Physics – Fluid Dynamics
Scientific paper
2005-01-03
Physics
Fluid Dynamics
12 pages, 7 figures, Submitted to Phys. Rev. E. See also http://www.physics.utoronto.ca/nonlinear
Scientific paper
10.1103/PhysRevE.72.046311
We describe a local-power law scaling theory for the mean dimensionless electric current $Nu$ in turbulent electroconvection. The experimental system consists of a weakly conducting, submicron thick liquid crystal film supported in the annulus between concentric circular electrodes. It is driven into electroconvection by an applied voltage between its inner and outer edges. At sufficiently large voltage differences, the flow is unsteady and electric charge is turbulently transported between the electrodes. Our theoretical development, which closely parallels the Grossmann-Lohse model for turbulent thermal convection, predicts the local-power law $Nu \sim F(\Gamma) {\cal R}^{\gamma} {\cal P}^{\delta}$. ${\cal R}$ and ${\cal P}$ are dimensionless numbers that are similar to the Rayleigh and Prandtl numbers of thermal convection, respectively. The dimensionless function $F(\Gamma)$, which is specified by the model, describes the dependence of $Nu$ on the aspect ratio $\Gamma$. We find that measurements of $Nu$ are consistent with the theoretical model.
Daya Zahir A.
Morris Stephen W.
Tsai Peichun
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