Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T09:40:53.761Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase-synchronization properties of laminar cylinder wake for periodic external forcings

Published online by Cambridge University Press:  05 October 2020

M. A. Khodkar Open the ORCID record for M. A. Khodkar [Opens in a new window]  and
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]
M. A. Khodkar*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA90095, USA
Kunihiko Taira
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA90095, USA
*
†Email address for correspondence: mkhodkar@ucla.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the synchronization properties of the two-dimensional periodic flow over a circular cylinder using the principles of phase-reduction theory. The influence of harmonic external forcings on the wake dynamics, together with the possible synchronization of the vortex shedding behind the cylinder to these forcings, is determined by evaluating the phase response of the system to weak impulse perturbations. These horizontal and vertical perturbations are added at different phase values over a period, in order to develop a linear one-dimensional model with respect to the limit cycle that describes the high-dimensional and nonlinear dynamics of the fluid flow via only a single scalar phase variable. This model is then utilized to acquire the theoretical conditions for the synchronization between the cylinder wake and the harmonic forcings added in the global near-wake region. Valuable insights are gained by comparing the findings of the present research against those rendered by the dynamic mode decomposition and adjoint analysis of the wake dynamics in earlier works. The present analysis reveals regions in the flow which enable phase synchronization or desynchronization to periodic excitations for applications such as active flow control and fluid-structure interactions.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Flow Control: Flow Control
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , R1
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arnold, V. I. 1997 Mathematical Methods of Classical Mechanics. Springer.Google Scholar
Bewley, T. R. 2001 Flow control: new challenges for a new renaissance. Prog. Aerosp. Sci. 37 (1), 21–58.CrossRefGoogle Scholar
Colonius, T. & Taira, K. 2008 A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. Comput. Meth. Appl. Mech. Engng 197, 2131–2146.CrossRefGoogle Scholar
Ermentrout, G. B. & Terman, D. H. 2010 Mathematical Foundations of Neurosience. Springer.CrossRefGoogle Scholar
Herbert, T., Bertolotti, F. P. & Santos, G. R. 1987 Floquet analysis of secondary instability in shear flows. In Stability of Time Dependent and Spatially Varying Flows (ed. Dwoyer, D. L. & Hussaini, M. Y.), pp. 43–57. Springer.CrossRefGoogle Scholar
Herrmann, B., Oswald, P., Semaan, R. & Brunton, S. L. 2020 Modeling synchronization in forced turbulent oscillator flows. arXiv:2001.12000.Google Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Iima, M. 2019 Jacobian-free algorithm to calculate the phase sensitivity function in the phase reduction theory and its applications to Kármán's vortex street. Phys. Rev. E 99, 062203.CrossRefGoogle ScholarPubMed
Kawamura, Y. & Nakao, H. 2013 Collective phase description of oscillatory convection. Chaos 23, 043129.CrossRefGoogle ScholarPubMed
Kawamura, Y. & Nakao, H. 2015 Phase description of oscillatory convection with a spatially translational mode. Physica D 295–296, 11–29.CrossRefGoogle Scholar
Kuramoto, Y. 1984 Chemical Oscillations, Waves, and Turbulence. Springer.CrossRefGoogle Scholar
Kuramoto, Y. & Nakao, H. 2019 On the concept of dynamical reduction: the case of coupled oscillators. Phil. Trans. R. Soc. Lond. A 377, 20190041.Google ScholarPubMed
Luchini, J., Giannetti, F. & Pralits, J. O. 2009 Structural sensitivity of the finite-amplitude vortex shedding behind a circular cylinder. In Proceedings of the IUTAM Symp. Unsteady Sep. Flows Control (ed. Braza, M. & Hourigan, K.), pp. 151–160. Springer.CrossRefGoogle Scholar
Munday, P. M. & Taira, K. 2013 On the lock-on of vortex shedding to oscillatory actuation around a circular cylinder. Phys. Fluids 25, 013601.CrossRefGoogle Scholar
Nair, A. G., Brunton, S. L. & Taira, K. 2018 Networked-oscillator-based modeling and control of unsteady wake flows. Phys. Rev. E 97, 063107.CrossRefGoogle ScholarPubMed
Nair, A. G., Taira, K., Brunton, B. W. & Brunton, S. L. 2020 Phase-based control of fluid flows. arXiv:2004.10561.Google Scholar
Nakao, H. 2016 Phase reduction approach to synchronisation of nonlinear oscillators. Contemp. Phys. 57 (2), 188–214.CrossRefGoogle Scholar
Pikovsky, A., Rosenblum, M. & Kurths, J. 2001 Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press.CrossRefGoogle Scholar
Rigas, G., Morgans, A. S. & Morrison, J. F. 2017 Weakly nonlinear modelling of a forced turbulent axisymmetric wake. J. Fluid Mech. 814, 570–591.CrossRefGoogle Scholar
Roma, A. M., Peskin, C. S. & Berger, M. J. 1999 An adaptive version of the immersed boundary method. J. Comput. Phys. 153, 509–534.CrossRefGoogle Scholar
Taira, K. & Colonius, T. 2007 The immersed boundary method: a projection approach. J. Comput. Phys. 225, 2118–2137.CrossRefGoogle Scholar
Taira, K. & Nakao, H. 2018 Phase-response synchronization for analysis of periodic flows. J. Fluid Mech. 846, R2.CrossRefGoogle Scholar