 
Summary: Convection under rotation for Prandtl numbers near 1:
Linear stability, wavenumber selection, and pattern dynamics
Yuchou Hu,1,2
Robert E. Ecke,1
and Guenter Ahlers2
1
CondensedMatter and Thermal Physics Group, Center for Nonlinear Studies, Los Alamos National Laboratory,
Los Alamos, New Mexico 87545
2
Department of Physics and Center for Nonlinear Sciences, University of California, Santa Barbara, California 93106
Received 4 December 1996
RayleighBeŽnard convection with rotation about a vertical axis was studied with the shadowgraph imaging
method up to a dimensionless rotation rate of 22. Most of the results are for a cylindrical convection cell
with a radiustoheight ratio 40 that contained CO2 at 33.1 bars with a Prandtl number 0.93. Measure
ments of the critical Rayleigh number Rc and wave number kc for 0 22 agree well with predictions based
on linear stability analysis. Above onset and with rotation, the average wave number and details of the pattern
dynamics were studied. For 5, the initial onset was to a pattern of straight or slightly curved rolls. For
0.1 T/ Tc 1 0.5 but below the onset of spiraldefect chaos, rotation with 8 produced weak
perturbations of nonrotating patterns. Typically, this gave an ``Sshaped'' distortion of the zerorotation pattern
of straight or somewhat curved rolls. Rotation had a stronger effect on the source and motions of dislocation
