Characterizing the edge of chaos for a shear flow model.

We characterize the edge of chaos, the boundary which separates initial conditions which lead to chaotic behavior from those which directly decay to the laminar state, for a nine-dimensional shear flow model. This boundary is the eight-dimensional stable manifold of an unstable periodic orbit, whose properties are characterized. Furthermore, we compute the probability that perturbations of a given energy will lead to transient chaos before decaying to the laminar state, or to a nontrivial attractor for a range of Reynolds numbers. Finally, we consider the relationship between the edge of chaos and linear transient growth, a mechanism which may trigger nonlinear effects that lead to turbulence in shear flows.