While I would extend Venice’s naval supremacy in the Mediterranean even further back than the period you mentioned (possibly all the way to the eleventh century) at the end of the day it is going to be difficult to prove a counterfactual. The only real answer to “Why the Ottomans didn’t set on a war of conquest against Venice,” is, “Because they didn’t.” Nonetheless, I do think there are a few interesting elements to examine through which we can try postulate (as accurately as we can) as to why the Ottomans were discouraged from sailing up the Adriatic. A short answer is that conflict in Mediterranean Europe wasn’t always as simple as a mere matching of forces.

I think there are three factors to consider when examining the relationship between the Republic of Venice and the Ottoman Empire:

• From the Ottoman perspective, we need to assess the institutional ability to organize and launch successful naval expeditions against Venice. In the great games of international power politics, how many resources was the Ottoman court willing to commit to a naval invasion of a faraway rival, considering the existence of existential threats closer to home? In other words, what would the Ottomans believe they stood to gain from this commitment, and could it justify the cost?

• Was a naval invasion by the Ottomans up the Adriatic logistically feasible?

• How effective was the Venetian navy, really?

Self-preservation, and not necessarily expansion, is one of the principal objectives of “The State” as a concept. And in this light, existential threats do not exclusively come from abroad. The state, especially in the pre-enlightenment era, generally existed to protect a certain class of enfranchised people. This could mean protecting those people from another state, but also protecting those people from the internal threats of revolt or strife (either by mollifying the disenfranchised, or neutralizing them; most typically via a combination of both). All this to say that war, especially wars of conquest, are not exactly a priority for a state with stable institutions. Conflict between states is often the consequence of specific conditions, and those same conditions often shape the course of the conflict itself. Were there ever the conditions for the Ottoman Empire to set out to conquer Venice? The answer is no.

A wrench might be thrown in my logic considering the specific history of the the Ottomans: they do have a tendency to engage in wars of conquest (especially early in their history) but these conflicts nonetheless looked very different from their conflicts with the Venetians: Ottoman territorial expansion preferred contiguous targets with which they had extended history of interactions, and whose absorption into their empire could be justified on religious grounds, on the grounds of eliminating a troublesome (or threatening) neighbor, or even admittedly for plunder. All of these justifications helped Sultans garner support from within their own court, and ensured the productive participation of all enfranchised parties within the empire. But while the Ottoman Empire and the Republic of Venice did come to blows several times over their history, none of these aforementioned justifications for a full-blown war of conquest ever materialized. A given Sultan might have at some point wished it (we’ll see gaps here and there in my knowledge of Ottoman history, this is probably one of them) but the conditions to organize such a conflict were just never there.

Indeed, the Ottomans and Venetians actually enjoyed a fairly symbiotic relationship for much of their coexistence. Merchants from Venice were granted privileged concessions (an entire quarter of Istanbul) and representation (their own consul and court system) within the Empire, while the Ottomans maintained the largest “Fondaco,” or warehouse-cum-embassy, in Venice. When the two did fight wars, they were often over specific disputes, in other words the outcome of a specific set of circumstances. I actually wrote about the specific conditions around which individual wars broke out between the Venetians and the Ottomans in this older answer.

But even if hypothetically some conniving Sultan or Vizier were to garner enough internal support to ignore threats on the Empire’s borders on Balkans, North Africa, or the Levant, and instead devote time and resources to what will be an incredibly costly war of conquest or plunder against Venice, would this have been feasible?

Probably not. It is one thing to organize a landing relatively close to the Ottoman mainland, on an island like Crete or Cyprus less than a day’s voyage from Greece or Anatolia. It is quite another to sail for days or weeks up the Adriatic: Until the 18th century, all mediterranean transport galleys needed to make landfall at night, and most harbors would have raised their chains and shut their gates at the sighting of an Ottoman fleet, meaning the alternative to risky landings along the untamed coast would be to stage bloody sieges to take harbors by force (the necessity to make landfall at night is why the Venetians absorbed communities along the Dalmatian coast, and also negotiated concessions in places like Ancona and Otranto). Thus carving out the footholds to move a sufficiently large army up the Adriatic would take weeks or months. If the Ottoman force were to achieve this without disintegrating (and before the trade winds turned, which also meant they would be attacking Venice in the autumn, or most likely in the winter) and the Sultan or Vizier responsible for the plan managed to keep their head on their shoulders, the city of Venice would still have to be besieged.

Setting aside the fact that without modern artillery it is impossible to lay siege to Venice, Ottoman navigators would know full well that in order to reach Venice from the Adriatic they would have to navigate through the three “Bocche di Porto” channels connecting the lagoon to the sea. This would entail sailing into the lagoon in single file, which had been demonstrated to be a bad idea early in Venice’s history (Franks and Magyars did not fair well when they attempted to do just that in the tenth century) and this tactic could only lead to assured disaster once the Venetians started casting gunpowder artillery in the Arsenal. An undermanned Venice could struggle to defend all three channels (as the Venetians struggled in their war against Genoa in the 13th century) and galleys might force their way through at Chioggia (the furthest channel from the city, but also the swampiest) during high tide, but then the galleys would be stuck in a swampy part of the lagoon and would have to wait for the right combination of tide and wind to turn and sail up to blockade Venice. Alternatively, the Ottomans could land on one of the barrier islands like Pellestrina, but this also had a historical precedent (also featuring the Franks in the tenth century) and was not a serviceable alternative, as the besiegers would be within range of Venetian artillery without having done anything to cut off the city from its supply lines to the mainland. All this, of course, assuming the Venetians were disinterested in defending their city until the very last moment.

At a time when most of Europe did not have standing armies, the Venetians did maintain a small professional navy (mostly tasked with conducting pirate sweeps). But this was not the main advantage that the Venetians had in naval affairs (sure it probably helped some, but that’s not the point). Indeed, Venice’s professional navy was more consequence than cause, and just one of many things demonstrating how strongly venetian society was linked to the sea. In times of war, no other community could call upon as many ships and sailors in such a short notice as Venice could (just think that Venice was one of Europe's largest cities for much of its history). And while in peacetime the hundreds of working men and women at the Venetian Arsenal produced standardized galleys for the great trade convoys which seasonally traveled east and back; in wartime, the Arsenal set to work converting all a manner of mercantile vessels populating the lagoon into warships, while also turning out purpose-built war galleys (at peak efficiently, admittedly only achieved when foreign dignitaries were visiting, the arsenal workers could lay a keel in the morning and produce a fully-fitted war galley by that same evening). Where their adversaries had to plan, finance, and build fleets, the Venetians could commandeer an enormous amount of ships at a moments notice, and immediately man those ships with seasoned sailors who also happened to be the Republic’s citizens, highly motivated to defend their Republic and their livelihoods against foreign encroachment.

I'll write a short conclusion after the jump below.