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Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows

Published online by Cambridge University Press:  12 August 2020

Leandra I. Abreu Open the ORCID record for Leandra I. Abreu [Opens in a new window] ,
André V. G. Cavalieri Open the ORCID record for André V. G. Cavalieri [Opens in a new window] ,
Philipp Schlatter Open the ORCID record for Philipp Schlatter [Opens in a new window] ,
Ricardo Vinuesa Open the ORCID record for Ricardo Vinuesa [Opens in a new window]  and
Dan S. Henningson
Leandra I. Abreu*
Affiliation:
São Paulo State University (UNESP), Campus of São João da Boa Vista, 13876-750SP, Brazil Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900SP, Brazil
André V. G. Cavalieri
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900SP, Brazil
Philipp Schlatter
Affiliation:
KTH Mechanics, Linné FLOW Centre, StockholmSE-100-44, Sweden
Ricardo Vinuesa
Affiliation:
KTH Mechanics, Linné FLOW Centre, StockholmSE-100-44, Sweden
Dan S. Henningson
Affiliation:
KTH Mechanics, Linné FLOW Centre, StockholmSE-100-44, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers $Re_{\tau } = 180$ and $550$. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.

JFM classification

Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A11
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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