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Considering both full water worlds mostly out of water and ice, and rocky planets that just have a bit too much of it - would polar caps form on them if the conditions are roughly similar to modern Earth? Or the lack of large landmasses would turn the whole hemispheres of the planet into one giant Gulfstream due to there being no obstructions for the warmer water to replace sinking cold polar water and equating the whole planet's temperature, much like the atmosphere currents of a tidally locked planet can prevent its atmosphere to liquify on the night side?

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Yes.

Polar ice caps would defnitely form, if the world is such the the average polar air temperature is well below freezing.

The question is whether the ice would remain in the polar region or drift away and melt.

For a deep ocean world, without any shallow geographic features, the waterflow will be very similar to the airflow around it. i.e. Alternating regions of laminar east-west flow, with regions of more turbulent cyclic flows inbetween.

Something like this:
enter image description here

This will mostly keep the polar water just spinning in place, with limited circulation to lower latitudes, keeping the ice cap in place.

If however the ocean world has significant underwater geographical features (sunken continents), and especially if some of these continents approach or breach the water surface, the oceanic currents will adopt the large, circulating Oceanic Gyre patterns familiar on earth.

enter image description here

With these Oceanic Gyres in place, the polar ice will want to be pulled along with the current, and require either a solid rock foundation(Antartica) or being sufficiently landlocked (Arctic regions) to stay in place.

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  • $\begingroup$ "The question is whether the ice would remain in the polar region or drift away and melt." But if the caps did float away and melt wouldn't water at the poles continually re-freeze to make more cap? $\endgroup$
    – Len
    Apr 21, 2021 at 18:38
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The Arctic Ocean has an ice cap despite the Gulf Stream's access through the Greenland and Barrents Seas. As long as the polar surface waters are cold enough for part of the year for frazil or "grease" ice to form, your ocean world can have ice caps.

Water planets can be ice-free, have ice caps like Earth's Arctic Ocean, be mostly (a cold "eyeball" planet) or entirely covered in ice (like Ganymede), and, if deep enough, have icy floors below their liquid surface.

Not only can ocean worlds have ice caps, they may be more habitable than those without:

Traditional definitions of the habitable zone assume that habitable planets contain a carbonate-silicate cycle that regulates $\text{CO}_2$ between the atmosphere, surface,and the interior. Such theorieshave been used to cast doubt on the habitability ofocean worlds. However, Levi et al (2017) have recently proposed a mechanism by which $\text{CO}_2$ is mobilized between the atmosphere and the interior of an ocean world. At high enough $\text{CO}_2$ pressures, sea ice can become enriched in $\text{CO}_2$ clathrates and sink after a threshold density is achieved. The presence of subpolar sea ice is of great importance for habitability in ocean worlds. It may moderate the climate and is fundamental in current theories of life formation in diluted environments. – The Ice Cap Zone: A Unique Habitable Zone for Ocean Worlds, Ramses M. Ramirez and Amit Levi[PDF]

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  • $\begingroup$ The Arctic Ocean is expected to be ice-free in the summer beginning sometime between 2030 and 2050. Polar ice caps in conditions like Earth are not guaranteed to be a thing. $\endgroup$ Dec 4, 2020 at 3:42
  • $\begingroup$ @KeithMorrison It's not going to be ice-free simply because of the Gulf Stream or it would have been ice-free through recorded history. $\endgroup$
    – rek
    Dec 4, 2020 at 6:24
  • $\begingroup$ I never said it was because of the Gulf Stream. Look up the latest climatological modelling. $\endgroup$ Dec 4, 2020 at 8:01
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There would be two main variables I can think of. Firstly the amount of radiation received by the planet from its sun (temperature). Assuming you take an Earth sized planet orbiting a sun like star then that basically comes down to how far out from the star the planet orbits. Note: there are people on this forum who can and probably have already calculated what happens if you were to arbitrarily increase/decrease the Earths distance from the Sun and the impact on climate. Push the Earth far enough out (e.g past Mars) and it would be a ice ball.) So do a search of the site.

Secondly there is the depth of the oceans. If you have large continental sub surface land masses at polar latitudes then depending on the depth of the water covering them and their geography they might interrupt oceanic convection currents enough to allow permanent ice caps to form. But the water level above the continent would have to be shallow, very shallow for this to come into play. If the ocean over the land mass is more than a few meters deep it probably wont be enough to let ice settle in place.

So that just leaves Sea Ice! depending on its distance from the sun and its degree of inclination (seasonal period) you could have a water covered world where, during the winter period masses of sea ice form in the extreme polar regions then drift off on the prevailing currents. Get enough ice forming quickly enough and depending on how strong the wind and water currents are you might get temporary floating ice fields forming during winter in the northern and southern polar regions, alternating so that only one pole as ice at any one time.

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...And from my search online, the results are confusing. I've found a scientific article about atmospheres on water worlds:

https://web.archive.org/web/20180825152625/paoc.mit.edu/paoc/papers/aqua.pdf

It says the following:

Millennial time-scale simulations yield a mean state in which ice caps reach down to 55° of latitude and both the atmosphere and ocean comprise eastward- and westward-flowing zonal jets, whose structure is set by their respective baroclinic instabilities.

But then there are these guys:

https://journals.ametsoc.org/view/journals/clim/19/18/jcli3874.1.xml

And they say it will be essentially the opposite of that:

The WaterWorld climate is significantly warmer than that observed for the modern reference (Fig. 3). The annual average air surface temperature is 27.5°C, with a shallow equator-to-pole temperature gradient from 33°C in the Tropics to 13°C over the polar islands. Only small areas drop below freezing in winter, and those are over the polar islands—there is no sea ice formed at any time of year.

So I guess the real answer is that it can be both and the writer's free to choose whenever his Waterworld has ice caps or don't?

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  • $\begingroup$ All of these simulations (which are not a lot better than guesses as we have no ground truth to compare them against) depend on insolation. A plant further from its Sun or with a dimmer sun will be more likely to have ice or will have more ice. Closer and hotter, less ice. No one can meaningfully give you an (accurate) general answer, $\endgroup$
    – Mark Olson
    Dec 5, 2020 at 19:08
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Simple: You need a region that has a maximum mean temperature of 271 K. Seawater freezes at a lower temperature than freshwater, and we already have polar regions of this very world with the needed temperature. But as the surface is covered completely by water, that’ll be a double-edged sword. Low-lying clouds work to reflect energy back into space and higher up ones help trap it. Water has a low albedo and high emissivity, so it absorbs lots of energy during the day, and loses a good amount of it as well.

Water vapour is a greenhouse gas, but water having a high specific heat capacity means that it takes a good amount of time to heat up and cool down. So, you don’t want to place your planet too close to its sun(s). It’s that simple.

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  • $\begingroup$ Ah, but here's another interesting question, would water on an ocean planet be actually seawater or freshwater? Since there are no continents to wash salts and minerals into the sea from... $\endgroup$ Dec 5, 2020 at 1:49
  • $\begingroup$ That's definitely a factor. $\endgroup$ Dec 5, 2020 at 4:47

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