I get that after Octavian consolidated his power as Emperor of Rome, Rome had no major opposition on the shores of the Mediterranean. But I don't find any mention of major sea battles in the Mediterranean until the sixteenth century, when the great clashes between the Ottomans and Christians took place, particularly Lepanto. Rome had long since ceased to be a major power. Why was the Mediterranean a seeming quiet zone for so long?
I am not sure I properly understand your question. Therefore I may ask a bit of clarification: what do you consider a major battle? Are you talking about the size of the fleets involved? the relevance for a decisive conflict? the historical significance within a wider context?
I say this because I remember a good number of naval battles involving the Maritime Republics in Italy, the Kingdom of Aragon or the Byzantine.
For example the Republic of Genoa inflicted a major blow to the power of Pisa with the battle of Meloria in 1284. Later Genoa, still on the rise, destroyed the Venetian fleet at Curzola in 1298 and almost a hundred years later threatened the Venetian mainland during the war of Chioggia (1378-81).
Both Genoa and Venice could at the time muster more than 100 ships and were often involved in commercial conflicts which at times evolved into major wars.
Should I take from your question that you consider these episodes of lesser importance - as they might very well be in the context of european history - or that you ignored them?