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Bifurcations in annular electroconvection with an imposed shear | | Zahir A. Daya
; Vatche B. Deyirmenjian
; Stephen W. Morris
; | | Date: |
24 Feb 2001 | | Subject: | Pattern Formation and Solitons; Chaotic Dynamics | nlin.PS nlin.CD | | Abstract: | 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 dimensionless number ${cal R}$, analogous to the Rayleigh number, which is $propto V^2$ and the Reynolds number ${cal R}e$ of the azimuthal shear flow. The geometrical and material properties of the film were characterized by the radius ratio $alpha$, and a Prandtl-like number ${cal P}$. Using measurements of current-voltage characteristics of a large number of films, we examined the onset of electroconvection over a broad range of $alpha$, ${cal P}$ and ${cal R}e$. 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 $alpha$ and ${cal R}e$. | | Source: | arXiv, nlin.PS/0102031 | | Other source: | [GID 203144] pmid11580427 | | Services: | Forum | Review | PDF | Favorites | |
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