Modal and nonmodal global instabilities of rotating incompressible axisymmetric boundary layer

Abstract

This study discusses the modal and non-modal global instabilities of the boundary layer produced on a rotating circular cylinder. An investigation was conducted on a flow of in-compressible fluid over a rotating cylinder of fixed length. The rotation effect of a cylinder generates pressure gradient and centrifugal force radially. The Reynolds number (Re) and rotation rate (S) were calculated using the cylinder’s radius. The Spectral collocation approach discretizes the 3D stability equations in cylindrical polar coordinates, resulting in an initial value problem. Computations were performed for azimuthal wave numbers, N = 0, 1, 2, and 3, Re = 2600, 5200, and 20800, and S = 0.0, 0.5, 1.0, and 2.0. The transient energy growth ($G\left(t\right)$) and optimal disturbances were computed by appropriately superimposing the global modes. The perturbation structure that maximizes $G\left(t\right)$ has been analyzed. The S enhances the optimal value of $G\left(t\right)$ for a specific Re and N. The highest $G\left(t\right)$ was observed for helical mode $N=1$ at low Re and for axisymmetric mode $N=0$ at higher Re. The disturbances’ spatial structure has been elongated in the shear direction and has grown and intensity as $S$ and $Re$ have increased. The perturbation structures are qualitatively distinct for $N=0$ and $N=1$. The energy budget components have been notably impacted by the alterations in the base-flow caused by the influence of $S$.