Bjarnsen is a viking of Torgund's clan. He appears in the season 2 episode "Chapter 4: The Eternal Warriors" and he tie-in novel "Hilda and the White Woff". The character does not appear in the graphic novels.
Bjarnsen is a slender build, adult male, with orange hair, a beard, and mustache. He wears a helmet, and fights with two small axes that glow with blue light when he uses them. He has blue warpaint on his face.
Not much is known about Olaf's personality, other than that, like his fellow vikings, he wants the Medallion of Sigurd to get rid of his fear.
When first seen, Bjarnsen, along with the rest of his clan, has been trapped in an endless fight against their rivals, the Knudsen clan, over the Medallion of Sigurd. Each night the two clans fight, after which the winners take the Medallion, and Sigurd secretly brings the defeated vikings back to life so they can reclaim the medallion.
Bjarnsen is seen participating in a battle twice; the first time his clan wins. During the fight, Torgund orders David, who agreed to be their messenger boy, to tell Bjarnsen to bring up the right flank, but by the time David relays this order, Bjarnsen has already done so. He then gives David an axe with the orders to bring it to Elof, but David never gets the chance.
The second time Bjarnsen is in a fight, his clan loses and he gets killed. Like so many times before, he is brought back to life by Sigurd, but this time Hilda encourages Sigurd to tell the truth and stop his revenge. Bjarnsen is last seen when he and his clan begin to test the potion that Sigurd used to revive them.