Charge transport scaling in turbulent electroconvection

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 approximately F(gamma)R(gamma)P(delta). R and 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.