Aspect-ratio dependence of charge transport in turbulent electroconvection

We present measurements of the normalized charge transport or Nusselt number Nu as a function of the aspect ratio Gamma for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-Benard convection, we develop the relevant theoretical framework in which we discuss the local power-law scaling of Nu with a dimensionless electrical forcing parameter R. For these experiments where 10(4)less than or similar toRless than or similar to2x10(5) we find that Nusimilar toF(Gamma)R-gamma with either gamma=0.26 (+/-0.02) or gamma=0.20 (+/-0.03), in excellent agreement with the theoretical predictions of gamma=1/4 and 1/5. Our measurements of the aspect-ratio dependence of Nu for 0.3less than or equal toGammaless than or equal to17 compares favorably with the function F(Gamma) from the scaling theory.