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Hairpin-like optimal perturbations in plane Poiseuille flow

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

URI
http://hdl.handle.net/10985/10316
DOI
10.1017/jfm.2015.320
Date
2015
Journal
Journal of Fluid Mechanics

Abstract

In this work it is shown that hairpin vortex structures can be the outcome of a nonlinear optimal growth process, in a similar way as streaky structures can be the result of a linear optimal growth mechanism. With this purpose, nonlinear optimizations based on a Lagrange multiplier technique coupled with a direct-adjoint iterative procedure are performed in a plane Poiseuille flow at subcritical values of the Reynolds number, aiming at quickly triggering nonlinear effects. Choosing a suitable time scale for such an optimization process, it is found that the initial optimal perturbation is composed of sweeps and ejections resulting in a hairpin vortex structure at the target time. These alternating sweeps and ejections create an inflectional instability occurring in a localized region away from the wall, generating the head of the primary and secondary hairpin structures, quickly inducing transition to turbulent flow. This result could explain why transitional and turbulent shear flows are characterized by a high density of hairpin vortices.

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