Fractal Stability Border in Plane Couette Flow

We study the dynamics of localized perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds numbers and small amplitude of the initial state the perturbation decays on a viscous time scale t. For Reynolds number larger than about 200, chaotic transients appear with lifetimes longer than the viscous one. Depending on the type of the perturbation, isolated initial conditions with infinite lifetime appear for Reynolds numbers larger than about 270--305. In this third regime, the lifetime as a function of Reynolds number and amplitude is fractal. These results suggest that in the transition region the turbulent dynamics is characterized by a chaotic repeller rather than an attractor.