Ryan & Pittman in their book, Noah's Flood, (see post #11) estimate that the flood ocurred in 5,600BC and that all the areas just outside the freshwater Black Sea were very arid, almost desert.
When the 'plug' at the Bosporus broke through, the water in the Black Sea rose about one foot a day and most people would have been able to leave with whatever they could carry with them.
About the only place to go was up the river valleys that feed into the Black Sea. They speculate that the edge of the Black Sea supported a huge population of farmers (early irrigation farming) and fishermen. They also speculate that the refugees from the flood spread out all over Europe, bringing the first serious farming and their language with them. Linguistic studies support such a scenario.
I happen to think that the Caucasian mummies, Riddle Of The Desert Mummies, found in the Tarim Basin (In China) may be some of the descendents of refugees from this flood.