Shear-flow transition: the basin boundary

Details Shear-flow transition: the basin boundary Shear-flow transition: the basin boundary

2009-04-17

arxiv.org/abs/0904.2764v1

Physics

Fluid Dynamics

11 pages; submitted for publication in Nonlinearity

Scientific paper

The structure of the basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) often used to model transition to turbulence in shear flows. The basin boundary contains not only an equilibrium point Xlb but also a periodic orbit P, and it is the latter that mediates the transition. Orbits starting near Xlb relaminarize. We offer evidence that this is due to the extreme narrowness of the region complementary to basin of attraction in that part of phase space near Xlb. This leads to a proposal for interpreting the 'edge of chaos' in terms of more familiar invariant sets.

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