Effect of Aspect Ratio on Optimal Disturbances of Duct Flows

Abstract

The linear temporal stability of the Poiseuille flow through a rectangular duct is considered. The effect of the duct aspect ratio on the transient growth of disturbances, which causes the so-called subcritical laminar–turbulent transition, is studied numerically. In particular, it is shown that an increase in the aspect ratio promotes the subcritical transition in almost the entire considered range of the duct aspect ratios except a relatively narrow range, where the increase suppresses the transient growth of disturbances. Such peculiarity is qualitatively explained by considering the nonmodal stability of more simplified plane channel flow.

Keywords

• linear hydrodynamic stability
• nonmodal instability
• optimal disturbances
• symmetries of disturbances
• viscous duct flows