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Transient growth in the flow past a three-dimensional smooth roughness element

Published online by Cambridge University Press:  08 May 2013

S. Cherubini ,
M. D. De Tullio ,
P. De Palma  and
G. Pascazio
S. Cherubini*
Affiliation:
DMMM, CEMeC, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy DynFluid, Arts et Metiers ParisTech, 151, Boulevard de l’Hopital, 75013 Paris, France
M. D. De Tullio
Affiliation:
DMMM, CEMeC, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
P. De Palma
Affiliation:
DMMM, CEMeC, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
G. Pascazio
Affiliation:
DMMM, CEMeC, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
*
†Email address for correspondence: s.cherubini@gmail.com
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Abstract

This work provides a global optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of smooth three-dimensional roughness elements. Amplification mechanisms are described which can bypass the asymptotical growth of Tollmien–Schlichting waves. Smooth axisymmetric roughness elements of different height have been studied, at different Reynolds numbers. The results show that even very small roughness elements, inducing only a weak deformation of the base flow, can localize the optimal disturbance characterizing the Blasius boundary-layer flow. Moreover, for large enough bump heights and Reynolds numbers, a strong amplification mechanism has been recovered, inducing an increase of several orders of magnitude of the energy gain with respect to the Blasius case. In particular, the highest value of the energy gain is obtained for an initial varicose perturbation, differently to what found for a streaky parallel flow. Optimal varicose perturbations grow very rapidly by transporting the strong wall-normal shear of the base flow, which is localized in the wake of the bump. Such optimal disturbances are found to lead to transition for initial energies and amplitudes considerably smaller than sinuous optimal ones, inducing hairpin vortices downstream of the roughness element.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 724 , 10 June 2013 , pp. 642 - 670
Copyright
©2013 Cambridge University Press 

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