The simple answer is obviously that it was another one of the many miracles that took place in the teivah. The Ba’al Shevet Mussar in his sefer Agadas Eliyohu on the Yerushalmi (Pesochim 1:1) writes that some animals breath in the bad air that human’s breath out, and the bad air, that they omit is good air for humans. Since all types of animals were in the teivah it balanced out, and the air was filtered via these animals.
Another answer, is based on the Chazal that Og survived the mabul by hanging on to the outside of the teivah and Noach fed him through a small hole. Perhaps it was through this hole that the air was filtered.
Another answer, perhaps, is that the Gemara in Zevochim discusses an animal called a re’am which was too big to fit inside the teivah. The Gemara says the re’am survived by placing its head and mouth inside the teivah. Perhaps through this whole the air was filtered.The Medrash says that Og survived the flood by hanging onto the teivah, where Noach gave him food each day through a small hole in the ship. The Gemara (Niddah 61a) states that Sichon and Og were brothers. Sichon could not have been born after the flood, for all the giants perished in the flood, but if Sichon was born in the antediluvian era, how did he survive the flood? The Daas Z’keinim (Bamidbar 21:34) explains that after giving birth to Og, his mother became pregnant with Sichon, at which point she left their father and married one of Noach’s sons, which gained her entry to the teivah. If she was already pregnant before the onset of the flood, and Noach was confined to the teivah for one year (Rashi 8:14), she must have given birth to Sichon inside the teivah, where he remained for the duration of the flood. (R’ Ozer Alport)
The Netziv posits that the raven and dove that Noach sent out were not taken from the pairs that Hashem commanded him (6:19) to bring into the teivah to preserve their existence. Rather, since Noach was a respected individual prior to the flood, he followed the practice of noblemen at that time of owning pet birds, which were considered part of his household and therefore eligible to be brought into the teivah (7:1). Accordingly, Noach’s decision to send the raven and dove to check whether the water had receded did not jeopardize their species in any way, for a pair of each still remained in the teivah. While Noach’s pet raven was content to remain near his house, the dove was trained to fly long distances to deliver letters and transport small objects in its mouth. Thus, when Noach dispatched the raven and it saw that the teivah was surrounded by water, it simply flew around in circles because it was unaccustomed to flying long distances. The dove was comfortable with traveling long distances, but on its initial mission, it did not find anything to bring back in its mouth, so it did not return directly to Noach, but rather (8:9): אל התיבה – “close to the teivah”, for it had failed in its task and feared that its master would not allow it to return empty-handed. Observing this, Noach understood what had transpired and compassionately took the dove in his hand to warm it up and restore its strength. The Netziv writes that this teaches us that if we ask somebody to do something for us but he does not succeed through no fault of his own, rather than getting angry and blaming him, we should still be grateful for his efforts and greet him warmly. (R’ Ozer Alport)
The Shevus Yaakov (3:31) differentiates between different types of אות and explains that the concept that one should not engage in two אותות simultaneously only applies to signs that are similar in nature and therefore should not overlap, such as keeping Shabbos and wearing tefillin. It does not restrict the performance of other mitzvos that happen to be called אות but represent completely different signs and do not conflict, such as a rainbow which symbolizes Hashem’s covenant to never again destroy the earth. Thus, a person who sees a rainbow on Shabbos should indeed recite the appropriate berachah. (R’ Ozer Alport)
Rabbi Moshe Atik notes that Parshas Noach concludes (11:32) by recording the death of the non-Jewish Terach. As soon the baal korei finishes the public reading of the parsha with this pasuk that mentions Terach’s death, he immediately recites kaddish. (Torah Teasers)
