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Ambiguity in mean-flow-based linear analysis

Karban, U. and Bugeat, B. and Martini, E. and Towne, A. and Cavalieri, A. V. G. and Lesshafft, L. and Agarwal, A. and Jordan, P. and Colonius, T. (2020) Ambiguity in mean-flow-based linear analysis. Journal of Fluid Mechanics, 900 . Art. No. R5. ISSN 0022-1120. doi:10.1017/jfm.2020.566.

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Linearisation of the Navier–Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier–Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation, and can be modified under nonlinear transformation of variables. For example, we show that using primitive and conservative variables leads to differences in the singular values and modes of the resolvent operator for turbulent jets, and that the differences become more severe as variable-density effects increase. This lack of uniqueness of mean-flow-based linear analysis provides new opportunities for optimising models by specific choice of variables while also highlighting the importance of carefully accounting for the nonlinear terms that act as a forcing on the resolvent operator.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Karban, U.0000-0003-0803-0581
Martini, E.0000-0002-3144-5702
Towne, A.0000-0002-7315-5375
Cavalieri, A. V. G.0000-0003-4283-0232
Lesshafft, L.0000-0002-2513-4553
Jordan, P.0000-0001-8576-5587
Colonius, T.0000-0003-0326-3909
Additional Information:© The Author(s), 2020. Published by Cambridge University Press. Received 12 May 2020; revised 27 June 2020; accepted 6 July 2020. Published online by Cambridge University Press: 06 August 2020. This work has received funding from the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme under grant agreement no. 785303. The authors report no conflict of interest.
Funding AgencyGrant Number
European Research Council (ERC)785303
Subject Keywords:jet noise
Record Number:CaltechAUTHORS:20200824-094426276
Persistent URL:
Official Citation:Karban, U., Bugeat, B., Martini, E., Towne, A., Cavalieri, A., Lesshafft, L., . . . Colonius, T. (2020). Ambiguity in mean-flow-based linear analysis. Journal of Fluid Mechanics, 900, R5. doi:10.1017/jfm.2020.566
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105069
Deposited By: Tony Diaz
Deposited On:24 Aug 2020 17:02
Last Modified:16 Nov 2021 18:39

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