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Invariant solutions and visualization of dynamics in plane Couette flow

Gibson, JF (Georgia Institute of Technology)

Tuesday 09 September 2008, 11:30-11:50

Seminar Room 1, Newton Institute


It has recently become possible to compute precise equilibrium, traveling wave, and periodic orbit solutions to pipe and plane Couette flow at moderate Reynolds numbers. These invariant solutions capture the complex dynamics of rolls and streaks (coherent structures) in wall-bounded flows and provide a framework for understanding turbulent flows as dynamical systems. We present (1) a number of weakly unstable equilibria, traveling waves, and periodic orbits of plane Couette flow, (2) visualizations of their physical and state-space dynamics, and (3) statistics on how frequently the solutions appear within turbulent flows. What emerges is a picture of moderate-Reynolds turbulence as a walk among a set of weakly unstable invariant solutions.

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