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Koopman-mode decomposition of the cylinder wake
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-8209-1449
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 726, 596-623 p.Article in journal (Refereed) Published
Abstract [en]

The Koopman operator provides a powerful way of analysing nonlinear flow dynamics using linear techniques. The operator defines how observables evolve in time along a nonlinear flow trajectory. In this paper, we perform a Koopman analysis of the first Hopf bifurcation of the flow past a circular cylinder. First, we decompose the flow into a sequence of Koopman modes, where each mode evolves in time with one single frequency/growth rate and amplitude/phase, corresponding to the complex eigenvalues and eigenfunctions of the Koopman operator, respectively. The analytical construction of these modes shows how the amplitudes and phases of nonlinear global modes oscillating with the vortex shedding frequency or its harmonics evolve as the flow develops and later sustains self-excited oscillations. Second, we compute the dynamic modes using the dynamic mode decomposition (DMD) algorithm, which fits a linear combination of exponential terms to a sequence of snapshots spaced equally in time. It is shown that under certain conditions the DMD algorithm approximates Koopman modes, and hence provides a viable method to decompose the flow into saturated and transient oscillatory modes. Finally, the relevance of the analysis to frequency selection, global modes and shift modes is discussed.

Place, publisher, year, edition, pages
2013. Vol. 726, 596-623 p.
Keyword [en]
instability, nonlinear dynamical systems, vortex shedding, Dynamic mode decompositions, Frequency selection, Linear combinations, Linear techniques, Oscillatory mode, Self excited oscillation, Single frequency, Vortex shedding frequency, Algorithms, Circular cylinders, Eigenvalues and eigenfunctions, Hopf bifurcation, Nonlinear analysis, Plasma stability, Oscillating flow, algorithm, bifurcation, cylinder, eigenvalue, nonlinearity, trajectory, wake
National Category
Fluid Mechanics and Acoustics
URN: urn:nbn:se:kth:diva-134488DOI: 10.1017/jfm.2013.249ISI: 000327870600011ScopusID: 2-s2.0-84883199345OAI: diva2:666987
Swedish Research Council, VR-2010-3910

QC 20131125

Available from: 2013-11-25 Created: 2013-11-25 Last updated: 2014-01-10Bibliographically approved

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Bagheri, Shervin
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Stability, Transition and ControlLinné Flow Center, FLOW
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