Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?

摘要

The instability of a streak and its nonlinear evolution are investigated bydirect numerical simulation (DNS) for plane Poiseuille flow at Re=3000. It issuggested that there exists a traveling-wave solution (TWS). The TWS islocalized around one of the two walls and notably resemble to the coherentstructures observed in experiments and DNS so far. The phase space structurearound this TWS is similar to a saddle point. Since the stable manifold of thisTWS is extended close to the quasi two dimensional (Q2D) energy axis, theapproaching process toward the TWS along the stable manifold is approximatelydescribed as the instability of the streak (Q2D flow) and the succeedingnonlinear evolution. Bursting corresponds to the escape from the TWS along theunstable manifold. These manifolds constitute part of basin boundary of theturbulent state.