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Role of parasitic modes in nonlinear closure via the resolvent feedback loop

Rosenberg, Kevin and Symon, Sean and McKeon, Beverley J. (2019) Role of parasitic modes in nonlinear closure via the resolvent feedback loop. Physical Review Fluids, 4 (5). Art. No. 052601. ISSN 2469-990X.

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We use the feedback formulation of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)], where the nonlinear term in the Navier-Stokes equations is treated as an intrinsic forcing of the linear resolvent operator, to educe the structure of fluctuations in the range of scales (wave numbers) where linear mechanisms are not active. In this region, the absence of dominant linear mechanisms is reflected in the lack of low-rank characteristics of the resolvent and in the disagreement between the structure of resolvent modes and actual flow features. To demonstrate the procedure, we choose low Reynolds number cylinder flow and the Couette equilibrium solution EQ1, which are representative of very low-rank flows dominated by one linear mechanism. The former is evolving in time, allowing us to compare resolvent modes with dynamic mode decomposition (DMD) modes at the first and second harmonics of the shedding frequency. There is a match between the modes at the first harmonic but not at the second harmonic where there is no separation of the resolvent operator's singular values. We compute the self-interaction of the resolvent mode at the shedding frequency and illustrate its similarity to the nonlinear forcing of the second harmonic. When it is run through the resolvent operator, the “forced” resolvent mode shows better agreement with the DMD mode. A similar phenomenon is observed for the fundamental streamwise wave number of the EQ1 solution and its second harmonic. The importance of parasitic modes, labeled as such since they are driven by the amplified frequencies, is their contribution to the nonlinear forcing of the main amplification mechanisms as shown for the shedding mode, which has subtle discrepancies with its DMD counterpart.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Rosenberg, Kevin0000-0001-6101-3823
Symon, Sean0000-0001-9085-0778
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:© 2019 American Physical Society. Received 6 February 2019; published 1 May 2019. The support of ONR under Grants No. N00014-17-1-2307 and No. N00014-17-1-3022 and ARO under Grant No. W911NF-17-1-0306 is gratefully acknowledged.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-17-1-2307
Office of Naval Research (ONR)N00014-17-1-3022
Army Research Office (ARO)W911NF-17-1-0306
Issue or Number:5
Record Number:CaltechAUTHORS:20190501-124814530
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95138
Deposited By: Tony Diaz
Deposited On:01 May 2019 20:40
Last Modified:09 Mar 2020 13:19

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