THE ROLE OF THE HAIRPIN VORTEX SOLUTION ON LAMINAR-TURBULENT TRANSITION OF PLANE COUETTE FLOW AT MODERATE REYNOLDS NUMBER

The shooting method is employed to outline a structural aspect of phase space of plane Couette flow, associated with laminar-Turbulent transition at moderate Reynolds numbers (Re ∼ 104). The basin boundary separating the laminar and the turbulent attractors in the phase space is emerged out of trajectories starting from initial conditions constituted by superposition of three distinct exact steady solutions of PCF, including the Hairpin Vortex Solution (Itano & Generalis (2009); Gibson et al. (2009)) and the so-called Nagata's solution (Nagata (1990)). The result implies that HVS is on the basin boundary even at moderate Reynolds numbers, and that one of the unstable manifolds of HVS heads towards the NBW, which lies on the basin boundary.