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Resolvent-based estimation of turbulent channel flow using wall measurements

Published online by Cambridge University Press:  24 September 2021

Filipe R. Amaral Open the ORCID record for Filipe R. Amaral [Opens in a new window] ,
André V.G. Cavalieri Open the ORCID record for André V.G. Cavalieri [Opens in a new window] ,
Eduardo Martini Open the ORCID record for Eduardo Martini [Opens in a new window] ,
Peter Jordan Open the ORCID record for Peter Jordan [Opens in a new window]  and
Aaron Towne Open the ORCID record for Aaron Towne [Opens in a new window]
Filipe R. Amaral*
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
Eduardo Martini
Affiliation:
Département Fluides, Thermique, Combustion, Institut Pprime, CNRS–Université de Poitiers–ENSMA, 86000 Poitiers, France
Peter Jordan
Affiliation:
Département Fluides, Thermique, Combustion, Institut Pprime, CNRS–Université de Poitiers–ENSMA, 86000 Poitiers, France
Aaron Towne
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
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Abstract

We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martini et al. (J. Fluid Mech., vol. 900, 2021, p. A2) showed that the resolvent-based estimator is optimal when the true space–time forcing statistics are utilised, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterise these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models – an eddy-viscosity model and white-noise forcing – and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer layer, but only using the true forcing statistics allows accurate estimation of large-scale logarithmic-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.

JFM classification

Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , A17
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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