(Painting by Wayne Potrafka)
Both the arks (תיבות) of Moshe and Noach drifted upon the face of the water. The arks of Moshe and Noach drew down the words (תיבות) and letters of the Torah. The waters of the flood were brought down because of the sins committed against Hashem. The inhabitants of the world were also guilty of sexual immorality (פגמו בברית) until the point when the words and letters of the Torah could no longer sustain the world. Even during the time of Noach before the Torah was given to Klal Yisroel the world was sustained by the words and letters of the Torah, because the Torah predates the existence of the world. It was from the Torah that the world was created as is known. And, even so the world was commanded to fulfill the Seven Noahide Laws, which at the time, the existence of the world was dependent upon them. The inhabitants of the world transgressed these laws. Therefore, the words and letters of the Torah could no longer deter the waters of the sea and the depths, and because of this the waters rushed forth until the flood came.
Noach, who was a tzaddik, was saved by the ark, which literally drew down words and letters, that is through the letters and words of Torah that Noach merited to fulfill. Through this he was worthy of entering the ark, and the ark then had the durability to drift upon the waters. He and his family and future offspring were saved, and the world was sustained.
These concepts are also true in regard to Moshe's ark, which saved him by drifting on the face of the water. This is because in the future he would receive the Torah, which constricts the waters of the great sea... However, Noach wasn't worthy of receiving the letters of the Torah, because he used the תיבה - ark/words of Torah - to save himself and his family alone. Moshe on the other hand, used the תיבה - ark/ words of Torah - to save all of Klal Yisroel, and gave them the letters and words of the Torah to all of Yisroel and the generations of the world.