A low-dimensional model for chaos in open fluid flows

A forced Landau–Stuart equation is studied in order to derive a low-dimensional model describing the temporal behavior of a paradigm open flow, the two-dimensional forced cylinder wake. Numerical results from the model exhibit several characteristics of circle maps, and compare qualitatively to previous experimental results for an oscillating cylinder wake. The low-dimensional model is also shown to reduce to a circle map in the limit of small forcing amplitudes. Observation of circle map dynamics in the forced Landau–Stuart equation strengthens the conjecture that globally unstable fluid flows are amenable to a dynamical systems approach focusing on the study of low-dimensional iterative maps. The established connection between the Landau–Stuart equation and the circle map unifies certain aspects of spatiotemporal stability and low-dimensional chaos theory.