I was having a discussion with my Xbox live friends about the civil war when the question of Alduins motives came up. We were referring to Ulfric escaping and continuing the war, which seems to be in Alduin's best interest so more souls can be sent to Sovngarde to feed his power. My friend says that he got lucky, and just flew out of the time rift and had no idea what was going on, and it was just simply destined. I said this was too coincidental, and that he would have flown out right after Torygg's death, since this completes the prophecy. My friend also said that Alduin wouldn't be able to see everything going on without someone seeing him, which is true, and the dragon cult doesn't exist anymore, so there's no humans to gather intel for him, and besides that, he's Alduin the world eater. He wouldn't need to think up a strategy because he's confident in his power. So what do you guys think? Did he fly in by chance in that direction right after flying out of the time rift, or did he plan this out? Maybe to kill the dovahkiin? If so, why wouldn't he just let them cut your head off? And how did he find everything out if he did plan this attack?

I think Alduin was just looking for a place to mess up and Helgen seemed like the best.

I believe Ulfric accepting the fact that He is going to die is what released Alduin from the Time Wound.
By Nord (and Dunmer and Imperial) tradition Ulfric is the winner of the duel, and the legitimate High King. He may have known that an attempt was being made to free him, but when He saw the actual number of Imperials in Helgen, He became resigned to his fate.
Alduin was freed by this happening, and became curious who this young Dova in Helgen was.

I always thought it was a chance encounter. When he was smacked through time, he ended up right there at Helgen and decided to do what he did best. As far as he's concerned, the Dragon War was still raging.

What is interesting is that he took a few moments to look at you when he landed on the tower before doing a shout that knocked everyone down. Maybe he was taking a moment to assess the situation?

He may have been just as lost as our Dovahkiin was. Only after Dovahkiin killed the dragon ouside Whiterun did he realize what was going on.