Effects of weak noise on oscillating flows: Linking quality factor, floquet modes, and koopman spectrum

Physics of Fluids

Volumn 26, Issue 9, 2014, Pages

  Bagheri, Shervin ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

BLUFF BODY WAKES; COHERENT STRUCTURE; DETERMINISTIC SYSTEMS; DIFFERENT FREQUENCY; EVOLUTION OPERATOR; FLOQUET ANALYSIS; MODE DECOMPOSITION; SELF-SUSTAINED OSCILLATIONS;

OSCILLATING FLOW;

EID: 84907487329     PISSN: 10706631     EISSN: 10897666     Source Type: Journal    
DOI: 10.1063/1.4895898     Document Type: Article

References (30)

1. D. J. Tritton, Physical Fluid Dynamics, 2nd ed. (Oxford University Press, Oxford, 1988).
2. V. Jegadeesan and R. I. Sujith, "Experimental investigation of noise induced triggering in thermoacoustic systems," Proc. Combust. Inst. 34, 3175 (2013).10.1016/j.proci.2012.05.003
3. T. C. Lieuwen, "Phase drift characteristics of self-excited, combustion-driven oscillations," J. Sound Vib. 242, 893 (2001).10.1006/jsvi.2000.3395
4. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows (Springer Verlag, New York, 2001).
5. P. Gaspard, "Trace formula for noisy flows," J. Stat. Phys 106, 57 (2002).10.1023/A:1013167928166
6. P. Huerre, "Open shear flow instabilities," in Perspectives in Fluid Dynamics, edited by G. K. Batchelor, H. K. Moffatt, and M. G. Worster (Cambridge University Press, Cambridge, UK, 2000), pp. 159-229.
7. I. Mezi?, "Spectral properties of dynamical systems, model reduction and decompositions," Nonlinear Dyn. 41, 309 (2005).10.1007/s11071-005-2824-x
8. I. Mezi?, "Analysis of fluid flows via spectral properties of the koopman operator," Annu. Rev. Fluid Mech. 45, 357-378 (2013).10.1146/annurev-fluid-011212-140652
9. S. Bagheri, "Koopman-mode decomposition of the cylinder wake," J. Fluid Mech. 726, 596 (2013).10.1017/jfm.2013.249
10. C. W. Rowley, I. Mezi?, S. Bagheri, P. Schlatter, and D. S. Henningson, "Spectral analysis of nonlinear flows," J. Fluid Mech. 641, 115 (2009).10.1017/S0022112009992059
11. P. J. Schmid, "Dynamic mode decomposition of numerical and experimental data," J. Fluid Mech. 656, 5 (2010).10.1017/S0022112010001217
12. P. Schmid, L. Li, M. Juniper, and O. Pust, "Applications of the dynamic mode decomposition," Theo. Comput. Fluid Dyn. 25, 249 (2011).10.1007/s00162-010-0203-9
13. P. J. Goulart, A. Wynn, and D. Pearson, "Optimal mode decomposition for high dimensional systems," in Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii (IEEE, 2012). Available at: http://control.ee.ethz.ch/~goularpa/.
14. C. W. Rowley, I. Mezi?, S. Bagheri, P. Schlatter, and D. S. Henningson, "Reduced-order models for flow control: balanced models and koopman modes," in Seventh IUTAM Symposium on Laminar-Turbulent Transition, edited by P. Schlatter and D. S. Henningson (Springer, 2009), pp. 43-50.
15. K. Chen, J. H. Tu, and C. W. Rowley, "Variants of dynamic mode decomposition: Boundary condition, koopman, and fourier analyses," J. Nonlinear Sci. 22, 887 (2012).10.1007/s00332-012-9130-9
16. J. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz, "On dynamic mode decomposition: Theory and applications," preprint arXiv:1312.0041 (2013).
17. D. Duke, J. Soria, and D. Honnery, "An error analysis of the dynamic mode decomposition," Exp. Fluids 52, 529 (2012).10.1007/s00348-011-1235-7
18. P. Luchini, F. Giannetti, and J. Pralits, "Structural sensitivity of the finite amplitude vortex shedding behind a cicular cylinder," in IUTAM Symposium on Unsteady Separated Flows and their Control, edited by M. Braza and K. Hourigan (Springer Science & Business Media, 2009).
19. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer Verlag, New York, 1983).
20. B. Øksendal,Stochastic Differential Equations: An Introduction with Applications (Springer-Verlag, Heidelberg, New York, 2000).
21. We are assuming that observables are twice differentiable and have a compact support.
22. B. Koopman, "Hamiltonian systems and transformations in Hilbert space," Proc. Natl. Acad. Sci. U.S.A. 17, 315 (1931).10.1073/pnas.17.5.315
23. G. Froyland, O. Junge, and P. Koltai, "Estimating long-term behavior of flows without trajectory integration: The infinitesimal generator approach," SIAM J. Numer. Anal. 51, 223 (2013).10.1137/110819986
24. P. Gaspard and S. Tasaki, "Liouvillian dynamics of the Hopf bifurcation," Phys. Rev. E 64, 056232 (2001).10.1103/PhysRevE.64.056232
25. H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer Verlag, New York, 1996).
26. P. Cvitanovi?, "Chapter "Noise"," in Chaos: Classical and Quantum, edited by P. Cvitanovi?, R. Artuso, R. Mainieri, G. Tanner, and G. Vattay (Niels Bohr Institute, Copenhagen, 2013).
27. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems (Springer Verlag, Berlin, 1984).
28. P. Gaspard, "The correlation time of mesoscopic chemical clocks," J. Chem. Phys. 117, 8905 (2002).10.1063/1.1513461
29. J. M. Chomaz, "Global instabilities in spatially developing flows: Non-normality and nonlinearity," Annu. Rev. Fluid Mech. 37, 357 (2005).10.1146/annurev.fluid.37.061903.175810
30. S. Bagheri, E. Akervik, L. Brandt, and D. S. Henningson, "Matrix-free methods for the stability and control of boundary layers," AIAA J. 47, 1057 (2009).10.2514/1.41365