Bifurcations in annular electroconvection with an imposed shear
Bifurcations in annular electroconvection with an imposed shear
Physical Review E, 64, 036212 (2001).
Zahir A. Daya
Center for Nonlinear Studies,
Los Alamos National Laboratory, Los Alamos, NM 87545
V. B. Deyirmenjian and
Stephen W. Morris
Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
We report an experimental study of the primary bifurcation in
electrically-driven convection in a freely suspended film. A weakly
conducting, submicron thick smectic liquid crystal film was supported by
concentric circular electrodes. It electroconvected when a sufficiently large
voltage V was applied between its inner and outer edges. The film could
sustain rapid flows and yet remain strictly two-dimensional. By rotation of
the inner electrode, a circular Couette shear could be independently imposed.
The control parameters were a Rayleigh-like number R and
the Reynolds number Re of the azimuthal shear flow. The geometrical
and material properties of the film were characterized by the radius ratio a,
and a Prandtl-like number P. Using measurements of
current-voltage characteristics of a large number of films, we examined the
onset of electroconvection over a broad range of a, P and
Re. We compared this data quantitatively to the results of linear
stability theory. This could be done with essentially no adjustable
parameters. The current-voltage data above onset were then used to infer the
amplitude of electroconvection in the weakly nonlinear regime by fitting them
to a steady-state amplitude equation of the Landau form. We show how the
primary bifurcation can be tuned between supercritical and subcritical by
changing a and Re.
