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Synchronization of low Reynolds number plane Couette turbulence

Published online by Cambridge University Press:  17 December 2021

Marios-Andreas Nikolaidis Open the ORCID record for Marios-Andreas Nikolaidis [Opens in a new window]  and
Petros J. Ioannou Open the ORCID record for Petros J. Ioannou [Opens in a new window]
Marios-Andreas Nikolaidis*
Affiliation:
Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens, 157 84, Greece
Petros J. Ioannou
Affiliation:
Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens, 157 84, Greece Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
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Abstract

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$, that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.

JFM classification

Nonlinear Dynamical Systems: Chaos Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alves Portela, F., Papadakis, G. & Vassilicos, J.C. 2020 The role of coherent structures and inhomogeneity in near-field interscale turbulent energy transfers. J. Fluid Mech. 896, A16.CrossRefGoogle Scholar
Bakas, N.A. & Ioannou, P.J. 2013 Emergence of large scale structure in barotropic $\beta$-plane turbulence. Phys. Rev. Lett. 110, 224501.CrossRefGoogle ScholarPubMed
Bretheim, J.U., Meneveau, C. & Gayme, D.F. 2015 Standard logarithmic mean velocity distribution in a band-limited restricted nonlinear model of turbulent flow in a half-channel. Phys. Fluids 27, 011702.CrossRefGoogle Scholar
Clark Di Leoni, P., Mazzino, A. & Biferale, L. 2020 Synchronization to big data: nudging the Navier–Stokes equations for data assimilation of turbulent flows. Phys. Rev. X 10, 011023.Google Scholar
Constantinou, N.C., Farrell, B.F. & Ioannou, P.J. 2016 Statistical state dynamics of jet–wave coexistence in barotropic beta-plane turbulence. J. Atmos. Sci. 73 (5), 2229–2253.CrossRefGoogle Scholar
Craik, A.D.D. & Criminale, W.O. 1986 Evolution of wavelike disturbances in shear flow: a class of exact solutions of the Navier–Stokes equations. Proc. R. Soc. Lond. A 406, 13–26.Google Scholar
Doering, C. & Gibbon, J.D. 1995 Applied Analysis of the Navier–Stokes Equations. Cambridge University Press.CrossRefGoogle Scholar
Duraisamy, K., Iaccarino, G. & Xiao, H. 2019 Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51 (1), 357–377.CrossRefGoogle Scholar
Farrell, B.F., Gayme, D.F. & Ioannou, P.J. 2017 A statistical state dynamics approach to wall-turbulence. Phil. Trans. R. Soc. A 375 (2089), 20160081.CrossRefGoogle ScholarPubMed
Farrell, B.F. & Ioannou, P.J. 1993 Stochastic forcing of perturbation variance in unbounded shear and deformation flows. J. Atmos. Sci. 50, 200–211.2.0.CO;2>CrossRefGoogle Scholar
Farrell, B.F. & Ioannou, P.J. 2012 Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow. J. Fluid Mech. 708, 149–196.CrossRefGoogle Scholar
Farrell, B.F. & Ioannou, P.J. 2017 Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow. Phys. Rev. Fluids 2 (8), 084608.CrossRefGoogle Scholar
Farrell, B.F., Ioannou, P.J., Jiménez, J., Constantinou, N.C., Lozano-Durán, A. & Nikolaidis, M.-A. 2016 A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow. J. Fluid Mech. 809, 290–315.CrossRefGoogle Scholar
Foias, C., Manley, O., Rosa, R. & Temam, R. 2001 Navier–Stokes Equations and Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Foias, C. & Prodi, G. 1967 On the global behavior of non-stationary solutions of the Navier–Stokes equations in dimension 2. Rendiconti del Seminario Matematico della Universit à di Padova 39, 1–34.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gamahara, M. & Hattori, Y. 2017 Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2, 054604.CrossRefGoogle Scholar
Hayashi, K., Ishihara, T. & Kaneda, Y. 2003 Predictability of 3D isotropic turbulence—effect of data assimilation—. In Statistical Theories and Computational Approaches to Turbulence (ed. Y. Kaneda & T. Gotoh), pp. 239–247. Springer.CrossRefGoogle Scholar
Henshaw, W.D., Kreiss, H.-O. & Yström, J. 2003 Numerical experiments on the interaction between the large- and small-scale motions of the Navier–Stokes equations. Multiscale Model. Simul. 1 (1), 119–149.CrossRefGoogle Scholar
Inubushi, M. & Goto, S. 2020 Transfer learning for nonlinear dynamics and its application to fluid turbulence. Phys. Rev. E 102, 043301.CrossRefGoogle ScholarPubMed
Inubushi, M., Takehiro, S.-i. & Yamada, M. 2015 Regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence. Phys. Rev. E 92, 023022.CrossRefGoogle Scholar
Keefe, L., Moin, P. & Kim, J. 1992 The dimension of attractors underlying periodic turbulent Poiseuille flow. J. Fluid Mech. 242, 1–29.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kolmogorov, A. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Ladyzhenskaya, O.A. 1975 A dynamical system generated by the Navier–Stokes equations. J. Sov. Maths 3 (4), 458–479.CrossRefGoogle Scholar
Lalescu, C.C., Meneveau, C. & Eyink, G.L. 2013 Synchronization of chaos in fully developed turbulence. Phys. Rev. Lett. 110, 084102.CrossRefGoogle ScholarPubMed
Ling, J. & Templeton, J. 2015 Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier–Stokes uncertainty. Phys. Fluids 27 (8), 085103.CrossRefGoogle Scholar
Lozano-Durán, A. & Bae, H.J. 2020 Self-critical machine-learning wall-modeled LES for external aerodynamics. Anual Research Briefs 2020, Standford University. 2020, 197–210.Google Scholar
Marston, J.B., Chini, G.P. & Tobias, S.M. 2016 Generalized quasilinear approximation: application to zonal jets. Phys. Rev. Lett. 116 (21), 214501.CrossRefGoogle ScholarPubMed
Nikitin, N. 2008 On the rate of spatial predictability in near-wall turbulence. J. Fluid Mech. 614, 495–507.CrossRefGoogle Scholar
Nikitin, N. 2018 Characteristics of the leading Lyapunov vector in a turbulent channel flow. J. Fluid Mech. 849, 942–967.CrossRefGoogle Scholar
Pecora, L.M. & Carroll, T.L. 1990 Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824.CrossRefGoogle ScholarPubMed
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2014 Turbulence statistics in Couette flow at high Reynolds number. J. Fluid Mech. 758, 327–343.CrossRefGoogle Scholar
Robinson, J.C. 2001 Infinite-Dimensional Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge University Press.Google Scholar
Thiesset, F., Danaila, L. & Antonia, R.A. 2014 Dynamical interactions between the coherent motion and small scales in a cylinder wake. J. Fluid Mech. 749, 201–226.CrossRefGoogle Scholar
Thomas, V., Lieu, B.K., Jovanović, M.R., Farrell, B.F., Ioannou, P.J. & Gayme, D.F. 2014 Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow. Phys. Fluids 26, 105112.CrossRefGoogle Scholar
Tracey, B.D., Duraisamy, K. & Alonso, J.J. 2015 A machine learning strategy to assist turbulence model development. AIAA Paper 2015-1287.CrossRefGoogle Scholar
Vela-Martín, A. 2021 The synchronisation of intense vorticity in isotropic turbulence. J. Fluid Mech. 913, R8.CrossRefGoogle Scholar
Wang, M. & Zaki, T.A. 2021 State estimation in turbulent channel flow from limited observations. J. Fluid Mech. 917, A9.CrossRefGoogle Scholar
Yang, X.I.A., Zafar, S., Wang, J.-X. & Xiao, H. 2019 Predictive large-eddy-simulation wall modeling via physics-informed neural networks. Phys. Rev. Fluids 4, 034602.CrossRefGoogle Scholar
Yoshida, K., Yamaguchi, J. & Kaneda, Y. 2005 Regeneration of small eddies by data assimilation in turbulence. Phys. Rev. Lett. 94, 014501.CrossRefGoogle ScholarPubMed
Yström, J. & Kreiss, H.-o. 1998 A numerical study of the solution to the 3D incompressible Navier–Stokes equations with forcing function. Research Report. UCLA Computational and Applied Mathematics Reports, 98-31.Google Scholar

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