The hydrodynamic stability of plane Poiseuille flow of superfluid is studied using modal and non-modal analysis. Two modes of instability are predicted, in normal mode stability analysis of the normal fluid, one caused by viscosity similar to the classical mode and another due to mutual friction between superfluid and normal fluid. The mutual friction mode occurs at high wavenumbers, which are stable wavenumbers in classical plane Poiseuille flow. A high superfluid vortex line density alone is not enough to induce instability in normal fluid; a localization of vortex lines is shown to play a major role. The extent of vortex line concentration required to cause instability depends on the density itself. Non-modal instability analysis shows that oblique waves are stronger than streamwise waves, unlike the scenario in classical plane Poiseuille flow.
The instances of vortex ring evolving in confined domains is observed in biological and engineering flows. The evolution of a vortex ring inside a non-axisymmetric confinement and the effect of this confinement on the decay of the ring is investigated in this paper. A square confinement is chosen for this purpose. The effect of confinement ratio (CR), defined as the ratio of the diameter of vortex ring to the size of confinement, is studied in detail. The asymmetry caused by the confinement on the ring is noted by measuring its properties on two different planes, namely the Y-plane and the diagonal plane. The asymmetry on the vortex ring is qualitatively observed to be dependent on CR.
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