In his autobiographical Res Gestae (22.4), Augustus states: "I furnished for the people a representation of a naval battle, across the Tiber, where there is now the Grove of the Caesars." This consisted of an artificial lake 1800 feet long and 1200 broad, the grand performance being part of the dedication of the Temple of Mars Ultor in 2 B.C. The Grove of the Caesars (Nemus Caesarum) honored Augustus' grandsons Lucius and Gaius Caesar (who died in the years 2 and 4 A.D.). The site was in Trastevere, near the present-day church of S. Cosimato. (source: R.H. Rodgers' translation of 'De Aquaeductu Urbis Romae" of Frontinus (2003). Above an artist's impression). Dr Rabun Taylor put much effort in investigating the location and the backgrounds of the ancient naumachia of caesar Augustus and its water supply by the Aqua Alsietina in Transtiberim in Rome, as known from Frontinus 11.1: "I do not understand what motivated Augustus ... to bring in the Aqua Alsietina .... It has no commendable quality ... It may be that when Augustus set about building his naumachia he brought in this water in a conduit of its own to avoid drawing upon more wholesome supplies".
Above reconstructions with intake and outlet (top) and the naumachia's weir system with three weir settings (from: "Public Needs and Private Pleasures", R. Taylor 2000)
Emperor Napoleon commissioned the construction of an amphitheater in Milano (Italy). It was built in just two years time, an ellipse of 238m long and 116m wide, that could hold 30.000 people (1/4th of the total polulation of Milano at that time). The inauguration was on June 17th, 1807.
Famous was the naumachia held in that year in the presence of Napoleon, similar to the one above. The photo should be of 1807 (source:
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A popular form of entertainment was the naumachia (sham naval battle on articial lakes). These not-so-sham battles were the most elaborate of all spectacles offered at Roman celebrations. The contestants butchered one another until one side or the other was eliminated; the victors, if they fought bravely, were occasionally given their freedom. The Emperor Domitian had the arena of the Coliseum flooded and reproduced an historic naval battle. Special piping was installed under the floor for flooding. The arena, however, proved to be too small. Roman historians report that Domitian staged sham naval battles with almost regular fleets, having dug an artificial lake near the Tiber River and surrounded it with seats. His enthusiasm was so great he continued to watch contests amid heavy rains (Suetonius, trans. by Rolfe, 1951). Generally the aqueduct with poorest quality water was used to fill the naumachia.

According to Suetonius (Dom. 5), Trajan used stone from a naumachia to repair the Circus Maximus after a fire. There is some evidence that Trajan built his own naumachia. This would probably have had a non-trivial impact on the management of the water supply. Either they needed a supply of water to constantly refresh them in order to avoid turning them into mosquito breeding grounds, or they were only filled when needed and then emptied. Either way, a considerable anount of water would have been required for them.

From the thesis of Evan J. Dembskey on The aqueducts of Ancient Rome