Water in the interior of a very large continent

Question

Consider a world that is much larger than Earth, but has Earthlike conditions on the surface. (Including gravity = 1g, by some suitable unobtainium.) Clearly, the surface could be covered in a large number of small continents and oceans, but I'm also interested in the possibility of larger ones.

Consider, specifically, a continent a million miles wide, surrounded on all sides by an ocean a million miles wide. What would conditions be like in the interior of the continent?

An obvious first guess is that nearly all the area of the continent would be far from the ocean and therefore, lacking a source of water, would be bone-dry desert.

On the other hand, thinking about it a bit more, there would surely be some water even in the center of the continent, by the second law of thermodynamics. If every water molecule were removed from the interior and dumped into the ocean, this would be a low-entropy state; some water will spontaneously diffuse over the whole area, until a state of maximum entropy is reached. In other words, as you journey from the coast toward the interior, the quantity of water per square mile will decrease for the first few thousand miles, but eventually reach a nonzero floor and stay there. So the second guess is that even the center of the continent will not be absolutely dry.

Then again, even though there is a nonzero quantity of water per square mile, that doesn't necessarily mean liquid water. Third guess: maybe the amount will be small enough that the humidity never approaches one hundred percent, so it all stays as water vapor and there is never any liquid water.

But there is differential heating between night and day, and between rock formations with higher and lower albedo. Wind blows across land of different elevations. Chaotic fluid dynamics applies. There is, in short, still weather. Could the weather ever concentrate water vapor enough to produce occasional rain?

Does it matter if there are some lakes and small seas? Consider a sea one thousand miles wide, in the center of the continent. It seems unlikely that it will matter whether the elevation is equal to the ocean half a million miles away. Either way, the water seems likely to end up scattered in the form of vapor across the whole continent. But then, what distinguishes that case from a much larger sea? If there is a sea half a million miles wide within the continent, that seems obviously likely to persist. What is the important factor distinguishing them?

What is the most effective way to keep a very large continent habitable, without chopping it up into a lot of ordinary continents?

Answer 1

I will assume that unobtanium and the vast size of your planet leave it simply as a very large Earth with no other side effects.

It might be possible for water to fall as rain even in the centre of your vast super continent under the right conditions. This could happen if the prevailing winds blew across the continent in an area where the humidity was relatively high and the diurnal day night temperature difference was not that high.

Vast quantities of humid area could be transported for hundreds of thousands of miles over long periods, across vast flat plains provided the air temperature never reached the dew point.

If far into the interior of the continent there was a range of mountains the humid air could be pushed up and over the mountains and most importantly cooled. At this point it would rain.

Even if the changing seasons brought a cooler climate before the humid air reached its destination and the rain was deposited onto the vast plain, it would have no-where to flow to and would likely remain in the vicinity as damp ground or swamp until the temperature rose the following year where upon warm winds would evaporate it.

With damp ground and sunshine vegetation might grow all along this vast corridor with rains coming in the winter and the water evaporating in the summer with the humidity always being driven further inland by the prevailing wind.

Answer 2

Its worse than you think

First I am only answering your first question, answering all of them would be a treatise on deserts , water cycles, tectonics, and climate.

For context Earth had super continents, Pangea being the most famous. The center was desert because distance itself acts to drain moisture content form air. You are talking about something thousands of times larger. If there is no ocean for millions of miles there will be no water in the center, its too far for it to travel. You would need hundreds of gigantic lakes for the lake effect to even get the center to normal desert dryness. This is not just a desert it is drier than any earth desert. your inland seas will not stay wet they will evaporate.

Even the planets wind cells are working against you, the wind cells will have turned over (gone through spiral rotation) so many times over this distance that they will act as massive dehydrators removing what little water might be in the air.

Diagrams help here.

On the updraft portion of the spiral the air looses moisture, causing a lot of rain and drying the air, without this water the air on the downdraft side is very dry creating arid lands on earth. But here this cycle is repeated over and over without the moisture being replenished in the air, this is normally done by water being picked up from the evaporation oceans. on earth the cycle only turns over once or twice before it is back over ocean. But here that is not the case, so the air gets drier and drier with each step forward in the cycle, over hundreds or thousands of cycles there is nothing left. You may have thousands of miles of lush land before it runs out but by the time you are half a million miles inland there is nothing left. Cells moving in the opposite direction carry water away as fast as it is brought in so there is no long term progression inland.,

The center of this desert will be so dry multicellular life will be impossible, even unicellular life might not work.

Answer 3

The only source for water in the interior of land(of any size) is from water-bearing air crossing the coast heading inland.

Yes, water can evaporate from one part of the land, form clouds, and rain again, but this process only shuffles water from one bit of land to another, it does not add to the sum of water on the land.

So, very simple math:
If the outside edge of a form is proportional to the radius of the form, and the surface area is proportional to the SQUARE of the radius of the form, what happens to the ratio of circumference to surface, as the radius becomes ridonkulously large?

Because the maximum water influx of that piece of land is quite linear related to the coastal line, and the surface over which the water must be distributed is proportional to the surface area.

So absolutely guaranteed, if you indefinitely increase the size of your continent, you indefinitely decrease the total water that enters (measured per surface area).

As for just how dry it would get: A lot drier than the middle of the Gobi desert. Even a lot drier than the Atacama desert, with its ~ 1mm of annual rainfall. Possibly as dry as central antartica, with precipitation of about -1.5mm/year (ice sublimates faster than it snows there)

Answer 4

Frame Challenge: Plate Tectonics

The difference between an Ocean and dry ground more than anything relies on differences in elevation. Achieving these differences mostly comes from plate tectonics. Every square meter of the Earth's crust has pressure building up under it from the mantel, but that pressure will generally migrate to where the crust is already thin to relieve itself. However, if the distance between two fault lines is too great, then the pressure will build up under a thicker part of the crust until it breaks out forming a new fault line.

This new fault line will push the plates apart creating a new low area for an ocean to form. So, instead of seeing a world with a million mile super contenant, and a million mile ocean, you will more likely see a world with continental shelves and oceans of similar size to those we have had on Earth, but a lot more of them.

Pangea lasted about 100 million years because Earth is small enough to let it come together before new conditions forced it apart, but on a world of the size you are discussing, you will never see all of the continents able to come together before pressure starts breaking them up again.