Linear stability of laminar plane Poiseuille flow of helium II under a nonuniform mutual friction forcing

The calculation of the stability characteristics of superfluid helium II is complicated by the fact that we have to consider the interaction of two ve locity fields: the normal fluid and the superfluid. We consider 2D channel flow and concentrate on the linear stability of the normal fluid under a mu tual friction forcing from the superfluid. The linear stability of the supe rfluid component is also briefly discussed. We consider nonuniform distribu tions of superfluid vorticity, leading to a nonuniform mutual friction forc ing. We derive a modified Orr-Sommerfeld equation for the stability of the normal fluid component and find the neutral stability curves for the normal fluid. We identify a new branch to the neutral stability curve, which can significantly lower the critical Reynolds number of the normal fluid flow. (C) 2001 American Institute of Physics.