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
September 1998
Abstract
We present experimental results for early transients near the onset of
convection of an ethanol-water mixture
in cylindrical containers heated from below. The separation ratio of
the mixture was c'20.08, and the aspect
ratios G[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 u. The
azimuthal symmetry of the pattern
depended strongly on G. For G510.91 odd azimuthal modes were preferred,
while for G511.53 even modes
dominated. We measured the spatial and temporal growth rates at various
e[DT/DT c 21 for different azi-muthal
modes and compared the results for the two aspect ratios. We found
the temporal growth rates to be
proportional to e, but the spatial growth rates were essentially independent
of e. 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 higher-order
azimuthal modes grew significantly in
amplitude.
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