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Network structure of two-dimensional decaying isotropic turbulence

Published online by Cambridge University Press:  15 April 2016

Kunihiko Taira ,
Aditya G. Nair  and
Steven L. Brunton
Kunihiko Taira*
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA
Aditya G. Nair
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA
Steven L. Brunton
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
*
†Email address for correspondence: ktaira@fsu.edu
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Abstract

The present paper reports on our effort to characterize vortical interactions in complex fluid flows through the use of network analysis. In particular, we examine the vortex interactions in two-dimensional decaying isotropic turbulence and find that the vortical-interaction network can be characterized by a weighted scale-free network. It is found that the turbulent flow network retains its scale-free behaviour until the characteristic value of circulation reaches a critical value. Furthermore, we show that the two-dimensional turbulence network is resilient against random perturbations, but can be greatly influenced when forcing is focused towards the vortical structures, which are categorized as network hubs. These findings can serve as a network-analytic foundation to examine complex geophysical and thin-film flows and take advantage of the rapidly growing field of network theory, which complements ongoing turbulence research based on vortex dynamics, hydrodynamic stability, and statistics. While additional work is essential to extend the mathematical tools from network analysis to extract deeper physical insights of turbulence, an understanding of turbulence based on the interaction-based network-theoretic framework presents a promising alternative in turbulence modelling and control efforts.

JFM classification

Turbulent Flows: Isotropic turbulence Mathematical Foundations: Mathematical Foundations Vortex Flows: Vortex interactions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , R2
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Copyright
© 2016 Cambridge University Press 

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References

Albert, R. & Barabási, A.-L. 2002 Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (1), 47–97.Google Scholar
Albert, R., Jeong, H. & Barabási, A.-L. 2000 Error and attack tolerance of complex networks. Nature 406, 378–382.Google Scholar
Barabási, A.-L. & Albert, R. 1999 Emergence of scaling in random networks. Science 286, 509–512.Google Scholar
Barrat, A., Barthélemy, M., Pastor-Satorras, R. & Vespignani, A. 2004a The architecture of complex weighted networks. Proc. Natl Acad. Sci. USA 101 (11), 3747–3752.Google Scholar
Barrat, A., Barthélemy, M. & Vespignani, A. 2004b Weighted evolving networks: coupling topology and weighted dynamics. Phys. Rev. Lett. 92 (22), 228701.Google Scholar
Barrat, A., Barthélemy, M. & Vespignani, A. 2008 Dynamical Processes on Complex Networks. Cambridge University Press.Google Scholar
Benzi, R. & Colella, M. 1992 A simple point vortex model for two-dimensional decaying turbulence. Phys. Fluids A 4 (5), 1036–1039.Google Scholar
Benzi, R., Paladin, G. & Vulpiani, A. 1990 Power spectra in two-dimensional turbulence. Phys. Rev. A 42 (6), 3654–3656.Google Scholar
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427–451.Google Scholar
Brachet, M. E., Meneguzzi, M. & Sulem, P. L. 1986 Small-scale dynamics of high-Reynolds-number two-dimensional turbulence. Phys. Rev. Lett. 57 (6), 683–686.Google Scholar
Brunton, S. L. & Noack, B. R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67 (5), 050801.CrossRefGoogle Scholar
Caldarelli, G. 2007 Scale-Free Networks. Oxford University Press.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Cohen, R. & Havlin, S. 2010 Complex Networks: Structure, Robustness and Function. Cambridge University Press.Google Scholar
Cornelius, S. P., Kath, W. K. & Motter, A. E. 2013 Realistic control of network dynamics. Nat. Commun 4, 1942.Google Scholar
Davidson, P. A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Dorogovtsev, S. N. 2010 Lectures on Complex Networks. Oxford University Press.Google Scholar
Farazmand, M. M., Kevlahan, N. K.-R. & Protas, B. 2011 Controlling the dual cascade of two-dimensional turbulence. J. Fluid Mech. 668, 202–222.Google Scholar
Floyd, R. W. 1962 Algorithm 97: shortest path. Comm. ACM 5 (6), 345.Google Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.Google Scholar
Gad-el-Hak, M. 2000 Flow Control: Passive, Active, and Reactive Flow Management. Cambridge University Press.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.Google Scholar
Joslin, R. D. & Miller, D. N.(Eds) 2009 Fundamentals and Applications of Modern Flow Control, AIAA.Google Scholar
Kaiser, E., Noack, B. R., Cordier, L., Spohn, A., Segond, M., Abel, M., Daviller, G., Osth, J., Krajnović, S. & Niven, R. K. 2014 Cluster-based reduced-order modelling of a mixing layer. J. Fluid Mech. 754, 365–414.Google Scholar
Kida, S. 1985 Numerical simulation of two-dimensional turbulence with high-symmetry. J. Phys. Soc. Japan 54 (8), 2840–2853.Google Scholar
Kraichnan, R. H. & Montgomery, D. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547–619.Google Scholar
Lesieur, M. 2008 Turbulence in Fluids, 4th edn. Springer.Google Scholar
Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. 2011 Controllability of complex networks. Nature 473 (7346), 167–173.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
Mesbahi, M. & Egerstedt, M. 2010 Graph Theoretic Methods in Multiagent Networks. Princeton University Press.Google Scholar
Nair, A. G. & Taira, K. 2015 Network-theoretic approach to sparsified discrete vortex dynamics. J. Fluid Mech. 768, 549–571.CrossRefGoogle Scholar
Newman, M. E. J. 2003 The structural and function of complex networks. SIAM Rev. 45 (2), 167–256.CrossRefGoogle Scholar
Newman, M. E. J. 2010 Networks: An Introduction. Oxford University Press.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rubinov, M. & Sporns, O. 2010 Complex network measures of brain connectivity: uses and interpretations. NeuroImage 52, 1059–1069.Google Scholar
Taylor, G. I.1918 On the dissipation of eddies. Reports and Memoranda 598. Aero. Res. Comm.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Weiss, J. B., Provenzale, A. & McWilliams, J. C. 1998 Lagrangian dynamics in high-dimensional point-vortex systems. Phys. Fluids 10 (8), 1929–1941.Google Scholar
Yan, G., Tsekenis, G., Barzel, B., Slotine, J.-J., Liu, Y.-Y. & Barabási, A.-L. 2015 Spectrum of controlling and observing complex networks. Nat. Phys 11, 779–786.Google Scholar