While the recently published Turney & Brown paper presents some nice data and argues convincingly that the start of Neolithic expansion in Europe roughly coincides with the ~8300 yr BP age estimate for the catastrophic flooding of the Black Sea, this correlation does not necessarily suggest a cause-and-effect relationship. The question is still open: yes, the flooding might have caused the migration, but it is also possible that the two events are independently related to the same climatic changes. Very few of the radiocarbon dates, representing the earliest Neolithic sites in Europe, come from the territory of present-day Romania, yet one would expect that the low-lying areas along the lower Danube River would be the first places to be colonized by the population forced out from the inundated shelves of the Black Sea that are the widest east of the Danube Delta. Why are early Neolithic settlements so scarce in this area, which is good for agriculture? In their 1998 book, Ryan and Pitman suggest that Vinca farmers showed up abruptly along the Danube valley, soon after the flooding occurred. The earliest Vinca settlements however are dated at 7500 yr BP, so there is a gap of a few hundred years between the flood and these first settlements. That seems too long; in addition, even if the initial displacement of people living near the Black Sea resulted in the expansion of agriculture into Southeastern Europe, it is questionable how much effect this flooding had on the spread of Neolithic people into Northwestern Europe. It is unlikely that the main motivation to cross the English Channel for people living in today’s Northern France was that their ancestors were scared off the shores of the Black Sea many hundreds of years before.
The image below is a screenshot from Google Earth, showing the data published by Turney and Brown. The Neolithic locations are color-coded according to their age, red being the oldest, and dark blue being the youngest. The KMZ file (made with GPS Visualizer and some help from Matlab) is available here.
Regarding the link between the Black Sea flood and Noah’s story — I think it is an interesting idea, but not much more. There were and there will be numerous large floods that affect human lives and human history, and the one featured in the Bible is so generic that it will be difficult to unequivocally link it to any specific event. In addition, the catastrophic flooding of the Black Sea might have been catastrophic only in a geological sense; calculations suggest that it took 34 years to erase the 155 m difference in water level between the Black Sea and the Mediterranean. The slow and relentless rise of the sea must have been disquieting and annoying to people living close to the shore, but, unless they built their huts in the middle of the Bosporus, it probably was not as traumatic for most of them as Hurricane Katrina was for lots of Gulf Coast residents.
The recent (I mean geologically recent) history of the Black Sea region is certainly fascinating and the controversy surrounding the exact sequence and nature of the events can only result in more top-notch oceanographic and archeologic research. And that is always exciting.