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Towards a quantitative comparison between global and local stability analysis

Published online by Cambridge University Press:  18 April 2017

L. Siconolfi ,
V. Citro ,
F. Giannetti Open the ORCID record for F. Giannetti [Opens in a new window] ,
S. Camarri Open the ORCID record for S. Camarri [Opens in a new window]  and
P. Luchini
L. Siconolfi
Affiliation:
DICI, Università di Pisa, Via Girolamo Caruso, 56122 Pisa, Italy
V. Citro
Affiliation:
DIIN, Universitá degli Studi di Salerno, Via Giovanni Paolo II, 84084 Fisciano (SA), Italy
F. Giannetti*
Affiliation:
DIIN, Universitá degli Studi di Salerno, Via Giovanni Paolo II, 84084 Fisciano (SA), Italy
S. Camarri
Affiliation:
DICI, Università di Pisa, Via Girolamo Caruso, 56122 Pisa, Italy
P. Luchini
Affiliation:
DIIN, Universitá degli Studi di Salerno, Via Giovanni Paolo II, 84084 Fisciano (SA), Italy
*
†Email address for correspondence: [email protected]
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Abstract

A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed sphere. In all the cases considered, both the estimated unstable eigenvalue and the spatial shape of the associated eigenmode are determined by local stability analysis, and they are compared with the reference counterparts obtained at a definitely higher computational cost by a fully three-dimensional global stability analysis. It is shown that the results of local stability analysis, when the higher-order correction term is included, are in excellent agreement with those obtained by global stability analysis. It is also shown that the retained correction term is of crucial importance in this perspective, leading to a remarkable improvement in accuracy with respect to the classical saddle-point estimation.

JFM classification

Instability: Absolute/convective instability Instability: Instability Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 147 - 164
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Copyright
© 2017 Cambridge University Press 

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