Symmetry Breaking in Nonlinear Convection

  • N. O. Weiss
Part of the NATO ASI Series book series (NSSB, volume 225)


In idealized two-dimensional convection the system possesses D 2 symmetry and the fundamental solution (a single roll) has point symmetry about its axis. This symmetry can be broken in a pitchfork bifurcation giving rise to mixed-mode solutions connecting branches of pure single-roll and two-roll solutions. Numerical experiments provide examples of symmetry-breaking in the nonlinear regime, where the bifurcation structure can be related to physical properties of the flow. In ther-mosolutal convection oscillations lose first spatial and then temporal symmetry. In compressible magnetoconvection there are transitions from steady single-roll solutions to mixed-mode quasiperiodic and periodic solutions, and also from single-roll standing wave to two-roll travelling wave solutions. Three-dimensional convection allows a richer variety of transitions.


Rayleigh Number Hopf Bifurcation Point Symmetry Pitchfork Bifurcation Travel Wave 
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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • N. O. Weiss
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

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