Territorial sea is the continuous strip of land to the territory (land), in which the State exercises its sovereignty and jurisdiction. The extension is no longer delimited by the State, being subject to manifestations of the International Law that disciplines the matter. Same as adjacent sea, coastal sea, territorial sea.
What first comes to my mind is that one or more rivers feature very prominently in these civilizations: the Nile in the Egyptian and the Tigris and Euphrates in the Babylonian.