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

Pickering, Ethan and Rigas, Georgios and Schmidt, Oliver T. and Sipp, Denis and Colonius, Tim (2021) Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets. Journal of Fluid Mechanics, 917 . Art. No. A29. ISSN 0022-1120. doi:10.1017/jfm.2021.232.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Pickering, Ethan0000-0002-4485-6359
Rigas, Georgios0000-0001-6692-6437
Schmidt, Oliver T.0000-0002-7097-0235
Sipp, Denis0000-0002-2808-3886
Colonius, Tim0000-0003-0326-3909
Additional Information:© The Author(s), 2021. Published by Cambridge University Press. Received 21 May 2020; revised 17 February 2021; accepted 15 March 2021. The LES study was performed at Cascade Technologies, with support from ONR and NAVAIR SBIR project, under the supervision of Dr J.T. Spyropoulos. The main LES calculations were carried out on DoD HPC systems in ERDC DSRC. This research was supported by a grant from the Office of Naval Research (grant no. N00014-16-1-2445) with Dr S. Martens as program manager. E.P. was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. The authors report no conflict of interest.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-16-1-2445
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Subject Keywords:turbulence modelling, jets, turbulence theory
Record Number:CaltechAUTHORS:20200629-081623820
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Official Citation:Pickering, E., Rigas, G., Schmidt, O., Sipp, D., & Colonius, T. (2021). Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets. Journal of Fluid Mechanics, 917, A29. doi:10.1017/jfm.2021.232
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104111
Deposited By: Tony Diaz
Deposited On:29 Jun 2020 15:21
Last Modified:13 May 2021 16:40

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