Instabilities in superfluid plane Poiseuille flow

Modal and non-modal analysis of superfluid He-II is carried out in this paper. Landau's two fluid model for superfluid flow is assumed and stability of both normal fluid and superfluid are considered separately by taking the effect of the other through mutual friction. Stability of normal fluid, with a numerically calculated base flow, shows Tollmien-Schlichting mode of instability similar to classical fluids. Non-modal analysis shows the transient growth of perturbations at sub-critical Reynolds numbers. Mutual friction is found to have a stabilizing effect on normal fluid. Superfluid, with an inviscid uniform profile is found to be linearly stable for all wave numbers. Non-modal analysis rules out the possibility of transient growth of perturbations and sub-critical transition. The presence of turbulence in superfluid brings in a possibility that an initial uniform base flow is getting altered due to the action of mutual friction and this altered profile is likely to become unstable.