The posuk in Bereishis 7,20 says that the waters rose above the mountains 15 amos. But why was this so? It's understandable why the mountains had to be covered with water, but why did the waters have to rise another fifteen amos to complete the destruction of the world?
After I asked the question, an answer occurred to me when I remembered that Rashi on a later posuk makes a calculation to show that Noach's ark was submerged 11 amos (cubits) in the water. Why does Rashi tell us this bit of seemingly trivial information? To answer our question:
Hashem allowed Noach and everything in the ark to escape the waters of destruction, but it appears that it wasn't enough that they were protected by the ark, they had to actually escape the destructive sphere of the waters, which was until the top of the mountains. The waters above that level were not destructive because above the mountains there was nothing left to destroy.
Therefore, Hashem continued with the deluge until the ark was raised above this sphere. And since we know from Chazal that the domain of a person extends four amos in each direction, Noach and the ark had to be four amos above the sphere of destruction, that is, four amos above the mountains. And since, as Rashi proves, the ark was submerged in the water 11 amos, the total height of the waters needed for Noach to escape was 15 amos. So it seems to me.