Subcritical transition in plane Poiseuille flow as a linear instability process

In this work, a transition scenario is demonstrated, in which most of the stages are followed analytically. The transition is initiated by the linear transient growth mechanism in plane Poiseuille flow subjected to an infinitesimally small secondary disturbance. A novel analytical approximation of the linear transient growth mechanism enables us to perform a secondary linear stability analysis of the modified base-flow. Two possible routes to transition are highlighted here, both correspond to a small secondary disturbance superimposed on a linear transient growth. The first scenario is initiated by four decaying odd normal modes which form a counter-rotating vortex pair; the second is initiated by five even decaying modes which form a pair of counter-rotating pairs. The approximation of the linear transient growth stage by a combination of minimal number of modes allows us to follow the transition stages analytically by employing the multiple time scale method. In particular, the secondary instability stage is followed analytically using linear tools, and is verified by obtaining transition in a direct numerical simulation initiated by conditions dictated by the transient growth analytical expressions. Very good agreement is observed, verifying the theoretical model. The similarities between the two transition routes are discussed and the results are compared with similar results obtained for plane Couette flow. Published by AIP Publishing.