Transition to turbulence in plane poiseuille flow

A transition to turbulence scenario in plane Poiseuille flow (PPF) initiated by Transient Growth (TG) associated with four streamwise elongated vortices is studied. Although the energy growth of this initial disturbance is less than that associated with two vortices, this combination is chosen because of its ability to generate relatively strong wall-normal inflection points in the velocity profile. It is shown that the TG stage is well approximated by using only the first five least stable even modes. Furthermore, the temporal modification of the base-flow includes the development of an inflection point in the wall-normal direction. Consequently, the modified base-flow becomes unstable with respect to three-dimensional infinitesimal secondary waves. The analytical predictions of key stages during this process are validated by direct numerical simulation (DNS). Moreover, the temporal evolution of the vortical structures through the process is well captured by the analytical model except for the last stage before breakdown to turbulence, where a packet of hairpin vortices is formed.