Elucidation and control of coherent structures and large-scale turbulence structures based on saddle solutions

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The aim of this work is to elucidate or control coherent structures and large-scale turbulence structures using unstable periodic and steady traveling-wave solutions to the Navier-Stokes equation. In a plane Couette system dynamical flow behavior in transition to turbulence has been characterized in terms of the unstable manifold of the periodic orbit on the basin boundary between laminar and turbulent attractors, while a drag reduction has been accomplished by use of control input confined to the near-wall regions. The traveling-wave solution has been discovered in square-duct flow to be used for demonstration of direct relevance between coherent structures and turbulence-driven secondary flow.