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Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow

Published online by Cambridge University Press:  10 December 2020

Petrônio A. S. Nogueira Open the ORCID record for Petrônio A. S. Nogueira [Opens in a new window] ,
Pierluigi Morra Open the ORCID record for Pierluigi Morra [Opens in a new window] ,
Eduardo Martini Open the ORCID record for Eduardo Martini [Opens in a new window] ,
André V. G. Cavalieri Open the ORCID record for André V. G. Cavalieri [Opens in a new window]  and
Dan S. Henningson Open the ORCID record for Dan S. Henningson [Opens in a new window]
Petrônio A. S. Nogueira*
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, 12228-900, Brazil
Pierluigi Morra
Affiliation:
Department of Mechanics, Linné FLOW Centre, SeRC, KTH Royal Institute of Technology,SE-100 44Stockholm, Sweden
Eduardo Martini
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, 12228-900, Brazil
André V. G. Cavalieri
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, 12228-900, Brazil
Dan S. Henningson
Affiliation:
Department of Mechanics, Linné FLOW Centre, SeRC, KTH Royal Institute of Technology,SE-100 44Stockholm, Sweden
*
†Present address: Department of Mechanical and Aerospace Engineering, Laboratory for Turbulence Research in Aerospace and Combustion, Monash University, Clayton, Australia. Email address for correspondence: petronio@ita.br
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Abstract

An analysis of the statistics of the nonlinear terms in resolvent analysis is performed in this work for turbulent Couette flow at Reynolds number 400. Data from a direct numerical simulation of a minimal flow unit is used to compute the covariance matrix of the velocity. From the same data, we computed the nonlinear terms of the Navier–Stokes equations (treated as forcing), which allowed us to compute the covariance matrix of the forcing. The quantitative relation between the two covariances via the resolvent operator is confirmed here for the first time, accounting for relevant signal processing issues related to the windowing procedure for frequency-domain quantities. Such exact correspondence allowed the eduction of the most relevant force components for the dominant structures in this flow, which participate in the self-sustaining cycle of turbulence: (i) streamwise vortices and streaks, and (ii) spanwise-coherent fluctuations of spanwise velocity. The results show a dominance by a subset of the nonlinear terms for the prediction of the full statistics of streamwise vortices and streaks; a single term is seen to be dominant for spanwise motions. A relevant feature observed in these cases is that the forcing covariance is dominated by its first eigenfunction, showing that nonlinear terms also have a coherent structure at low frequencies in this flow. Different forcing components are also coherent between them, which leads to constructive and destructive interferences that greatly modify the flow response. These are key features of forcing ‘colour’ for the present flow.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A32
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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