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Optimal wave packets in a boundary layer and initial phases of a turbulent spot

Published online by Cambridge University Press:  27 May 2010

S. CHERUBINI ,
J.-C. ROBINET ,
A. BOTTARO  and
P. DE PALMA
S. CHERUBINI*
Affiliation:
DIMEG, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy SINUMEF Laboratory Arts et Metiers ParisTech, 151, Bd. de l'Hopital, 75013 Paris, France
J.-C. ROBINET
Affiliation:
SINUMEF Laboratory Arts et Metiers ParisTech, 151, Bd. de l'Hopital, 75013 Paris, France
A. BOTTARO
Affiliation:
DICAT, Università di Genova, Via Montallegro 1, 16145 Genova, Italy
P. DE PALMA
Affiliation:
DIMEG, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
*
†Email address for correspondence: s.cherubini@gmail.com
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Abstract

The three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 656 , 10 August 2010 , pp. 231 - 259
Copyright
Copyright © Cambridge University Press 2010

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