Stability of a laminar helium II flow under a non-uniform mutual friction forcing

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 stabil ity of the normal fluid velocity profile under a mutual friction forcing fr om the superfluid. Previous work has shown that superfluid vortex lines wil l be attracted to regions in the fluid where the normal fluid and superflui d velocities are equal, leading to a non-uniform distribution of these vort ex 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. (C) 2000 Els evier Science B.V. All rights reserved.