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Hairpin-like optimal perturbations in plane Poiseuille flow

Published online by Cambridge University Press:  25 June 2015

Mirko Farano ,
Stefania Cherubini ,
Jean-Christophe Robinet  and
Pietro De Palma
Mirko Farano
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy DynFluid Laboratory, Arts et Metiers ParisTech, 151 Boulevard de l’Hopital, 75013 Paris, France
Stefania Cherubini*
Affiliation:
DynFluid Laboratory, Arts et Metiers ParisTech, 151 Boulevard de l’Hopital, 75013 Paris, France
Jean-Christophe Robinet
Affiliation:
DynFluid Laboratory, Arts et Metiers ParisTech, 151 Boulevard de l’Hopital, 75013 Paris, France
Pietro De Palma
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Instability: Instability Instability: Nonlinear instability Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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