Submerged Structures in an Ocean World

[Jason K]

Suppose that there exists a rotating water planet, i.e. a planet with a fairly deep ocean, which contains a large structure of a particular geometry submerged within the ocean. If this structure was assembled within the ocean will it, once it reaches a steady state, rotate at the same rate as the planet, or will it rotate at a different rate due to friction and other interactions with the fluid?

The structure itself may be solid or hollow.

In the simplest case the structure is a thin torus that goes all the way around the planet at a particular depth.
More complicated geometries may include the net of a hosohedron, or that of a platonic solid, or the net of a (3-D) projection of, say, a dodecahedral prism.

So essentially, the question is if such a structure were to be build, would it eventually start rotating from the point of view of someone who rotates with the rotation of the planet.

The mass of the planet, depth of the ocean, rotational period, inner diameter of the structure, its orientation relative to the rotation axis of the planet, the mass of the structure, the density of the material of the walls or the interior and physical properties of the ocean can be given as parameters.
The cases which seem more interesting would be those where the mass of this structure would be much, much smaller than the mass of the planet and the interior diameter of the structure remains much smaller than the diameter of the planet or the depth of the ocean for that matter.

Any ideas on how to tackle this problem would be very appreciated!

 

[Drakkith]

For all intents and purposes the structure would rotate at the same rate as the planet. If not attached to the seabed, then because of water friction. But, really, it had to be constructed already rotating with the planet since a high speed water current would make any construction practically impossible.

 

[Jason K]

Yes, I am assuming that it would not be attached to the seabed and it would be constructed with an initial rotation - but would it maintain it? Would it also interact with tides? If the axis of its orientation was at an angle compared to the axis of rotation of the planet would it tumble?

 

[Nik_2213]

Don't forget ocean currents and turbidity flows...

 

[Drakkith]

Yes, I am assuming that it would not be attached to the seabed and it would be constructed with an initial rotation - but would it maintain it? Would it also interact with tides? If the axis of its orientation was at an angle compared to the axis of rotation of the planet would it tumble?

Assuming the structure is a significant fraction of the surface (i.e. it's really big) then it may as well be attached to the surface. Only the largest scale motions of the ocean would have any appreciable effect on it. For all intents, it will rotate with the planet just like a landmass would.

 

[snorkack]

There is a part of Earth ocean that does NOT rotate with Earth.
Around Antarctic, West Wind Drift circles the Earth unobstructed between Cape Horn and Antarctic.

You could build a torus around Earth and Antarctic. It would rotate with ocean/West Wind Drift, not Earth.

In an ocean planet, you could expect more currents that rotate at a rate different from planet/seafloor/the few islands sticking through. And building a structure at a given latitude, it would rotate with the local ocean.

A structure spanning different latitudes would be another matter - current forces transferred to it by friction would tend to shear it apart.

 

[hmmm27]

Yes, I am assuming that it would not be attached to the seabed and it would be constructed with an initial rotation - but would it maintain it? Would it also interact with tides? If the axis of its orientation was at an angle compared to the axis of rotation of the planet would it tumble?

Well first, if your artifact is a ring, then you have "the Ringworld problem". It's going to slide into the center of the planet and get squished - you need a 3d artifact for that, like three rings at 90deg to each other, or some caltrop exoskeleton thing.

You might be able to get away with it if the structure's lighter than water (?). Somebody else can field that one.

As far as tides are concerned, yes, of course. Tides are a gravity thing. If you have a decent sized moon you're going to get tides, and the structure will be under some stress.

"Tumble" ? ... no matter what orientation you place your ring, it's generally going to spin around at the orientation of the planet, because the water's going to drag it around, just like a leaf in a stream. Now, if you try to get something to spin around on its own normal axis, and that axis is different from the planet's, then yes it will precess and cause major problems.

 

[DaveC426913]

Yes, I am assuming that it would not be attached to the seabed and it would be constructed with an initial rotation - but would it maintain it?

THe short answer is: there is no reason why it would not maintain it.

If the axis of its orientation was at an angle compared to the axis of rotation of the planet would it tumble?

1000 miles per hour is too slow to provide sufficient torque, I'd think. It would certainly be swamped by the actions of currents.

Come to think of it - and correct me if I'm wrong - but your planet has little or no surface structures. That would result in very symmetric undersea currents. The currents wouldn't be deflected by continents as on Earth.

That would likely put some very strong torques on your structure - torques that are reinforced over its entire area.

That's very different dynamic.

These are air currents, but I see no reason why the ocean currents wouldn't follow the same pattern.

 

[Jason K]

Thanks all for your inputs! I appreciate all of it. I do think that it must be possible to calculate something about the dynamics of this system, but I'm not sure how exactly to develop a good model.

it may as well be attached to the surface

I'm interested in the motion of a free ring or other object. I essentially want to see if there are stable oscillating solutions to specific formulations of this problem. I'm also imagining the ocean to be very deep!

There is a part of Earth ocean that does NOT rotate with Earth.
Around Antarctic, West Wind Drift circles the Earth unobstructed between Cape Horn and Antarctic.

You could build a torus around Earth and Antarctic. It would rotate with ocean/West Wind Drift, not Earth.

Yes! I'm essentially thinking that on Earth and on other patterns atmospheric circulation is not identical to that of the the planet's spin. There are also apparent winding patterns due to the Coriolis force. These can be symmetric as well. So, that might drive some of the motion of a ring and cause some precession that's very regular. But would the motion be stable?

If you have a decent sized moon you're going to get tides, and the structure will be under some stress.

Yes, but even without a moon there should be stellar tides as well. These tides interacting with the object might cause it to drift or - even better, although not part of the original question - vibrate.

if you try to get something to spin around on its own normal axis, and that axis is different from the planet's, then yes it will precess and cause major problems

I actually do want it to precess, but I want it to be relatively stable. So a true steady state solution with no dynamics in the rotating frame may not be the best option, but perhaps a periodic solution may exist and be stable? I'm not sure how exactly to build the model though. I would like to have the motion driven by ocean currents interacting with the object. I do believe that the symmetry of the system can simplify any resulting model. But I still have little clarity on how to do that. But any motion caused by externally powered initial rotation of the object would probably die out quickly due to friction.

your planet has little or no surface structures. That would result in very symmetric undersea currents. The currents wouldn't be deflected by continents as on Earth.

That would likely put some very strong torques on your structure - torques that are reinforced over its entire area

Yes, I was essentially thinking of Hadley cells as an analogue. Although the density and interaction of a liquid may change the number? But multible atmospheric cells would drive ocean circulation to - I'd guess - at least two layers. These are reinforced by convective currents, between the poles and the equator and between the deep and the surface if there is a temperature and composition difference. But there could be more cells (?) and there could be an oceanic equivalent of the jet stream (?) but I cannot be certain about all that, ocean and atmospheric circulation are not in my field.
Thus the normal axis of this structure may oscillate due to ocean currents.
Another interesting phenomenon could be that the force felt at different portions of, say, a ring would normally set up waves that will propagate along it. Eventually due to the symmetry of the setup, and the fact that the ring is circular, then there may be a set of standing waves (which oscillate perpendicular to the ring itself). But I am not sure if these would be stable.

But the question is, how to best calculate these phenomena? How to get to a sufficiently simple model? Get some model of fluid flows as a function of coordinate and then integrate along revant curves of equal distance? Or perhaps there is some other method?

 

[DaveC426913]

Another interesting phenomenon could be that the force felt at different portions of, say, a ring would normally set up waves that will propagate along it. Eventually due to the symmetry of the setup, and the fact that the ring is circular, then there may be a set of standing waves (which oscillate perpendicular to the ring itself). But I am not sure if these would be stable.

Which would also raise the question of how rigid your ring is.

In order for those oscillations to take place, your ring must have some give to it.

If it is too rigid, it may not adapt well to local current shifts.

 

[DaveC426913]

I wasn't sure until your last post whether the motions were desirable - and, if so, whether they are desirable for the denizens, or just for the story (after all, it might make for a good story if the denizens were very unhappy about the motions).

What do you do about variations in depth? What does the ring do when it encounters shallow seamounts? Or are you planning to have its motions restricted to a local known-safe zone?

 

[Jason K]

Yes, the motions are desirable for the denizens. But it can only work if they are somewhat predictable!
I would think that an object like, say, a ring would not move freely, since if any part would get too close to the surface then there would be a tendency for that part to sink again, even if not much changes at the other end. So it should feel a restorative force for any displacement.
The ocean is global and very deep, there are no shallow regions, and the seafloor is either completely inaccessible or accessible only indirectly - although it might be useful to add one or two shallower regions for a number of reasons. If it bumps into them it might be interesting to see how this structure might be damaged, how characters may react, how they will repair it, or that the damage might reveal a shallower region.
But I also thought that the whole setup of the mechanics of a large but symmetric object within a global ocean is generally an interesting problem that I couldn't solve right away.

 

[olivermsun]

I'm essentially thinking that on Earth and on other patterns atmospheric circulation is not identical to that of the the planet's spin. There are also apparent winding patterns due to the Coriolis force. These can be symmetric as well. So, that might drive some of the motion of a ring and cause some precession that's very regular. But would the motion be stable?

I'm not sure I understand you mean here. Of course the circulation is not "identical" to the planet's spin, but the currents are affected (diverted) by the Coriolis force.

Yes, but even without a moon there should be stellar tides as well. These tides interacting with the object might cause it to drift or - even better, although not part of the original question - vibrate.

Are you thinking of solar tides?

Yes, I was essentially thinking of Hadley cells as an analogue. Although the density and interaction of a liquid may change the number? But multible atmospheric cells would drive ocean circulation to - I'd guess - at least two layers.

Why does the number of (meridional) atmospheric cells drive the number of (vertical) layers in the ocean?

These are reinforced by convective currents, between the poles and the equator and between the deep and the surface if there is a temperature and composition difference. But there could be more cells (?) and there could be an oceanic equivalent of the jet stream (?) but I cannot be certain about all that, ocean and atmospheric circulation are not in my field.

One of the key realizations about ocean circulation is that the atmospheric cells generally do not tend to drive deep convection in the ocean, except in one very atypical but important region. The sun beating down on the surface of the ocean also tends to suppress overturning.

What is your idea of an oceanic equivalent of the jet stream?

 

[Stephen Tashi]

Yes! I'm essentially thinking that on Earth and on other patterns atmospheric circulation is not identical to that of the the planet's spin. There are also apparent winding patterns due to the Coriolis force.

And the direction of currents varies with depth. Look up "Ekman transport".

 

[DaveC426913]

What is your idea of an oceanic equivalent of the jet stream?

If I understand the jetstream correctly, it runs along the boundary between adjacent Hadley cells. As a cold mass sags from the pole, it pushes into the temperate warm mass. The jet steam runs along the seam between the two. It should always be a cold mass poleward of the jetstream and a warm mass equatorward.

I'd expect a similar effect in water, though dampened significantly since water won't rise and fall as energetically as air.

 

[Jason K]

I'm not sure I understand you mean here. Of course the circulation is not "identical" to the planet's spin

Yes, I was editing that sentence and forgot to complete it before posting. The point is that there are organised flows on top of overall rotations.

Are you thinking of solar tides?

Yes. I still don't believe they should be called "solar" tides if the star in question is not the Sun.

(vertical) layers in the ocean?

I was talking about the number of longitudinal cells. I am suggesting that there are probably at least one for each hemisphere. That atmospheric structure may interact with the oceans. Also atmospheric cells will not drive convective flows, but if the structure of the two overlaps in some way then they could reinforce one another.
I don't think that the Earth is a particularly good model for ocean circulation in an ocean world, since there are no continents in the latter and the ocean is also much deeper.

I still need a workable model.

 

[olivermsun]

Yes, I was editing that sentence and forgot to complete it before posting. The point is that there are organised flows on top of overall rotations.

Okay.

Yes. I still don't believe they should be called "solar" tides if the star in question is not the Sun.

The physics are those of "solar" tides, but long as you are talking about tides caused by the local star and not distant stars, I don't think it matters too much what you call it.

I was talking about the number of longitudinal cells. I am suggesting that there are probably at least one for each hemisphere. That atmospheric structure may interact with the oceans. Also atmospheric cells will not drive convective flows, but if the structure of the two overlaps in some way then they could reinforce one another.

The structure of the atmospheric and oceanic circulations certainly do overlap — the ocean surface obviously drives what is going on in the atmosphere (after all, atmospheric heating and convection originates mostly at the surface), and the atmosphere drives the major part of the ocean circulation.

I don't think that the Earth is a particularly good model for ocean circulation in an ocean world, since there are no continents in the latter and the ocean is also much deeper.

The ocean is pretty darn deep on the Earth in terms of the bounding physics. As for continents in the way — there have been a number of model studies of "aquaplanets" that might provide useful guidance.

 

[Jason K]

In its core my question is a mechanics problem. The ocean flows are the external velocity field that acts on this object, causing it to move.
It seems that aquaplanets will have a banded structure - but there will be turbulent flows near the boundaries and they will have unexpected effects. The pattern is not necessarily exactly symmetric between the hemispheres either (although it will be close to being symmetric). Multiple aquatic layers may exist, as depth increases.
All these contribute to the system being quite complicated to be fully calculatable. But I was hoping that the symmetries of the system and of a simplified model might allow a meaningful calculation for the motion of a ring - vibrating or not - to be performed.

 

[Tiran]

Just a general comment - water is incompressible and has very high surface tension. And it has relatively high energy phase changes. So I really don't think you can compare it to atmospheric flows like the jet stream. I just don't think you could have the same sort of extremes in relative velocities.