And now for some history.. According to the Black Sea deluge theory by William Ryan and Walter Pitman, there was a large amount of water from melting glaciers that gathered outside the Bosporus and quickly pushed itself into the Black Sea thus flooding it.
As noted..
So how does this relate to the flood of the Mesopotamian? Easy... This same event happened in the Persian gulf, specifically at "The Strait of Hormuz" in the Persian Gulf thousands of years ago..As glaciers retreated, some of the rivers emptying into the Black Sea declined in volume and changed course to drain into the North Sea.[4] The levels of the lakes dropped through evaporation, while changes in worldwide hydrology caused sea level to rise. The rising Mediterranean finally spilled over a rocky sill at the Bosporus. The event flooded 155,000 km2 (60,000 sq mi) of land and significantly expanded the Black Sea shoreline to the north and west. According to the researchers, "Ten cubic miles [42 km3] of water poured through each day, two hundred times what flows over Niagara Falls ... The Bosporus flume roared and surged at full spate for at least three hundred days."
Many believe it was a breach of water that broke at "The Strait of Hormuz" at the lower end of the Persian gulf. When the Bible says the deep in Genesis 7:11, many think of the underground aquifers, but the deep can also simply mean the water from the oceans as in Genesis 1:2..
Mesopotamian Plain (Persian Gulf)
So where did the water go after the flood?
This is how the Persian Gulf looks today (below).. Obviously this wouldn't be big enough to kill everyone in the region. Actually I think the answer is pretty clear. If other regions of the world were also being breached by water, specifically areas like the Bosporus at the Black Sea, the water levels would have flown back out of the Persian Gulf to those other areas of the world. At least that is how I see it..
Mesopotamian Plain (Today)
Why didn't people disperse to other areas of the world before the flood?
There could be many reasons... Perhaps they were superstitious. Perhaps there were other areas of the world that were inhabitable back then like the ice sheets areas (see below). Perhaps there were ancient rivers or seas that prevented them from spreading. Other things to take in consideration are the other types of animals living at those times. Perhaps humans didn't have the means to protect themselves against these animals and stayed close together? We don't always know..
Ice Sheets