Geometry of state space in plane Couette flow

  • P. CvitanovićEmail author
  • J. F. Gibson
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 132)


A large conceptual gap separates the theory of low-dimensional chaotic dynamics from the infinite-dimensional nonlinear dynamics of turbulence. Recent advances in experimental imaging, computational methods, and dynamical systems theory suggest a way to bridge this gap in our understanding of turbulence. Recent discoveries show that recurrent coherent structures observed in wall-bounded shear flows (such as pipes and plane Couette flow) result from close passes to weakly unstable invariant solutions of the Navier-Stokes equations. These 3D, fully nonlinear solutions (equilibria, traveling waves, and periodic orbits) structure the state space of turbulent flows and provide a skeleton for analyzing their dynamics. We calculate a hierarchy of invariant solutions for plane Couette, a canonical wall-bounded shear flow. These solutions reveal organization in the flow's turbulent dynamics and can be used to predict directly from the fundamental equations physical quantities such as bulk flow rate and mean wall drag. All results and the code that generates them are disseminated through through our group's open-source CFD software and solution database and the collaborative e-book


Periodic Orbit Coherent Structure Proper Orthogonal Decomposition Unstable Manifold Invariant Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Center for Nonlinear ScienceGeorgia Institute of TechnologyAtlantaUSA

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