There is a good Wikipedia article about Mt Ararat. It is a supervolcano which is thought to have erupted around 2400 BCE. Rev James Ussher used Babble genealogy to place Noah's flood at 2300 BCE so how come Noah hadn't seen or heard of the eruption. In any case Mt Ararat is the highest peak in the Armenian Highlands/plateau at 5137m, the next two are over 1000metres lower with Aragats at 4095m and Suphan at 4058m.

Genesis 8v4 "on the seventeenth day of the seventh month the Ark came to rest on the Mts of Ararat v5but only by the 10th month did the mountain peaks become visible" So I recon that says the Ark was right at the top of the highest Mountain. Lesser Ararat is a peak close by but is 3896m and greater Ararat would have been clearly visible before an ark came to rest on the lesser one ( except if it was really foggy )

Youtube video Mount Ararat 2014 on DArtolomeo channel has hikers on filming from the peak and looks like most directions other peaks are too far away to see, except for a ridge which is maybe to lesser Ararat.

How far could the dove have flown in search of dry land ?
Genesis 8v6 has Noah wait a further 40 days after the 1st day of 10th Month = until the 10th day of 11th Month.. There are a further two weeks elapse messing around with the dove in v10 & v 12 which would take the date to 24th of 11th Month, minimum.
Genesis 8v13 says that on the first day of the first month of Noah's year 601 the land was dry. At any rate back in v9 this would only leave the dove 7 days to travel in search of dry land = 3.5 days each way. I read that the maximum a pigeon can travel in a day is 90 miles, so it could only have time to survey out 315 miles which can hardly justify the claim that it showed water was over all the surface of the Earth. [ Always remembering that the Ark was supposed to be on the highest peak in the region which would be over 1000 metres uncovered even before any other peaks were visible in extreme distance. ( the dove wasn't too bright, talk about bird brained )]
Anyway Mt Shkhara in Georgia near the S.E of Black Sea is 5193m and lie about 210 miles away as the crow flies  so might have been reachable by a dove with holyspirit GPS guidance. [Probably the dove just flew a few hundred yards down the mountain and hung out for a few days then flew back with a leaf ]
For the avoidance of doubt; I smell a rat,  I think it is quite possible none of the Noah story is real except for Mt Ararat.