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We describe a local-power law scaling theory for the mean dimensionlesselectric current $Nu$ in turbulent electroconvection. The experimental systemconsists of a weakly conducting, submicron thick liquid crystal film supportedin the annulus between concentric circular electrodes. It is driven intoelectroconvection by an applied voltage between its inner and outer edges. Atsufficiently large voltage differences, the flow is unsteady and electriccharge is turbulently transported between the electrodes. Our theoreticaldevelopment, which closely parallels the Grossmann-Lohse model for turbulentthermal convection, predicts the local-power law $Nu \sim F(\Gamma) {\calR}^{\gamma} {\cal P}^{\delta}$. ${\cal R}$ and ${\cal P}$ are dimensionlessnumbers that are similar to the Rayleigh and Prandtl numbers of thermalconvection, respectively. The dimensionless function $F(\Gamma)$, which isspecified by the model, describes the dependence of $Nu$ on the aspect ratio$\Gamma$. We find that measurements of $Nu$ are consistent with the theoreticalmodel.

Charge transport scaling in turbulent electroconvection