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Rayleigh-Bénard Convection with Rotation at Small Prandtl Numbers

  • Guenter Ahlers
  • Kapil M.S. Bajaj
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 115)

Abstract

This paper reviews past results from and future prospects for experimental studies of Rayleigh-Bénard convection with rotation about a vertical axis. At dimensionless rotation rates 0 ≤ Ω ≤ 20 and for Prandtl numbers σ ≃ 1, Küppers-Lortz-unstable patterns offered a unique opportunity to study spatio-temporal chaos immediately above a supercritical bifurcation where weakly-nonlinear theories in the form of Ginzburg-Landau (GL) or Swift-Hohenberg (SH) equations can be expected to be valid. However, the dependence of the time and length scales of the chaotic state on ε ≡ ΔT/ΔT C - 1 was found to be different from the expected dependence based on the structure of GL equations. For Ω ≳ 70 and 0.7 ≲ σ ≲ 5 patterns were found to be cellular near onset with local four-fold coordination. They differ from the theoretically expected Küppers-Lortz-unstable state. Stable as well as intermittent defect-free rotating square lattices exist in this parameter range.

Smaller Prandtl numbers ( 0.16 ≲ σ ≲ 0.7) can only be reached in mixtures of gases. These fluids are expected to offer rich future opportunities for the study of a line of tricritical bifurcations, of supercritical Hopf bifurcations to standing waves, of a line of codimension-two points, and of a codimension-three point.

Keywords

Prandtl Number Hopf Bifurcation Critical Rayleigh Number Tricritical Point Stationary Bifurcation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Guenter Ahlers
    • 1
  • Kapil M.S. Bajaj
    • 1
  1. 1.Department of Physics and Center for Nonlinear ScienceUniversity of CaliforniaSanta BarbaraUSA

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