Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the of these has been made time-periodic via Floquet theory focusing on time-asymptotic stability. However, little attention given to transient intracyclic periodic since no general tools exist its In this work, we explore potential using recent framework optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) extract information about both and pulsating Poiseuille flow. The analysis instantaneous OTD limit cycle leads identification dominant instability mechanism flow by comparing them with spectrum eigenmodes Orr–Sommerfeld operator. accordance evidence from direct numerical simulations, it is found that structures akin Tollmien–Schlichting waves feature over a large range pulsation amplitudes frequencies but low disappear during damping phase as amplitude increased beyond threshold value. maximum achievable non-normal growth rate was be nearly identical plane existence subharmonic perturbation cycles compared base documented first time