Defects of One - Dimensional Vortex Lattices

  • A. I. Chernykh
  • I. R. Gabitov
  • E. A. Kuznetsov
Part of the NATO ASI Series book series (NSSB, volume 320)


In the framework of the equation
$${{\psi }_{t}} = {{\psi }_{{xx}}} + \psi - {{\left| \psi \right|}^{2}}\psi ,$$
the dynamics of one-dimensional lattices of Taylor vortices in Couette flow and of rolls in weak supercritical convection is studied. It is shown that the propagation of the defects as transition areas between stable (according to Eckhaus) and unstable lattices depends significantly on the topological properties of the field ψ(x), i.e. the degree of mapping R 1S 1. The velocity of such defects has been determined. It has been clarified that the defects between stable lattices spread diffusively due to the conservation of the topological invariant.


Couette Flow Doppler Frequency Free Energy Density Vortex Lattice Linear Stage 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • A. I. Chernykh
    • 1
  • I. R. Gabitov
    • 2
  • E. A. Kuznetsov
    • 1
  1. 1.Institute of Automation and Electrometry Sib. BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.L.D. Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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