Global Instability and Transient Growth in a Model Fusifom Aneurysm with Steady Inflow

The stability of the flow through a model aneurysm is computed using a global linear stability analysis and a direct transient growth analysis. The geometry consists of sinusoidal expansion in a circular pipe. Dimensions are chosen to represent a human abdominal aortic aneurysm near to the critical bulge size requiring surgical intervention. The bulge length and maximum width are $2.9$ and $1.9$ times the pipe diameter, respectively. Subject to a steady inflow, the flow is found to be weakly unstable to quasi-periodic global eigenmodes with azimuthal wavenumbers of $4$ and $5$ at a Reynolds number (based on area-averaged velocity and pipe diameter) of $Re\approx 3900$. Perturbation structures in these eigenmodes are concentrated in the outer part of the bulge towards its downstream end. A transient growth analysis reveals that the flow is sensitive to transient disturbances beyond $Re=33$, well below the time-averaged Reynolds numbers of blood flow in the human abdominal aorta.