Firstly there was a gap of more then 100 years between the deluge and construction of the Tower of Babel.
Secondly, Noah after the flood didn't himself stop having children.
Read Genesis 9: 1 -
''And God blessed Noah and his sons and said to them, Be fruitful and multiply and fill the earth''
The scripture applies this to Noah as well as his sons, not just his sons.
Additional Children of Noah
Some 9th century manuscripts of the Anglo-Saxon Chronicles assert that Sceafa was the fourth son of Noah, from whom the House of Wessex traced their ancestry.
An early Arabic work known as Kitab al-Magall or the Book of Rolls mentions Bouniter, the fourth son of Noah, born after the flood, who allegedly invented astronomy and instructed Nimrod.
Martin of Opava (c. 1250), later versions of the Mirabilia Urbis Romae, and the Chronicon Bohemorum of Giovanni di Marignola (1355) make Janus (i.e., the Roman deity) the fourth son of Noah, who moved to Italy, invented astrology, and instructed Nimrod.
According to the monk Annio da Viterbo (1498), the Hellenistic Babylonian writer Berossus had mentioned 30 children born to Noah after the Deluge, including sons named Tuiscon, Prometheus, Iapetus, Macrus, "16 titans", Cranus, Granaus, Oceanus, and Tipheus. Also mentioned are daughters of Noah named Araxa "the Great", Regina, Pandora, Crana, and Thetis.