  We perform fully coupled two--dimensional numerical simulations of plane
channel helium II counterflows with vortex--line density typical of
experiments. The main features of our approach are the inclusion of the back
reaction of the superfluid vortices on the normal fluid and the presence of
solid boundaries. Despite the reduced dimensionality, our model is realistic
enough to reproduce vortex density distributions across the channel recently
calculated in three--dimensions. We focus on the coarse--grained superfluid and
normal fluid velocity profiles, recovering the normal fluid profile recently
observed employing a technique based on laser--induced fluorescence of
metastable helium molecules.
