Charge Transport Scalings 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 $Nu \sim F(\Gamma) {\cal R}^{\gamma} {\cal P}^{\delta}$. ${\cal R}$ 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.Comment: 12 pages, 7 figures, Submitted to Phys. Rev. E. See also http://www.physics.utoronto.ca/nonlinea

Pattern of inclusions inside rippled icicles

Icicles that have grown from slightly impure water develop ripples around their circumference. The ripples have a near-universal wavelength and are thought to be the result of a morphological instability. Using laboratory-grown icicles and various species of impurities, including fluorescent dye, we show that a certain fraction of the impurities remain trapped inside the icicle, forming inclusions within the ice. The inclusions are organized into chevron patterns aligned with the peaks of the ripples. Within the chevrons, a substructure of crescent-shaped structures is observed. We also examine the crystal grain structure of laboratory icicles, with and without impurities. We present the first detailed study of these growth patterns in the interior of icicles, and discuss their implications for the mechanism of the ripple-forming instability.Comment: 11 pages, 10 figures. To be published in Phys Rev