Wulf is the father of Melle and Eirik in the 10th century. Or is he? Seems like he was drinking a little too heavily from the dragon orchid beer, so his little brother Tor stepped in and get the job done. Gee thanks, Tor…
Wulf is the older brother and in charge of the entire Viking clan on Bloed Isle. He's the chief, which means he can take whichever wife he wants, and he just so happens to take the one lady that Tor's had his eye on. Did Wulf know this and do it just to spite his brother? Was he unaware? Either way, this decision doesn't turn out so well for him down the road.
It's clear that Wulf will do what's needed to keep peace on Bloed Isle and hang onto his wife and kids. He'll put up with some nonsense from his brother, but only up to a point. The first time that Tor makes a big deal about his claim to the twins, Wulf exiles him, but only for three years, which we're pretty sure counts as compassion in the 10th century. The second time, though, Wulf brushes off Tor's comments until he finally can't take it anymore, at which point he fights his brother to the death.
Despite killing his brother, Wulf isn't ruthless or cruel; he seems to really want to make things work with Tor. Sure, he doesn't like the guy (he did sleep with his wife and broadcast it, after all), but he'll put up with him as long as Tor keeps his trap shut. Even when Wulf strangles his little brother, he's not excited about it:
Tor's eyes stared at the ceiling, seeing nothing.
They could not see now, so they did not see the tears that ran down his brother's cheeks. (6.7.40-41)
See? Wulf does love his little brother and is bummed about killing him. Bummer for Wulf, even after Tor dies, the two are still fighting—and in the end, Tor gets what he wants. Or at least half of it. Wulf is forced to live with the loss of his son and the knowledge that his actions were at least partly responsible for all the craziness that went down on Bloed Isle that winter. It's a heck of a burden.