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Rayleigh-Benard convection with rotation at small Prandtl numbers Kapil M. S. Bajaj and Guenter Ahlers

Summary: Rayleigh-BeŽnard convection with rotation at small Prandtl numbers
Kapil M. S. Bajaj and Guenter Ahlers
Department of Physics and Quantum Institute, University of California, Santa Barbara, California 93106
Werner Pesch
Physikalisches Institut der Universitašt Bayreuth, 95440 Bayreuth, Germany
Received 7 December 2001; published 16 May 2002
We present experimental and theoretical results near the onset of the Rayleigh-BeŽnard convection with
rotation about a vertical axis in a fluid with a Prandtl number close to 0.18. In the experiment we used a
H2-Xe gas mixture with a separation ratio 0.22 and a Lewis number L 1.22 at various pressures and
dimensionless rotation rates up to 400. On the basis of a standard weakly nonlinear stability analysis, we
found a supercritical, stationary bifurcation for 13, which became subcritical over the range 13
160. For 160 a supercritical Hopf bifurcation precedes the stationary instability of the uniform state.
Following the unstable straight-roll fixed point in the subcritical regime by Galerkin methods we determined
the location of the saddlenode and the stability of the nonlinear two-dimensional straight-roll state. The rolls
were found to be unstable to three-dimensional Kušppers-Lortz perturbations for 3.8 160. Theoretical
results for a pure fluid with the same were qualitatively similar. Measurements using shadowgraph flow
visualization yielded a bifurcation line and an range of subcriticality, which agreed with the stability
analysis. In the subcritical range the experiment revealed a discontinuity of the pattern amplitude at onset, but
was unable to find any hysteresis. Patterns at onset fluctuated irregularly between the ground state and the
finite-amplitude state. In this parameter range the convection pattern further above onset was chaotically time


Source: Ahlers, Guenter - Department of Physics, University of California at Santa Barbara


Collections: Physics