Electroconvection in small cylindrical cavities

The problem of electroconvection of an insulating liquid enclosed in a cylindrical cavity with an aspect ratio Γ= R/d close to 1(2R is the cavity diameter and d the distance between the electrodes) is numerically approached by imposing no slip conditions on the lateral borders. This case, in which only one convective cell is present, is of great interest because for voltages just above the threshold of stability the power spectrum of experimentally measured current fluctuations is discrete. First, a fundamental frequency appears together with its harmonics and subharmonics, then biperiodic behavior and only for high enough values of the applied voltage the spectrum becomes continuous, and qualitatively similar to those measured in large aspect ratio systems. Stability and finite-amplitude electroconvection are investigated for different injection strengths by using a particle-type method, and considering a self-similar velocity field with cylindrical symmetry. The spectral features of the fluctuating component of the computed velocity amplitude are obtained and compared to the experimental ones.