Symmetry Breaking in Nonlinear Convection
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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.
KeywordsRayleigh Number Hopf Bifurcation Point Symmetry Pitchfork Bifurcation Travel Wave
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