Fractal Stability Border in Plane Couette Flow

Details Fractal Stability Border in Plane Couette Flow Fractal Stability Border in Plane Couette Flow

1997-04-18

arxiv.org/abs/chao-dyn/9704018v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, Latex, 4 eps-figures, submitted to Phys. Rev. Let

Scientific paper

10.1103/PhysRevLett.79.5250

We study the dynamics of localised perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds number and small amplitude of the initial state the perturbation decays on a viscous time scale $t \propto Re$. For Reynolds number larger than about 200, chaotic transients appear with life times longer than the viscous one. Depending on the type of the perturbation isolated initial conditions with infinite life time appear for Reynolds numbers larger than about 270--320. In this third regime, the life time as a function of Reynolds number and amplitude is fractal. These results suggest that in the transition region the turbulent dynamics is characterised by a chaotic repeller rather than an attractor.

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