The Colosseum was flooded for mock naval battles during the opening games in 80 CE. The arena was built in a low lying area that had been an artificial lake within Nero's Domus Aurea. The lake had been fed by water from the nearby Aqua Claudia aqueduct which likely could have been used to flood the Colosseum. Archeologists believe they have found a drain beneath the arena that connects to the Cloaca Maxima, the city's main sewer. Both flooding and draining would have taken time, perhaps all day, so it doesn't seem likely that it was a regular event.
The Emperor Domitian, who was assassinated in 96 CE, ordered the building of a complex of tunnels, cages, elevators and trapdoors beneath the Colosseum which made flooding impossible, so the window in which nauachia could be stage was only about 16 years.
I read a story many years ago - I don't recall where and it may have been fictional - about an event held in the flooded Colosseum. Boats with naked slave girls playing lyres and singing were rowed around the arena. At a signal, the rowers, who were below decks, opened trapdoors and swam out; causing the boats to begin sinking. At the same time crocodiles and hippos were released into the arena. Hippos may seem docile but they are extremely dangerous. One slave girl bumped into a hippo while trying to swim to safety. The hippo chomped down on her with its massive teeth and cut her in two.
Domitian is traditional considered to have instituted the first Empire wide persecution of Christians (Nero's was confined to Rome itself). Historians are uncertain if this is true. There are no contemporary accounts and the martyrdom stories set in his reign were writen over a century later. But, if it is true, then the first execution of Christians in the Colosseum took place during his reign.
