Abstract
The question of the stability of a laminar helium II flow is complicated by the fact that we must consider the interaction of two velocity fields: the velocity of the superfluid component and the velocity of the normal fluid component. We shall consider 2-D channel flow and concentrate on the stability of the normal fluid velocity profile under a mutual friction forcing from the superfluid. Previous work has shown that superfluid vortex lines will be attracted to regions in the fluid where the normal fluid and superfluid velocities are equal, leading to a non-uniform distribution of these vortex lines. Thus the mutual friction forcing will not be uniform. We choose a Gaussian superfluid vorticity distribution and examine the effect of this forcing on the stability of the normal fluid velocity profile.
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