Chaos transition despite linear stability
- 1 November 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 50 (5) , 3705-3711
- https://doi.org/10.1103/physreve.50.3705
Abstract
We present a linearly stable model in two complex dimensions that can be triggered by an initial perturbation or external noise to exhibit chaotic dynamics although all linear perturbations are damped. The transition to chaos is caused by an interplay between transient linear growth and nonlinear, energy conserving mixing. The linear growth mechanism is due to the non-normality of the linearized dynamics in the vicinity of the stationary point. We consider this combined mechanism of non-normal growth and nonlinear mixing as a model for a new but often realized transition scenario from laminar flow to turbulence.Keywords
This publication has 7 references indexed in Scilit:
- On the role of linear mechanisms in transition to turbulencePhysics of Fluids, 1994
- Variance maintained by stochastic forcing of non-normal dynamical systems associated with linearly stable shear flowsPhysical Review Letters, 1994
- Perturbation growth in shear flow exhibits universalityPhysics of Fluids A: Fluid Dynamics, 1993
- Hydrodynamic Stability Without EigenvaluesScience, 1993
- Energy growth in viscous channel flowsJournal of Fluid Mechanics, 1993
- Energy dissipation in shear driven turbulencePhysical Review Letters, 1992
- Onset of Turbulence in a PipeZeitschrift für Naturforschung A, 1988