Floquet stability analysis of a two axisymmetric layers of oscillatory flow near a flexible wall as a model to study the flow induced in syringomyelia cavities

Syringomyelia is a disorder characterized by the accumulation of fluid in the spinal cord, forming macroscopic fluid-filled cavities, called syrinxes, the growth of which can lead to progressive neurological damage. It is widely accepted that both the hydrodynamics of the cerebrospinal fluid in the spinal subarachnoid space and the motion of the fluid inside the syringomyelia cavities, play an important role in their formation and growth. In the present work we are concerned with the coupling between the motion in these two fluid layers, driven by the flexible nature of the spinal-cord nervous tissue that separates them, and with their stability dynamics. In particular, we have studied a model problem involving the Floquet stability analysis of the oscillatory flow of two axisymmetric layers of fluid separated by an initially undeformed flexible wall, that is modelled as spring-backed plate. We have carried out an analysis for a wide range of flow and wall parameters, whose results show that, for different levels of coupling between the difference of forces (pressure and tangential stresses) across the wall and the wall deformation, a critical value of the Reynolds number exists above which the flow becomes unstable to perturbations.