magnitude as the small differences in elevation we're considering. In other words, if one uses the actual gravitational potential for a non-rotating oblate spheroid, is the Gulf of Mexico at a higher gravitational potential than Minnesota?

The gulf of Mexico is actually lower gravity than Minnesota, for 2 reasons. The rotation effect, which you mention is bigger as you move towards the equator and that's the larger of the 2 effects but being further away from the center of mass also reduces gravity. You might think because there's more land under you that you'd weigh more, but you're also further from the center of mass, so the effect is that, even when you factor out rotation, you weigh slightly less in the Gulf of Mexico than in Minnesota, just as you weigh less at the top of Mt. Everest than at the food of Everest. explained here

• As there are tides in rocks, how much is the river effected by tides? – Jitter Sep 30 '15 at 10:42
• There are tidal forces everywhere, but the forces are only noticeable over very large distances like oceans and generally east to west. Individual rocks don't experience tides in any noticable way. But entire rocky planets do. The earth has a small tidal well as the moon or sun pass over-head. Rivers, running east to west over an entire continent should experience tides but the nature of rivers. Hmm. My hunch is yes they might, but also, tides in east-west running rivers would be hard to see due to the nature of the river. I like the Tide-River question. – userLTK Sep 30 '15 at 20:51
• If the Earth stopped rotating all the water would boil off. Even Planets with no visible water rotate on their axis...some like Jupiter massively so...so basically the Earth will never stop rotating. Since this appears to be a primordial fact don't expect the courses of major rivers to change much...if ever. Even if Continents were to drift these Rivers would still flow...though maybe not as Rivers anymore. – Doctor Zhivago Aug 23 '16 at 4:57

protected by Qmechanic♦Apr 9 '17 at 6:26

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