  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.
