平面クエット系における層流-乱流吸引域境界上の周期解の不安定多様体(安定性・乱流 安定性(2),一般講演)

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  • The unstable manifold of the periodic solution on the basin boundary between laminar and turbulent attractors in a plane Couette system

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The unstable manifold of the quiescent periodic orbit (Kawahara and Kida 2001) for plane Couette flow is computed numerically at Reynolds number Re=400. The dimension of the unstable manifold in phase space is only two, while the stable manifold of the periodic solution has the remain of dimension, implying that the periodic solution and its stable manifold form the basin boundary between laminar and turbulent attractors. State points with amplitude just beyond a critical value for transition to turbulence are observed to approach the periodic orbit transiently, and then they are found to exhibit transition nearly along the unstable manifold of the periodic orbit. As a consequence, dynamical behaviour of transition starting with slightly super-critical amplitude can be described in terms of the unstable manifold of the periodic orbit.

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