Turbulent Bursts, Inertial Sets and Symmetry-Breaking Homoclinic Cycles in Periodic Navier-Stokes Flows

  • Basil Nicolaenko
  • Zhen-Su She
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 55)


We investigate bursting regimes of two-dimensional Kolmogorov flows. We link these dynamics with symmetry-breaking heteroclinic connections which generate persistent homoclinic cycles. Small-scale turbulent dynamics prevail in a neighborhood of these heteroclinic connections, while large-scale dynamics are associated to hyperbolic tori. These intermittent turbulent regimes are a prime example of dynamics on an inertial set (or exponential attractor) of the Navier-Stokes equations.


Vortex Convection Manifold Vorticity Actual Element 


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Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Basil Nicolaenko
    • 1
    • 2
  • Zhen-Su She
    • 3
  1. 1.Department of MathematicsArizona State UniversityTempeUSA
  2. 2.Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  3. 3.Applied and Computational MathematicsPrinceton UniversityPrincetonUSA

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