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Data-driven resolvent analysis

Herrmann, Benjamin and Baddoo, Peter J. and Semaan, Richard and Brunton, Steven L. and McKeon, Beverley J. (2021) Data-driven resolvent analysis. Journal of Fluid Mechanics, 918 . Art. No. A10. ISSN 0022-1120. doi:10.1017/jfm.2021.337.

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Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input–output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due to its potential to reveal structures in turbulent flows, to guide sensor/actuator placement and for flow control applications. However, resolvent analysis requires access to high-fidelity numerical solvers to produce the linearized dynamics operator. In this work, we develop a purely data-driven algorithm to perform resolvent analysis to obtain the leading forcing and response modes, without recourse to the governing equations, but instead based on snapshots of the transient evolution of linearly stable flows. The formulation of our method follows from two established facts: (i) dynamic mode decomposition can approximate eigenvalues and eigenvectors of the underlying operator governing the evolution of a system from measurement data, and (ii) a projection of the resolvent operator onto an invariant subspace can be built from this learned eigendecomposition. We demonstrate the method on numerical data of the linearized complex Ginzburg–Landau equation and of three-dimensional transitional channel flow, and discuss data requirements. Presently, the method is suitable for the analysis of laminar equilibria, and its application to turbulent flows would require disambiguation between the linear and nonlinear dynamics driving the flow. The ability to perform resolvent analysis in a completely equation-free and adjoint-free manner will play a significant role in lowering the barrier of entry to resolvent research and applications.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:© The Author(s), 2021. Published by Cambridge University Press. Received 15 October 2020; revised 2 March 2021; accepted 11 April 2021. We gratefully acknowledge L. Cordier, as well as the anonymous referees, for helpful comments and suggestions. This work was supported by the PRIME programme of the German Academic Exchange Service (DAAD) with funds from the German Federal Ministry of Education and Research (BMBF) and by the U.S. Army Research Office (ARO W911NF-17-1-0306). The authors report no conflict of interest.
Funding AgencyGrant Number
Deutscher Akademischer Austauschdienst (DAAD)UNSPECIFIED
Bundesministerium für Bildung und Forschung (BMBF)UNSPECIFIED
Army Research Office (ARO)W911NF-17-1-0306
Subject Keywords:low-dimensional models, machine learning
Record Number:CaltechAUTHORS:20210315-104726854
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Official Citation:Herrmann, B., Baddoo, P., Semaan, R., Brunton, S., & McKeon, B. (2021). Data-driven resolvent analysis. Journal of Fluid Mechanics, 918, A10. doi:10.1017/jfm.2021.337
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108429
Deposited By: Tony Diaz
Deposited On:19 Mar 2021 00:40
Last Modified:27 May 2021 20:25

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