Modelling the finite amplitude electroconvection in cylindrical geometry: characterization of chaos

Abstract

The long-standing problem of finite amplitude electroconvection in insulating liquids subjected to unipolar injection is now addressed in cylindrical geometry. The geometrical pattern appearing first in experiments above the stability threshold corresponds to hexagonal convective cells. The cylindrical geometry is chosen as a mathematically tractable approximation to the hexagonal cells. An axially symmetric convection cell is considered, with free-slip conditions on the lateral walls of the cell. The velocity field is assumed to be self-similar, and axial symmetry allows to derive it from a stream function. Finite amplitude electroconvection is analyzed by using the particle type method previously developed. The linear and non-linear criteria for instability are computed. The velocity amplitude is always time-dependent and chaotic. We computed the Lyapunov exponent for the time series obtained from the simulation.