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Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

Published online by Cambridge University Press:  28 April 2021

Ethan Pickering Open the ORCID record for Ethan Pickering [Opens in a new window] ,
Georgios Rigas Open the ORCID record for Georgios Rigas [Opens in a new window] ,
Oliver T. Schmidt Open the ORCID record for Oliver T. Schmidt [Opens in a new window] ,
Denis Sipp Open the ORCID record for Denis Sipp [Opens in a new window]  and
Tim Colonius
Ethan Pickering*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Georgios Rigas
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Oliver T. Schmidt
Affiliation:
Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
Denis Sipp
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: pickering@caltech.edu
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Abstract

Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic and supersonic conditions and show that the optimal eddy viscosity substantially improves the agreement between resolvent and SPOD modes, reaching over 90 % agreement at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-averaged Navier–Stokes eddy-viscosity resolvent model, with a single coefficient, provides substantial agreement between SPOD and resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.

JFM classification

Turbulent Flows: Turbulence modelling Wakes/Jets: Jets Turbulent Flows: Turbulence theory

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JFM Papers
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Journal of Fluid Mechanics , Volume 917 , 25 June 2021 , A29
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© The Author(s), 2021. Published by Cambridge University Press

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References

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