Instability modes and transition of pulsatile stenotic flow: pulse-period dependence

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Abstract
The instability modes arising within simple non-reversing pulsatile flows in a circular tube with a smooth axisymmetric constriction are examined using global Floquet stability analysis and direct numerical simulation. The sectionally averaged pulsatile flow is represented with one harmonic component superimposed on a time-mean flow. We have previously identified a period-doubling global instability mechanism associated with alternating tilting of the vortex rings that are ejected out of the stenosis throat with each pulse. Here we show that while alternating tilting of vortex rings is the primary instability mode for comparatively larger reduced velocities associated with long pulse periods (or low Womersley numbers), for lower reduced velocities that are associated with shorter pulse periods the primary instability typically manifests as azimuthal waves (Widnall instability modes) of low wavenumber that grow on each vortex ring. Convective shear-layer instabilities are also supported by the types of flow considered. To provide an insight into the comparative role of these types of instability, which have still shorter temporal periods, we also introduce high-frequency low-amplitude perturbations to the base flows of the above global instabilities. For the range of parameters considered, we observe that the dominant features of the primary Floquet instability persist, but that the additional presence of the convective instability can have a destabilizing effect, especially for long pulse periods.