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Minimal perturbations approaching the edge of chaos in a Couette flow

Article dans une revue avec comité de lecture
Author
CHERUBINI, Stefania
134975 Laboratoire de Dynamique des Fluides [DynFluid]
DE PALMA, Pietro
19097 Dipartimento di Ingegneria Meccanica e Gestionale [DIMEG]

URI
http://hdl.handle.net/10985/8971
DOI
10.1088/0169-5983/46/4/041403
Date
2014
Journal
Fluid Dynamics Research

Abstract

This paper provides an investigation of the structure of the stable manifold of the lower branch steady state for the plane Couette flow. Minimal energy perturbations to the laminar state are computed, which approach within a prescribed tolerance the lower branch steady state in a finite time. For small times, such minimal-energy perturbations maintain at least one of the symmetries characterizing the lower branch state. For a sufficiently large time horizon, such symmetries are broken and the minimal-energy perturbations on the stable manifold are formed by localized asymmetrical vortical structures. These minimal-energy perturbations could be employed to develop a control procedure aiming at stabilizing the low-dissipation lower branch state.

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