Instability of a vertical free convection boundary layer flow: Asymptotically from a perfectly flat one to a highly curved one

We investigate flow instability of the free convection boundary layer evolving along a vertical cylinder with a broad spectrum of surface curvatures. The random perturbation calculation shows that the boundary layer could filter disturbances for a high frequency band (HFB) and the single mode perturbation calculation determines the flow characteristic frequency ${f}_{c}$. The results suggest that as curvature $A$ increases, the characteristic frequency of the thermal boundary layer increases, while the disturbance amplitude decreases. The flow Reynolds stress is strongly amplified toward the downstream at ${f}_{c}$ and dramatically decreases at a decaying frequency ${f}_{c}$-3.5∆.