Shear-flow transition: the basin boundary

Abstract

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.

11 pages; submitted for publication in Nonlinearity

References in corpus (5)

• Travelling waves in pipe flow
• Scaling of the turbulence transition threshold in a pipe
• Transition in pipe flow: the saddle structure on the boundary of turbulence
• Relative periodic orbits in transitional pipe flow
• Basin boundary, edge of chaos, and edge state in a two-dimensional model

Cited by in corpus (6)

• Periodic orbits near onset of chaos in plane Couette flow
• Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow
• Transition to turbulence in shear flows
• Studying edge geometry in transiently turbulent shear flows
• Turbulent transition in a truncated one-dimensional model for shear flow
• A two-dimensional model of shear-flow transition