 
Summary: Analysis of transients for binary mixture convection in cylindrical geometry
Kristina Lerman, David S. Cannell, and Guenter Ahlers
Department of Physics and Center for Nonlinear Science, University of California at Santa Barbara, Santa Barbara, California 93106
Received 8 September 1998
We present experimental results for early transients near the onset of convection of an ethanolwater mixture
in cylindrical containers heated from below. The separation ratio of the mixture was 0.08, and the aspect
ratios r/d (r is the radius and d the height of the sample cell of two different containers were 10.91 and
11.53. For this system the onset of convection occurs via a subcritical Hopf bifurcation to traveling waves.
Beyond the bifurcation we found transient radially traveling waves whose amplitude grew in time. We decom
posed the transient patterns into azimuthal modes of the form cos m . The azimuthal symmetry of the pattern
depended strongly on . For 10.91 odd azimuthal modes were preferred, while for 11.53 even modes
dominated. We measured the spatial and temporal growth rates at various T/ Tc 1 for different azi
muthal modes and compared the results for the two aspect ratios. We found the temporal growth rates to be
proportional to , but the spatial growth rates were essentially independent of . Reflection coefficients
deduced from the spatial growth rates agree with theory reasonably well. As convection evolved, the patterns
collapsed onto one or more diameters, during which time higherorder azimuthal modes grew significantly in
amplitude. S1063651X 99 06403X
PACS number s : 47.54. r, 47.20.Ky, 47.27.Te, 47.20.Bp
I. INTRODUCTION
A thin, quiescent horizontal layer of fluid heated from
