I will smack both of you.
First of all, the Ottoman Empire was NOT limp. Grrrr. In the early stages of the Crimean War, the Ottomans DEFEATED the Russians in several battles in the Principalities (now Rumania). In the war of 1877-78, fighting one-on-one, the Ottomans held off the Russians for nearly a year despite being at war with Serbia and Montenegro, and being wracked by rebellion in Bulgaria and Bosnia due to a horrendous famine. In WWI, the Ottomans fought on seven fronts simultaneously (Mesopotamia, Palestine, Persia, Caucasus, Macedonia, Rumania, Galicia - not to mention the Gallipoli thing), after having fought the Italians and the Balkan Wars, then went on to fend off the British, French, Italian, Armenian, Greek and Russian invasions after the war - that's 12 years of continuous total warfare. Russia collapsed into anarchy after THREE years of war. Grrrr.
Second, an alliance between Russia and the Ottomans was eminently possible. It is very simplistic to assume that any one power was the mortal enemy of another. Russian and Ottoman interests frequently conflicted, but there was no overriding hostility between the two; the traditional Ottoman "mortal enemies" had been Persia and the Hapsburgs; later on the Ottomans became friends with both as their interests began to intersect. There were times in the 19th c when Russian influence was paramount in the Ottoman Empire, and although the Ottomans would treat any relationship with Russia with caution, there is nothing to prevent an alliance.
Likewise, France and Britain spend most of a 1,000 year period at war or as mutual arch-enemies. We might also note the the US-Russian conflict is now over and we are now friends.
How about Britain-US?