‘And the waters grew deeper and bore up the ark and it was lifted up above the earth. And the waters prevailed and increased with great abundance on the earth, and the ark went up on the face of the waters, and the waters prevailed in great abundance, and all the high mountains (or hills) that were under the whole heavens were covered. Fifteen cubits upwards did the waters prevail and the mountains were covered.'
This is a masterpiece of build up about the Flood. ‘The waters grew deeper --- the waters prevailed and increased with great abundance --- the waters prevailed in great abundance and all the high mountains (or hills) under the whole heavens were covered'. This is repetition with a purpose. Each step is an increase on the previous one as the listeners and readers are gripped by the expanding cataclysm. Furthermore we even see the gradual movement of the ark, as it is first lifted from the ground, then borne up on ‘the face of the waters' which have replaced the ‘face of the ground'. Then finally we have the fact that all the high mountains (or hills) are under water. The listeners and readers are carried along step by step with growing involvement. (One problem with the verse divisions is that we read them one by one rather than as a whole narrative).
The ‘high mountains' (or hills) that are covered are of course specifically those in Noah's vicinity. (For the meaning of ‘under the whole heavens' compare Deuteronomy 2:25). As far as the eye can see there is nothing but water, and when he makes his checks the ark clears whatever mountains they pass by over 15 cubits (7 metres). Alternately it could be that the ark required 15 cubits clearance. (Being thirty cubits deep it would require fifteen cubit clearance if it were rectangular).