Transient energy growth and resolvent analyses of the axisymmetric boundary layer with suction and injection

The present study involves bi-global non-modal and resolvent analyses of the incompressible boundary layer developing over a thin, long, horizontal circular cylinder under the influence of vectored, non-uniform wall transpiration. Transient growth and resolvent analyses are employed to identify the optimal structures of pair of input–output modes and associated energy gains over a time and frequency domains, respectively, providing insights into the dynamics of steady flow. The non-modal and resolvent gains are computed for three distinct transpiration profiles across five different vectored angles, corresponding to three different intensities and Reynolds numbers. The non-modal and resolvent energy gains are found to be higher for injection and lower for suction due to the amplification and decay of instability modes, respectively. Additionally, energy gains are found higher and lower for wall-normal uniform injection and suction profiles, respectively, compared to non-uniform profiles with other vectored angles in both analyses. Two-dimensional spatial structures of output modes in non-modal analysis reveal that the wave packets of optimal disturbances shift upstream and closer to the wall, with smaller cellular vortices for suction. In contrast, for injection, disturbances shift downstream and farther from the cylinder wall, with larger cellular vortices. The spatial structures of forcing-response modes indicate that the harmonic oscillations are located upstream, while the response characteristics are located downstream in the case of injection. However, in the case of suction, it is not possible to amplify the response modes downstream through harmonic forcing of the upstream flow due to the damping characteristics.