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Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow

McMullen, Ryan M. and Rosenberg, Kevin and McKeon, Beverley J. (2020) Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow. . (Unpublished)

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A resolvent-based reduced-order representation is used to capture time-averaged second-order statistics in turbulent channel flow. The recently-proposed decomposition of the resolvent operator into two distinct families related to the Orr-Sommerfeld and Squire operators [K. Rosenberg and B. J. McKeon, Efficient representation of exact coherent states of the Navier-Stokes equations using resolvent analysis, Fluid Dynamics Research 51, 011401 (2019)] results in dramatic improvement in the ability to match all components of the energy spectra and the uv cospectrum. The success of the new representation relies on the ability of the Squire modes to compete with the vorticity generated by Orr-Sommerfeld modes, which is demonstrated by decomposing the statistics into contributions from each family. It is then shown that this competition can be used to infer a phase relationship between the two sets of modes. Additionally, the relative Reynolds number scalings for the two families of resolvent weights are derived for the universal classes of resolvent modes presented by Moarref et al. [R. Moarref, A. S. Sharma, J. A. Tropp, and B. J. McKeon, Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels, Journal of Fluid Mechanics 734, 275 (2013)]. These developments can be viewed as a starting point for further modeling efforts to quantify nonlinear interactions in wall-bounded turbulence.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Rosenberg, Kevin0000-0001-6101-3823
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:The support of AFOSR under grant FA 9550-16-1-0361 and ONR under N00014-17-1-3022 is gratefully acknowledged. Additionally, the authors would like to thank Javier Jiménez for making the spectra for the Re_τ = 934 and Re_τ = 2003 simulations publicly available, as well as Adrián Lozano-Durán for sharing the spectra for Re_τ = 4219.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA 9550-16-1-0361
Office of Naval Research (ONR)N00014-17-1-3022
Record Number:CaltechAUTHORS:20200128-133412087
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100967
Deposited By: Tony Diaz
Deposited On:28 Jan 2020 23:28
Last Modified:28 Jan 2020 23:28

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