We use expansion-normalised variables to investigate the Bianchi type VII _ { 0 } model with a tilted \gamma -law perfect fluid .
We emphasize the late-time asymptotic dynamical behaviour of the models and determine their asymptotic states .
Unlike the other Bianchi models of solvable type , the type VII _ { 0 } state space is unbounded .
Consequently we show that , for a general non-inflationary perfect fluid , one of the curvature variables diverges at late times , which implies that the type VII _ { 0 } model is not asymptotically self-similar to the future .
Regarding the tilt velocity , we show that for fluids with \gamma < 4 / 3 ( which includes the important case of dust , \gamma = 1 ) the tilt velocity tends to zero at late times , while for a radiation fluid , \gamma = 4 / 3 , the fluid is tilted and its vorticity is dynamically significant at late times .
For fluids stiffer than radiation ( \gamma > 4 / 3 ) , the future asymptotic state is an extremely tilted spacetime with vorticity .