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On effectiveness of a rank-1 model of turbulent channels for representing the velocity spectra

Moarref, Rashad and Sharma, Ati S. and Tropp, Joel A. and McKeon, Beverley J. (2013) On effectiveness of a rank-1 model of turbulent channels for representing the velocity spectra. In: 43rd Fluid Dynamics Conference, June 24-27, 2013, San Diego, CA.

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We evaluate the efficacy of a gain-based rank-1 model, developed by McKeon & Sharma (J. Fluid Mech., 2010), for representing the energy spectra and the streamwise/wall-normal co-spectrum in a turbulent channel. This is motivated by our previous observation that the streamwise turbulent energy intensity is well approximated by the rank-1 model subject to a broadband forcing in the wall-parallel directions and a properly selected temporal intensity. In the present study, the evaluation is based on finding the optimal forcing spectrum that minimizes the deviation between the two-dimensional velocity spectra at different wall-normal locations obtained from direct numerical simulations at friction Reynolds number 2003 (Hoyas & Jiminénez, Phys. Fluids, 2006) and from the rank-1 model at equal Reynolds number. It is shown that the optimally forced rank-1 model captures the streamwise energy spectrum for streamwise wavelengths smaller than approximately 1000 viscous units throughout the channel. For larger wavelengths, the streamwise spectrum is matched in the outer region of the channel, i.e. wall-normal distances larger than approximately 0.15 times the channel half-height, and the mismatch close to the wall results in less than 5 percent error in the inner-scaled peak of the streamwise energy intensity. In addition, we show that the rank-1 model with optimal forcing captures the essential features of the wall-normal and spanwise spectra and the streamwise/wall-normal co-spectrum. We observe that the predicted magnitudes of the latter three spectra are smaller in the rank-1 model compared to the simulation results suggesting that a higher-order or different rank-1 model may be necessary for accurate representation of these spectra.

Item Type:Conference or Workshop Item (Paper)
Related URLs:
URLURL TypeDescription
Sharma, Ati S.0000-0002-7170-1627
Tropp, Joel A.0000-0003-1024-1791
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:© 2013 AIAA. The support of Air Force Office of Scientific Research under grants FA 9550-09-1-0701 (P.M. John Schmisseur) and FA 9550-12-1-0469 (P.M. Doug Smith) is gratefully acknowledged.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-09-1-0701
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0469
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AIAA Paper2013-2480
Record Number:CaltechAUTHORS:20150218-094025300
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54935
Deposited By: Jamie Sei
Deposited On:24 Feb 2015 23:34
Last Modified:10 Nov 2021 20:39

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