So it was usually the Ottomans declaring war?
AFAIK, wars of 1672 - 81, 1686 - 1700, 1710 - 11, 1735 - 39 and 1828 - 29 were started by the Russian side.
Or was the OE heavily provoked most of the times it declared war, by Russian demands infringing on sovereignty, or Russian support for rebels?
Or by the Ottoman support of the rebels (war of 1768 - 1774). It was quite simple, just keep trace of who was rebelling against whom: the "haidamaks" (Cossacks of the Western Ukraine who, while living on the PLC territory,
considered themselves Russian subjects because they viewed Catherine II as their protector from the Catholic Poles against whom they
rebelled) had been chasing the members of the Bar Confederation (who
rebelled against their king to defend both independence of the PLC and their traditional "liberties") all the way to the Ottoman territory and did some looting of the town Balta in which the confederates tried to hide. The Ottomans had been supporting Bar Confederation (which probably made them true defenders of the Polish independence, at least in this specific case) so the Sultan declared war on Russia with a resulting loss of the Crimea (both Khanate and the Ottoman-held places), Kabarda, and territory between Dnieper and Southern Bug Rivers.
In 1787 it was an ill-timed desire to return what was lost in the previous war.
In 1806 the Ottomans dismissed the rulers of Moldavia and Walachia without Russian consent required by Peace of Jassi (1791). BTW, not sure who started this war officially.