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On the role of eddy viscosity in resolvent analysis of turbulent jets

Published online by Cambridge University Press:  27 November 2024

Jakob G.R. von Saldern Open the ORCID record for Jakob G.R. von Saldern [Opens in a new window] ,
Oliver T. Schmidt Open the ORCID record for Oliver T. Schmidt [Opens in a new window] ,
Peter Jordan Open the ORCID record for Peter Jordan [Opens in a new window]  and
Kilian Oberleithner Open the ORCID record for Kilian Oberleithner [Opens in a new window]
Jakob G.R. von Saldern*
Affiliation:
Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, Berlin 10623, Germany
Oliver T. Schmidt
Affiliation:
Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
Peter Jordan
Affiliation:
Institut Pprime, CNRS/Université de Poitiers/ENSMA, 86962 Futuroscope Chasseneuil, France
Kilian Oberleithner
Affiliation:
Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, Berlin 10623, Germany
*
†Email address for correspondence: [email protected]
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Abstract

This study presents an approach to investigate the role of eddy viscosity in linearized mean-field analysis of broadband turbulent flows. The procedure is based on spectral proper orthogonal decomposition (SPOD), resolvent analysis and the energy budget of coherent structures and is demonstrated using the example of a turbulent jet. The focus is on the coherent component of the Reynolds stresses, the nonlinear interaction term of the fluctuating velocity component in frequency space, which appears as an unknown in the derivation of the linearized Navier–Stokes equations and which is the quantity modelled by the Boussinesq approach. For the considered jet the coherent Reynolds stresses are found to have a mostly dissipative effect on the energy budget of the dominant coherent structures. Comparison of the energy budgets of SPOD and resolvent modes demonstrates that dissipation caused by nonlinear energy transfer must be explicitly considered within the linear operator to achieve satisfactory results with resolvent analysis. Non-modelled dissipation distorts the energy balance of the resolvent modes and is not, as often assumed, compensated for by the resolvent forcing vector. A comprehensive analysis, considering different predictive and data-driven eddy viscosities, demonstrates that the Boussinesq model is highly suitable for modelling the dissipation caused by nonlinear energy transfer for the considered flow. Suitable eddy viscosities are analysed with regard to their frequency, azimuthal wavenumber and spatial dependence. In conclusion, the energetic considerations reveal that the role of eddy viscosity is to ensure that the energy the structures receive from the mean-field is dissipated.

JFM classification

Instability: Shear-flow instability Wakes/Jets: Jets Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , A51
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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