Edge State Switching in Plane Couette Flow*

Recent work on plane Couette flow that has streamwise period longer than the minimal unit identifies edge state switching from the lower-branch Nagata steady solution to a time-periodic solution (PO3) with comparable fluctuation amplitude to turbulence. This edge state switching results to a basin boundary metamorphosis, where the formation of the basin boundary also switches from the stable manifold of the time-periodic edge state to the stable manifold of the steady edge state. The switching is due to the creation of the vigorous PO3 at a homoclinic bifurcation. In contrast, time-periodic edge states in transitional wall-bounded shear flows typically originate from a saddle-node bifurcation. Another periodic orbit (PO2) originates from a different homoclinic bifurcation and exhibits period-doubling cascade that leads to a chaotic attractor. This chaotic attractor collides with PO3, and a boundary crisis occurs at a critical Reynolds number. Such bifurcation scenario is consistent with the occurrence of boundary crisis in transitional wall-bounded shear flows. For these kinds of flows, transient turbulence is observed at Reynolds number above the critical value.