Stabilization of flow past a rounded cylinder

We perform global linear stability analysis on low-\textit{Re} flow past a rounded cylinder. The cylinder corners are rounded with a radius $R$, normalized as $R^+=R/D$ where $D$ is the cylinder diameter, and its effect on the flow stability characteristics is investigated. We compute the critical Reynolds number ($Re_{cr}$) for the onset of first instability, and quantify the perturbation growth rate for the super-critical flows. It is found that \textit{the flow can be stabilized by partially rounding the cylinder}. Compared with the square and circular cylinders, the partially rounded cylinder has a higher $Re_{cr}$, attaining a maximum at around $R^+=0.30$, and the perturbation growth rate of the super-critical flows is reduced for $Re\le100$. We perform sensitivity analysis to explore the source of the stabilization. The growth rate sensitivity to base flow modification has two different spatial structures: the growth rate is sensitive to the wake backflow in a large region for square-like cylinders ($R^+\to0.00$), while only the near-wake backflow is crucial for circular-like cylinders ($R^+\to0.50$). The stability analysis results are also verified with those of the direct simulations and very good agreement is achieved.