Unstable periodic orbits and heteroclinic connections in plane Couette flow

Details Unstable periodic orbits and heteroclinic connections in plane Couette flow Unstable periodic orbits and heteroclinic connections in plane Couette flow

2008-10-10

arxiv.org/abs/0810.1974v1

Physics

Fluid Dynamics

Short paper accompanying video submitted to the Gallery of Fluid Motion for the 2008 meeting of the APS Division of Fluid Dyna

Scientific paper

Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of wall-bounded rolls and streaks and provide a framework for understanding low-Reynolds turbulent shear flows as dynamical systems. We present fluid dynamics videos of plane Couette flow illustrating periodic orbits, a close pass of turbulent flow to a periodic orbit, and heteroclinic connections between unstable equilibria.

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